Patent Publication Number: US-2022224551-A1

Title: Mutual authentication of confidential communication

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     The present application is a continuation of U.S. patent application Ser. No. 16/891,755, filed on Jun. 3, 2020, which is a continuation of U.S. patent application Ser. No. 15/736,243, filed on Dec. 13, 2017, which is a 371 National Phase of PCT Patent Application No. PCT/US2016/040590, filed on Jun. 30, 2016, and claims priority from U.S. Provisional Application No. 62/187,125, filed on Jun. 30, 2015, the entire contents of which are hereby incorporated by reference for all purposes. In addition, U.S. application Ser. No. 14/595,792, entitled “EFFICIENT METHODS FOR PROTECTING IDENTITY IN AUTHENTICATED TRANSMISSIONS” and filed on Jan. 13, 2015, and U.S. application Ser. No. 14/743,874, entitled “EFFICIENT METHODS FOR AUTHENTICATED COMMUNICATION” and filed on Jun. 18, 2015 are hereby incorporated by reference in their entirety for all purposes. 
    
    
     BACKGROUND 
     Ensuring that data is securely communicated between computers continues to be a concern. For instance, an attacker may attempt to eavesdrop on communications (e.g., by conducting a man-in-the-middle attack). Thus, an attacker may attempt to intercept data, such as a public key, that can be used to infer the identity of a user, a client computer, or a server computer. An attacker may also attempt to intercept identification data, such as a computer identifier or a public key of the computer, or authentication data, such as a password, transmitted by the computer. The intercepted data could be used to track the user device or it may be used for illicit purposes. Further complicating matters is the prior state of the computers before communicating. In some cases, the client computer and the server may not previously store a digital certificate of each other—in other words, the client computer and the server computer may not trust each other a priori. Conducting secure communications in such circumstances may pose a challenge. 
     Embodiments of the present invention address these and other problems individually and collectively. 
     BRIEF SUMMARY 
     Some embodiments of the invention relate to systems and methods for securely authenticating a computer. In some embodiments, a first computer may generate a first computer blinded public key using a first computer blinding factor and a first computer public key of the first computer. The first computer may generate a first shared secret using a first computer private key corresponding to the first computer public key, the first computer blinding factor, and a second computer public key of a second computer. The first computer may encrypt first authentication information of the first computer using the first shared secret to obtain first encrypted authentication information. In some embodiments, the first authentication information may include one or more of the first computer blinding factor, a time stamp, or a certificate of the first computer. The first computer may send to the second computer, a first message including the first computer blinded public key and the first encrypted authentication information. 
     The second computer may receive the first message including the first computer blinded public key and the first encrypted authentication information from the first computer. The second computer may generating the first shared secret using the first computer blinded public key and a second computer private key corresponding to the second computer public key. The second computer may decrypt the first encrypted authentication information using the first shared secret. The second computer may authenticate the first computer using the first authentication information. In response to authenticating the first computer, the second computer may encrypt second authentication information of the second computer based on the second computer private key and the first computer public key. The second computer may send a second message to the first computer including the second encrypted authentication information. The first computer may decrypt the second encrypted authentication information based on the first computer private key and the second computer public key. The first computer may authenticate the second computer based on the second authentication information. 
     Some embodiments of the invention relate to systems and methods for confidential communication between computers. A first computer may receive a first message including a second computer blinded public key from a second computer. The second computer blinded public may be generated by the second computer using a second computer blinding factor and a second computer public key that corresponds to a second computer private key. The first computer may generate a first computer blinded public key using a first computer blinding factor and a first computer public key. The first computer may generate a first shared secret using a first computer private key corresponding to the first computer public key, the first computer blinding factor, and the second computer blinded public key. The first computer may send a second message including the first computer blinded public key to the second computer. The second message may enable the second computer to generate the first shared secret using the first computer blinded public key, the second computer blinding factor, and a second computer private key corresponding to the second computer public key. The first computer and the second computer may communicate using the first shared secret. 
     Other embodiments are directed to systems, portable consumer devices, and computer readable media associated with methods described herein. 
     A better understanding of the nature and advantages of embodiments of the present invention may be gained with reference to the following detailed description and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a simplified message flow diagram illustrating secure communication between a client computer and a server computer, in accordance with some embodiments. 
         FIG. 2  shows a message flow diagram of a client computer and a server computer efficiently establishing dually confidential communications, in accordance with some embodiments. 
         FIG. 3  shows a message flow diagram of a client computer and a server computer establishing dually confidential communications based on mutual authentication, in accordance with some embodiments. 
         FIG. 4  shows a message flow diagram of a client computer and a server computer confidentially exchanging certificates for use in mutual authentication, in accordance with some embodiments. 
         FIG. 5  shows a message flow diagram of a client computer and a server computer performing dually confidential mutual authentication using a stored counter, in accordance with some embodiments. 
         FIG. 6  shows a message flow diagram of a client computer and a server computer performing dually confidential mutual authentication using a challenge, in accordance with some embodiments. 
         FIG. 7  shows a flowchart of a method performed by a first computer for establishing dually confidential communications with a second computer, in accordance with some embodiments. 
         FIG. 8  shows a flowchart of a method performed by a second computer for establishing dually confidential communications with a first computer, in accordance with some embodiments. 
         FIG. 9  shows a flowchart of a method performed by a first computer for performing mutual authentication with a second computer using dually confidential communications, in accordance with some embodiments. 
         FIG. 10  shows a flowchart of a computer-implemented method for performing communications between a first computer and second computer for mutual authentication, in accordance with some embodiments. 
         FIG. 11  shows a flowchart of a computer-implemented method for performing communications between a first computer and second computer for mutual authentication, in accordance with some embodiments. 
         FIG. 12  shows a method for secure communication using a client computer that is pre-loaded with a server computer certificate, in accordance with some embodiments. 
         FIG. 13  shows a method for secure communication using a client computer that is not pre-loaded with a server computer certificate, in accordance with some embodiments. 
     
    
    
     TERMS 
     Prior to discussing embodiments of the invention, description of some terms may be helpful in understanding embodiments. 
     The term “server computer” may include a computer or cluster of computing devices. For example, the server computer can be a large mainframe, a minicomputer cluster, or a group of servers functioning as a unit. In one example, the server computer may be a database server coupled to a Web server. The server computer may be coupled to a database and may include any hardware, software, other logic, or combination of the preceding for servicing the requests from one or more client computers. The server computer may comprise one or more computational apparatuses and may use any of a variety of computing structures, arrangements, and compilations for servicing the requests from one or more client computers. 
     The term “public/private key pair” may include a pair of linked cryptographic keys generated by an entity (e.g., a computer or an electronic device). The public key may be used for public functions such as encrypting a message to send to the entity or for verifying a digital signature which was supposedly made by the entity. The private key, on the other hand may be used for private functions such as decrypting a received message or applying a digital signature. The public key will usually be authorized by a body known as a Certification Authority (CA) which stores the public key in a database and distributes it to any other entity which requests it. The private key will typically be kept in a secure storage medium and will usually only be known to the entity. However, the cryptographic systems described herein may feature key recovery mechanisms for recovering lost keys and avoiding data loss. Public and private keys may be in any suitable format, including those based on RSA or elliptic curve cryptography (ECC). 
     A “digital signature” may refer to the result of applying an algorithm based on a public/private key pair, which allows a signing party to manifest, and a verifying party to verify, the authenticity and integrity of a document. The signing party acts by means of the private key and the verifying party acts by means of the public key. This process certifies the authenticity of the sender, the integrity of the signed document and the so-called principle of nonrepudiation, which does not allow disowning what has been signed. A certificate or other data that includes a digital signature by a signing party is said to be “signed” by the signing party. 
     A “certificate” or “digital certificate” may include an electronic document or data file that uses a digital signature to bind a public key with data associated with an identity. The certificate may include one or more data fields, such as the legal name of the identity, a serial number of the certificate, a valid-from and valid-to date for the certificate, certificate-related permissions, etc. A certificate may contain a “valid-from” date indicating the first date the certificate is valid, and a “valid-to” date indicating the last date the certificate is valid. A certificate may also contain a hash of the data in the certificate including the data fields. Unless otherwise noted, each certificate is signed by a certificate authority. 
     A “certificate authority” (CA) may include one or more server computers operatively coupled to issue certificates to entities. The CA may prove its identity using a CA certificate, which includes the CA&#39;s public key. The CA certificate may be signed by another CA&#39;s private key, or may be signed by the same CA&#39;s private key. The latter is known as a self-signed certificate. The CA may maintain a database of all certificates issued by the CA, and may also maintain a list of revoked certificates. 
     In a typical process, the certificate authority receives an unsigned certificate from an entity whose identity is known. The unsigned certificate includes a public key, one or more data fields, and a hash of the data in the certificate. The CA signs the certificate with a private key corresponding to the public key included on the CA certificate. The CA may then store the signed certificate in a database, and issue the signed certificate to the entity. 
     A “cryptographic nonce” may include any number, string, bit sequence, or other data value intended to be used in association with a single communication session. In some cases, a cryptographic nonce may be randomly or pseudo-randomly generated. Typically, a cryptographic nonce is of sufficient length as to make insignificant the likelihood of independently generating the same nonce value multiple times. 
     A “blinded key,” such as a “blinded public key” may include a key that has been obfuscated or otherwise modified from its original value by combination with another data element, such as a cryptographic nonce. For example, in elliptic curve cryptography, a public key may be multiplied by the nonce to generate a “blinded public key.” Similarly, a private key may be multiplied by the nonce to generate a “blinded private key.” The nonce may have the same bit-length as the public key and the private key. 
     An “ephemeral key pair” may include a public key (i.e., an “ephemeral public key”) and a private key (i.e., an “ephemeral private key) generated for use with a single transaction or other communication session. The ephemeral key pair may be of any suitable format, such as ECC or RSA. Typically, an ephemeral key pair may is deleted once the transaction or communication session has concluded. 
     A “static key pair” may include a public key (i.e., a “static public key”) and a private key (i.e., a “static private key”) maintained over a period of time. Typically, though not necessarily, a static private key may be stored securely, such as in a hardware security module (HSM) or secure element (SE). Typically, though not necessarily, a static public key may be bound to an identity through the use of a digital certificate. The static key pair may be of any suitable format, such as ECC or RSA. 
     A “shared secret” may include any data value or other information known only to authorized parties in a secure communication. A shared secret can be generated in any suitable manner, from any suitable data. For example, a Diffie-Hellman based algorithm, such as Elliptic-Curve Diffie-Hellman (ECDH) may be used to generate a shared secret from a private key and a public key. For example, a first computer may generate a first key pair include a first public key and a first private key. A second computer may generate a second key pair including a second public key and a second private key. The first computer may generate a shared secret using the second public key of the second computer and the first private key of the first computer. The second computer may generate the same shared secret using the first public key of the first computer and the second private key of the second computer. The first computer and the second computer may both use the shared secret to generate a session key. 
     The term “identification data” may include any data or information associated with a user or device. Examples of identification data may include a name of a user associated with the device, an organization associated with the device, payment information such as a primary account number (PAN) associated with the device, an expiration date of the device, a certificate associated with the device, an IMEI or serial number of the device, etc. 
     The term “authentication” generally refers to a process of establishing confidence in the identity of a user or a computer. Authentication may be performed by confirming the identity of a device using public key cryptography (e.g., encrypted data or digital signatures) for authentication information. 
     The term “authentication data” or “authentication information” may include any data or information suitable to authenticate a user or device. Examples of authentication data may include a password or passphrase, a secret key (e.g., a private key), a digital signature, an indication that the device is storing certain information, etc. 
     An “encryption key” may include any data value or other information suitable to cryptographically encrypt data. A “decryption key” may include any data value or other information suitable to decrypt encrypted data. In some cases, the same key used to encrypt data may be operable to decrypt the data. Such a key may be known as a symmetric encryption key. 
     A “session key” may include any key used to encrypt or decrypt data to be securely communicated. In some cases, a session key may be generated from a shared secret known both to a sending entity and a receiving entity. For example, the session key may be derived using a key derivation function and the shared secret. 
     DETAILED DESCRIPTION 
     Some embodiments of the invention relate to confidential communication systems and methods, and confidential mutual authentication systems and methods. 
     A first computer and a second computer may communicate over an unsecured network. In order to exchange secure communications, the first computer and the second computer may share a secret symmetric key used to encrypt communications. To prevent an eavesdropper from obtaining the secret symmetric key, the two computers can use public/private key pairs and separately generate the secret symmetric key using a public key of the other device and its own private key. 
     The public keys can be sent over the network, but this may allow a third party to determine the identity of one of the computers or eventually determine the shared symmetric key. It is possible to use ephemeral key pairs, but the generation of ephemeral key pairs for every new communication is computationally intensive. Embodiments can use static public/private key pairs for computational efficiency, where public keys of both computers can be blinded and then transmitted. The generation of the shared symmetric key can account for the blinding, as well as perform dynamic blinding for new communications, where the blinding factor can change with new communications. Further, in embodiments, the two computers can authenticate each other, even with the blinding of the public keys, e.g., by including the public keys in encrypted payloads, which can be decrypted by the other computer. 
     I. Secure Communications 
     A Diffie-Hellman key exchange may enable a first computer and a second computer to establish a secret symmetric key over an unsecured network without transmitting the secret symmetric key itself. The Diffie-Hellman key exchange may not be based on any information previous stored at the first or second computer before the key exchange. For example, a Diffie-Hellman based algorithm, such as Elliptic-Curve Diffie-Hellman (ECDH) may be used to generate a shared secret from a private key of a first computer and a public key of a second computer. For example, the first computer may generate a first key pair include a first public key and a first private key. The second computer may generate a second key pair including a second public key and a second private key. The first computer may send its first public key to the second computer and the second computer may send its second public key to the first computer. The first computer may generate a shared secret using the second public key of the second computer and the first private key of the first computer. The second computer may generate the same shared secret using the first public key of the first computer and the second private key of the second computer. The first computer and the second computer may both use the shared secret to generate a session key for encrypting communications. As such, the first computer and the second computer may establish secure communications over an unsecured network without using any pre-installed information. 
       FIG. 1  shows a simplified message flow diagram  100  illustrating secure communication between a client computer  120  and a server computer  160 , in accordance with some embodiments. The message flow diagram  100  may be used between any first computer and any second computer. The client/server distinction is of  FIG. 1  is exemplary and made to improve readability. In some embodiments, the client computer  120  may perform the operations described as being performed by the server computer  160 . In some embodiments, the server computer  160  may perform the operations described as being performed by the client computer  120 . 
     Referring to  FIG. 1 , the client computer  120  may store a client key pair comprising a client public key and a client private key corresponding to the client public key. The client key pair may be static. The server computer  160  may store a server key pair comprising a server public key and a server private key corresponding to the server public key. The server key pair may be static. The client computer  120  and the server computer  160  may communicate over an unsecured network  190  (e.g., the internet or a wireless local area network). The client computer  120  and the server computer  160  may perform a key exchange in order to establish secure communications over the unsecured network  190 . For example, the client computer  120  and the server computer  160  may perform a Diffie-Hellman key exchange as described above to establish a shared secret between the client computer  120  and the server computer  160 . The client computer  120  and the server computer  160  may each derive a session key from the shared secret for encrypting and decrypting communications between each other. 
     As shown in  FIG. 1 , the client computer  120  may transmit a request message to the server computer  180 . In some embodiments, the request message may include identification data. The client computer  120  may encrypt the identification data of the response message using the shared secret to obtain encrypted identification data. At  101 , the client computer  120  may transmit the request message including the encrypted identification data to the server computer  160  over an unsecured network  190 . 
     The server computer  160  may receive the request message from the client computer  120  via the unsecured network  190 . The server computer  160  may decrypt the encrypted identification data of the request message using the shared secret (e.g., using the session key derived from the shared secret). The server computer  160  may also verify the identification data based on data stored at the server computer  160 . The server computer  160  may encrypt payload data for the client computer  120  using the shared secret to obtain encrypted payload data. At  102 , the server computer  160  may transmit a response message including the encrypted payload data to client computer  120 . The server computer  160  may transmit the response data to the client computer  120  in response to verifying the identification data received from the client computer  120 . The client computer  120  may receive the response message and decrypt the encrypted payload data using the session key to obtain the payload data. As such, the client computer  120  and the server computer  160  may securely communicate over the unsecured network  190  by performing a Diffie-Hellman key exchange. 
     However, a Diffie-Hellman key exchange, such as the key exchange described above with respect to  FIG. 1 , may involve a first computer (e.g., the client computer  120 ) sending its first public key to a second computer (e.g., the server computer  160 ) and the second computer sending its second public key to the first computer. As such, an eavesdropping computer may track the identity of the first computer based on the first public key and it may also track the identity of the second computer based on the second public key. In addition, the eavesdropping computer may conduct a man-in-the-middle attack or imitate the first computer or the second computer. Some of the embodiments described below address these issues. 
     II. Efficient and Dually Confidential Communications 
     As discussed above, transmission of static public keys may enable an eavesdropping computer to track the identity of a computer. The eavesdropping computer may also conduct a man-in-the-middle attack or imitate the computer. Some embodiments may address this issue by blinding public keys such that they are confidential. 
       FIG. 2  shows a message flow diagram  200  of a client computer  220  and a server computer  260  efficiently establishing dually confidential communications, in accordance with some embodiments. In this message flow, the identify of both the client computer  220  and the server computer  260  remain confidential because only blinded public keys may be transmitted (e.g., over an unsecured network), instead of transmitting static public keys. The blinded public keys may be used to establish a shared secret for secure encrypted communication. In addition, the process of generating and using blinded public keys may be more efficient than alternative methods of providing confidential communication (e.g., methods generating and using ephemeral key pairs). 
     The message flow diagram  200  may be used between any first computer and any second computer. The client/server distinction is of  FIG. 2  is exemplary and made to improve readability. In some embodiments, the client computer  220  may perform the operations described as being performed by the server computer  260 . In some embodiments, the server computer  260  may perform the operations described as being performed by the client computer  220 . 
     Prior to the message flow of  FIG. 2 , the client computer  220  may store a client key pair  222  including a client public key  224  and a client private key  226  corresponding to the client public key  224 . The client key pair  222  may be a static key pair. The client computer  220  may also store a client certificate including the client public key  224 . Prior to the message flow of  FIG. 2 , the server computer  260  may store a server key pair  262  including a server public key  264  and a server private key  266  corresponding to the server public key  264 . The server key pair  262  may be a static key pair. The server computer  260  may also store a server certificate including the server public key  264 . 
     At  201 , the client computer  220  may generate a client blinding factor  228 . The client blinding factor may be a cryptographic nonce. A client blinding factor bit-length of the client blinding factor may be shorter than a client public key bit-length of the client public key  224 . At  202 , the client computer may generate a client blinded public key using the client public key and the client blinding factor. For example, the client computer may perform a multiplication operation on the client public key and the client blinding factor. Generating the client blinded public key using the client blinding factor  228  may be more computationally efficient (e.g., may use less computer resources) compared to generating an ephemeral key pair in embodiments where the client blinding factor bit-length of the client blinding factor is shorter than the client public key bit-length of the client public key. While the generation of the client blinded public key may be more computationally efficient, the client blinded public key may provide a similar level of security compared to the use of ephemeral keys since the client blinded public key and the ephemeral public key may have the same bit-length. At  203 , the client computer  203  may send the client blinded public key to the server computer. 
     The server computer  260  may receive the client blinded public key from the client computer  220 . At  204 , the server computer  260  may generate a server blinding factor  268 . The server blinding factor  268  may be a cryptographic nonce. A server blinding factor bit-length of the server blinding factor may be shorter than a server public key bit-length of the server public key  264 . At  205 , the server computer  260  may generate a server blinded public key using the server public key  264  and the server blinding factor  268 . For example, the server computer  260  may perform a multiplication operation on the server public key  264  and the server blinding factor  268 . 
     At  206 , the server computer  260  may generate a first shared secret using the client blinded public key received from the client computer  220 , the server private key  266 , and the server blinding factor  268 . The server computer  260  may derive a first session key for encrypting data using the first shared secret. The server computer  260  may encrypt server data for the client computer using the first session key derived from the first shared secret to obtain encrypted server data. For example, the server data may include the server certificate including the server public key. The server computer  260  may send the server certificate to the client computer  220  to enable the client computer  220  to authenticate the server computer  260 . At  207 , the server computer  260  may send the server blinded public key to the client computer  220 . The server computer may also send the encrypted server data to the client computer  220  at  207 . 
     The client computer  220  may receive the blinded server public key from the server computer  260 . The client computer  220  may also receive the encrypted server data. At  208 , the client computer  220  may generate the first shared secret using the blinded server public key received from the server computer  260 , the client private key  226 , and the client blinding factor  228 . The first shared secret generated by the client computer  220  may be the same as the first shared secret generated by the server computer  260 . The client computer  220  may derive the first session key for encrypting data using the first shared secret. The first session key generated by the client computer  220  may be the same as the first session key generated by the server computer  260 . 
     The client computer  220  may encrypt client data for the server computer  260  using the first session key derived from the first shared secret to obtain encrypted client data. For example, the client data may include the client certificate including the client public key  224 . The client computer  220  may send the client certificate to the server computer  260  to enable the server computer  260  to authenticate the client computer  220  The client computer  220  may send the encrypted client data to the server computer  260 . 
     The message flow of  FIG. 2  enables the client computer and the server computer to establish communications in a such a manner that the identity of both the client computer  220  and the server computer  260  are kept confidential (i.e., the communications are dually confidential). The client computer  220  and the server computer  260  may generate different blinding factors, and different corresponding blinded public keys, to be used for different communications. The client computer  220  and the server computer  260  may encrypt further communications for each other using the first session key derived from the first shared secret. 
     III. Mutual Authentication 
     A first computer and a second computer use the confidential communications described above to provide authentication information to one another in order to mutually authenticate each other. 
       FIG. 3  shows a message flow diagram  300  of a client computer  320  and a server computer  340  using dually confidential communications to establish mutual authentication, in accordance with some embodiments. The message flow diagram  300  may be used between any first computer and any second computer. The client/server distinction is of  FIG. 3  is exemplary and made to improve readability. In some embodiments, the client computer  320  may perform the operations described as being performed by the server computer  360 . In some embodiments, the server computer  360  may perform the operations described as being performed by the client computer  320 . 
     Prior to the message flow, the client computer  320  may store a client key pair  322  including a client public key  324  and a client private key  326  corresponding to the client public key  324 . The client key pair  322  may be a static key pair. The client computer  220  may also store a client certificate  332  including the client public key  324 . The client computer  320  may also store a server certificate  372  including a server public key  364 . The client computer  320  may have previously obtained the server certificate  372  through an initialization process. Prior to the message flow, the server computer  360  may store a server key pair  362  including the server public key  364  and a server private key  366  corresponding to the server public key  364 . The server key pair  362  may be a static key pair. The server computer  360  may also store the server certificate  372  including the server public key  364 . The server computer  360  may also store the client certificate  332  including the client public key  324 . The server computer  360  may have previously obtained the client certificate  332  through an initialization process. 
     At  301 , the client computer  320  may generate a client blinding factor  328 . The client blinding factor  328  may be a cryptographic nonce. A client blinding factor bit-length of the client blinding factor  328  may be shorter than a client public key bit-length of the client public key  324 . At  302 , the client computer  320  may generate a client blinded public key using the client public key  324  and the client blinding factor  328 . For example, the client computer  320  may perform a multiplication operation on the client public key  324  and the client blinding factor  328  to obtain the client blinded public key. 
     At  303 , the client computer  320  may generate a first shared secret using the client blinding factor  328 , the client private key  326 , and the server public key  364  of the server certificate  372 . The client computer  320  may derive a first session key for encrypting data using the first shared secret. At  304 , the client computer  320  may encrypt client data for the server computer using the first session key. At  304 , in some embodiments, the client computer  320  may encrypt the client blinding factor  328  using the first session key derived from the first shared secret to obtain an encrypted client blinding factor. At  304 , in some embodiments, the client computer  320  may also encrypt the client certificate  332  using the first session key derived from the first shared secret to obtain an encrypted client certificate. At  304 , in some embodiments, the client computer  320  may also encrypt the client public key  324  to obtain an encrypted client public key. In some embodiments, the client computer  320  may sign the client data using the client private key  326  to obtain a signature and the client computer  320  may encrypt the signature using the first shared secret to obtain an encrypted certificate. At  305 , the client computer may send the client blinded public key and encrypted client data to the server computer. The encrypted client data may include one or more of the encrypted client blinding factor, and the encrypted client certificate, the encrypted signature, and the encrypted client public key. 
     The server computer  360  may receive the client blinded public key and the encrypted client data from the client computer  320 . At  306 , the server computer  360  may generate the first shared secret using the client blinded public key and the server private key  366 . The first shared secret generated by the server computer  360  may by the same as the first shared secret generated by the client computer  320 . The server computer  360  may derive the first session key from the first shared secret. The first session key derived by the server computer  360  may be the same as the first session key derived by the client computer  320 . At  307 , the server computer  360  may decrypt the encrypted client data. In some embodiments, the server computer  360  may decrypt the encrypted blinding factor using the first session key to obtain the client blinding factor  328 . In some embodiments, the server computer  360  may decrypt the encrypted client certificate using the first session key to obtain the client certificate  332 . In some embodiments, the server computer  360  may decrypt the encrypted client public key using the first session key to obtain the client public key  324 . 
     At  308 , the server computer  360  may verify the client data. In some embodiments, the server computer  360  may verify the blinded client public key received from the client computer  320 . The server computer  360  may verify the blinded client public key by generating a generated blinded client public key using the client public key  324  of the client certificate  332  and the client blinding factor  328  and comparing the generated client blinded public key to the client blinded public key received from the client computer  320 . The server computer  360  may authenticate the client computer  320  based on verifying the client blinded public key. 
     In some embodiments, the server computer  360  may verify that the client public key received from the client computer corresponds to a client public key stored at the server computer or registered with the server computer. The server computer  360  may authenticate the client computer  320  based on verifying the client public key. 
     In some embodiments, the server computer  360  may verify the client certificate received from the client computer  320 . In some embodiments, the server computer  360  may verify the client certificate received from the client computer  320  using a client public key  324  stored at the server computer  360  or registered with the server computer  360 . The server computer  360  may authenticate the client computer  320  based on verifying the client certificate. 
     At  309 , in response to authenticating the client computer  320 , the server computer  360  may generate a server blinding factor  368 . The server blinding factor  368  may be a cryptographic nonce. A server blinding factor bit-length of the server blinding factor  368  may be shorter than a server public key bit-length of the server public key  364 . At  310 , the server computer  360  may generate a server blinded public key using the server public key  364  and the server blinding factor  368 . For example, the server computer  360  may perform a multiplication operation on the server public key  364  and the server blinding factor  368  to obtain the server blinded public key. 
     At  311 , the server computer  360  may generate a second shared secret using the client blinded public key, the server private key  366 , and the server blinding factor  368 . The second shared secret may be different than the first shared secret. The server computer  360  may derive a second session key for encrypting data using the second shared secret. At  312 , the server computer  360  encrypt server data for the client computer  320  using the second shared secret (e.g., using the second session key derived from the second shared secret). In some embodiments, the server computer  360  may encrypt the server blinding factor  368  using the second session key to obtain an encrypted server blinding factor. In some embodiments, the server computer  360  may encrypt the server certificate  372  using the second shared secret to obtain an encrypted server certificate. In some embodiments, the server computer  360  may sign the server data using the server private key  366  to obtain a signature and the server computer  360  may encrypt the signature using the second shared secret to obtain an encrypted signature. In some embodiments, the server computer  360  may encrypt the server public key  364  using the second shared secret to obtain an encrypted server public key. 
     At  313 , the server computer  360  may send the server blinded public key and the encrypted server data to the client computer  320 . The encrypted server data may include one or more of the encrypted server blinding factor, the encrypted signature, the encrypted server certificate, and the encrypted server public key. 
     The client computer  320  may receive the server blinded public key and the encrypted server data from the server computer  360 . At  314 , the client computer  320  may generate the second shared secret using the client private key  326 , the client blinding factor  328 , and the server blinded public key. The second shared secret generated by the client computer  320  may be the same as the second shared secret generated by the server computer  360 . The client computer  320  may derive the second session key using the second shared secret. The second session key generated by the client computer  320  may be the same as the second session key generated by the server computer  360 . 
     At  315 , the client computer  320  may decrypt the encrypted server data using the second shared secret (e.g., using the second session key derived from the second session key) to obtain the server data for the client computer. The server data may include one or more of the server blinding factor  368 , the server certificate  372 , and the server public key  364 . 
     At  316 , the client computer  320  may verify the server data. In some embodiments, the client computer  320  may verify the blinded server public key received from the server computer  360 . The client computer  320  may verify the blinded server public key by generating a generated blinded server public key using the server public key  364  or the server certificate  372  and the server blinding factor  368  and comparing the generated server blinded public key to the server blinded public key received from the server computer  360 . The client computer  320  may authenticate the server computer  360  based on verifying the server blinded public key. 
     In some embodiments, the client computer  320  may verify that the server public key received from the server computer  360  corresponds to a server public key stored at the client computer or registered with the client computer. The client computer  320  may authenticate the server computer  360  based on verifying the server public key. 
     In some embodiments, the client computer  320  may verify the server certificate received from the server computer  360 . In some embodiments, the client computer  320  may verify the server certificate received from the server computer  360  using a server public key stored at the client computer  320  or registered with the client computer  320 . The client computer  320  may authenticate the server computer  360  based on verifying the server certificate. 
     As such, the client computer  320  and the server computer  360  may mutually authenticate each other using a single confidential communication from the client computer  320  to the server computer  360  (e.g., the communication at  305 ) and a single confidential communication from the server computer  360  to the client computer  320  (e.g., the communication at  313 ). The client computer  320  and the server computer  360  may encrypt further communications for each other using the second session key derived from the second shared secret. 
     A. Initialization for Authentication 
       FIG. 4  shows a message flow diagram  400  of a client computer  420  and a server computer  460  confidentially exchanging certificates for use in mutual authentication, in accordance with some embodiments. The message flow diagram  400  may be used between any first computer and any second computer. The client/server distinction is of  FIG. 4  is exemplary and made to improve readability. In some embodiments, the client computer  420  may perform the operations described as being performed by the server computer  460 . In some embodiments, the server computer  460  may perform the operations described as being performed by the client computer  420 . 
     Prior to the message flow, the client computer  420  may store a client certificate  432  and the server computer  460  may store a server certificate  472 . While the message flow diagram of  FIG. 2  may enable a client computer and a server computer to exchange messages, the message flow diagram  400  of  FIG. 4  provides another exemplary message flow for exchanging certificates. The certificate exchange of  FIG. 4  may be part of an initialization process occurring before a mutual authentication process. 
     Prior to the message flow, the client computer  420  may store a client key pair  422  including a client public key  424  and a client private key  426  corresponding to the client public key  424 . The client computer  420  may also store the client certificate  432  including the client public key  424 . Prior to the message flow, the server computer  460  may store a server key pair  462  including a server public key  464  and a server private key  466  corresponding to the server public key  464 . The server computer  460  may also store the server certificate  472  including the server public key  464 . 
     At  401 , the client computer  420  may generate a client ephemeral key pair  434  including a client ephemeral public key  436  and a client ephemeral private key  438  corresponding to the client ephemeral public key  436 . At  402 , the client computer  420  may send the client ephemeral public key  436  to the server computer  460  (e.g., over a network). The server computer  460  may receive the client ephemeral public key  436  from the client computer  420 . 
     At  403 , in response to receiving the client ephemeral public key  436 , the server computer  460  may generate a server blinding factor  468 . The server blinding factor  468  may be a cryptographic nonce. A server blinding factor bit-length of the server blinding factor  468  may be shorter than a server public key bit-length of the server public key  464 . At  404 , the server computer  460  may generate a server blinded public key using the server public key  464  and the server blinding factor  468 . For example, the server computer  460  may perform a multiplication operation on the server public key  464  and the server blinding factor  468  to obtain the server blinded public key. 
     At  405 , the server computer  460  may generate a first shared secret using the client blinded public key, the server private key  466 , and the server blinding factor  468 . The server computer  460  may derive a first session key for encrypting data using the first shared secret. At  406 , the server computer  460  may encrypt the server data for the client computer  420  using the first shared secret (e.g., using the first session key derived from the first shared secret). In some embodiments, the server computer  460  may encrypt the server blinding factor  468  using the first shared secret (e.g., using the first session key derived from the first shared secret) to obtain an encrypted server blinding factor. In some embodiments, the server computer  460  may encrypt the server certificate  472  using the first shared secret to obtain an encrypted server certificate. In some embodiments, the server computer  460  may encrypt a counter using the first shared secret to obtain an encrypted counter. The encrypted server data may include one or more of the encrypted server certificate, the encrypted server blinding factor, and the encrypted counter. At  407 , the server computer  460  may send the server blinded public key and encrypted server data to the client computer  420 . 
     The client computer  420  may receive the server blinded public key and the encrypted server data from the server computer  460 . At  408 , the client computer  420  may generate the first shared secret using the server blinded public key and the client private key  426 . The first shared secret generated by the client computer  420  may be the same as the first shared secret generated by the server computer  460 . The client computer  420  may derive the first session key for encrypting data using the first shared secret. The first session key generated by the client computer  420  may be the same as the first session key generated by the server computer  460 . At  409 , the client computer  420  may decrypt the encrypted server data using the first shared secret (e.g., using the first session key derived from the first shared secret). In some embodiments, the client computer  420  may decrypt the encrypted server blinding factor using the first shared secret (e.g., using the first session key derived from the first shared secret) to obtain the server blinding factor. In some embodiments, the client computer  420  may decrypt the encrypted server certificate using the first shared secret to obtain the server certificate. In some embodiments, the client computer  420  may decrypt the encrypted counter using the first shared secret to obtain the counter. The client computer  420  may store the server data received from the server computer. In some embodiments, the client computer  420  may verify the server data. 
     At  410 , the client computer  420  may encrypt the client certificate  432  using the first shared secret to obtain an encrypted client certificate. At  411 , the client computer  420  may send the encrypted client certificate to the server computer  460 . 
     As such, the client computer  420  and the server computer  460  may confidentially exchange certificates to be stored at the respective computers. This process may be generally referred to as an initialization process since the client computer  420  and the server computer  460  may perform the mutual authentication process of  FIG. 3  after performing the process of  FIG. 4 . 
     B. Mutual Authentication Using a Time Stamp Counter 
     The mutual authentication processes describe above may be modified to include verification of additional information. For example, the mutual authentication may be based on a time stamp or a counter. The counter may be stored at the first computer and at the second computer. 
       FIG. 5  shows a message flow diagram  500  of a client computer  520  and a server computer  560  performing dually confidential mutual authentication using a timestamp or a stored counter, in accordance with some embodiments. The message flow diagram of  FIG. 5  may be used between any first computer and any second computer. The client/server distinction is of  FIG. 5  is exemplary and made to improve readability. In some embodiments, the client computer  520  may perform the operations described as being performed by the server computer  560 . In some embodiments, the server computer  560  may perform the operations described as being performed by the client computer  520 . 
     Prior to the message flow, the client computer  520  may store a client key pair  522  including a client public key  524  and a client private key  526  corresponding to the client public key  524 . The client key pair  522  may be a static key pair. The client computer  520  may also store a client certificate  532  including the client public key  562 . The client computer may also store a server certificate  572  including a server public key  564 . The client computer  520  may have previously obtained the server certificate  572  using the process described above with reference to  FIG. 2  or the initialization process described above with respect to  FIG. 4 . 
     The client computer  520  may also store a counter  574 . In some embodiments, the counter  574  may be a time counter or a clock. In some embodiments, the client computer  520  may have obtained the counter  574  from the server computer  560  using the process described above with reference to  FIG. 2  or the initialization process described above with respect to  FIG. 4 . The client computer  520  may establish the counter  574  with the server computer  560  such that a counter value of the counter  574  at the client computer  520  is the same as, or sufficiently close to, the counter value of the counter  574  stored at the server computer  560 . In embodiments where the counter  574  is a time counter, the counter value of the counter  574  may be a time stamp. In some embodiments, the counter  574  may be a numerical counter that increments by a variable value or by a fixed value after a certain condition has occurred (e.g., after a certain amount of time has passed or after a certain number of transmissions have been sent or received). 
     The server computer  560  may store a server key pair  562  including the server public key  564  and a server private key  566  corresponding to the server public key  564 . The server computer  560  may also store the server certificate  572  including the server public key  564 . 
     The server computer  560  may also store the client certificate  532  including the client public key  524 . The server computer  560  may have previously obtained the client certificate  532  through an initialization process, as described above. 
     The server computer  560  may also store the counter  574 . In some embodiments, the counter  574  may be a time counter or a clock. In some embodiments, the server computer  560  may have obtained the counter  574  from the client computer  520  using the process described above with reference to  FIG. 2  or the initialization process described above with respect to  FIG. 4 . The server computer  560  may establish the counter  574  with the client computer  520  such that a counter value of the counter  574  at the server computer  560  is the same as, or sufficiently close to, the counter value of the counter  574  stored at the client computer  520 . In embodiments where the counter  574  is a time counter, the counter value of the counter  574  may be a time stamp. In some embodiments, the counter  574  may be a numerical counter that increments by a variable value or by a fixed value after a certain condition has occurred (e.g., after a certain amount of time has passed or after a certain number of transmissions have been sent or received). 
     At  501 , the client computer  520  may generate a client blinding factor  528 . The client blinding factor  528  may be a cryptographic nonce. In some embodiments, the client computer  520  may generate the client blinding factor  528  based on a counter value of the counter  574 . A client blinding factor bit-length of the client blinding factor may be shorter than a client public key bit-length of the client public key. At  502 , the client computer  520  may generate a client blinded public key using the client public key  524  and the client blinding factor  528 . For example, the client computer  520  may perform a multiplication operation on the client public key  524  and the client blinding factor  528 . In some embodiments, where the client blinding factor  528  is based on the counter value, the client computer  520  may determine a client blinding factor remainder based on the client blinding factor  528  and the counter value. Accordingly, the client blinding factor  528  may be determined based on the client blinding factor remainder and the counter value. 
     At  503 , the client computer  520  may generate a first shared secret using the client blinding factor  528 , the client private key  526 , and the server public key  564  of the stored server certificate  572 . The client computer  520  may derive a first session key for encrypting data using the first shared secret. 
     At  504 , the client computer  520  may encrypt client data using the first shared secret. In some embodiments, the client computer  520  may encrypt the client blinding factor  528  using the first shared secret to obtain an encrypted client blinding factor. In some embodiments, the client computer  520  may encrypt may encrypt the client certificate  532  using the first shared secret to obtain an encrypted client certificate. In some embodiments, the client computer  520  may encrypt the counter value using the first shared secret to obtain an encrypted counter value. In some embodiments, the client computer  520  may encrypt the client public key  524  using the first shared secret to obtain an encrypted client public key. In some embodiments, the client computer  520  may sign the client data and encrypt the signature using the first shared secret to obtain an encrypted signature. In some embodiments, where the client blinding factor is based on the counter value, the client computer  520  may also encrypt the client blinding factor remainder using the first shared secret to obtain an encrypted client blinding factor remainder. 
     At  505 , the client computer  520  may send the client blinded public key encrypted client data to the server computer  560 . The encrypted client data may include one or more of the encrypted client blinding factor, the encrypted counter value, and the encrypted client certificate, the encrypted client public key, the encrypted signature, and the encrypted client blinding factor remainder. At  505 , in some embodiments, the encrypted client data sent to the server computer may include the encrypted client blinding factor remainder but not the encrypted client blinding factor or the encrypted counter value. 
     The server computer  560  may receive the client blinded public key and the encrypted client data from the client computer  520 . At  506 , the server computer  560  may generate the first shared secret using the client blinded public key and the server private key  566 . The first shared secret generated by the server computer  560  may by the same as the first shared secret generated by the client computer  520 . The server computer  560  may derive the first session key from the first shared secret. The first session key derived by the server computer  560  may be the same as the first session key derived by the client computer  520 . At  507 , the server computer  560  may decrypt the encrypted client data using the first session key. In some embodiments, the server computer may decrypt the encrypted client blinding factor using the first shared secret to obtain the client blinding factor. In some embodiments, the server computer may decrypt the encrypted counter value using the first shared secret to obtain the counter value. In some embodiments, the server computer may decrypt the encrypted client certificate using the first shared secret to obtain the client certificate. In some embodiments, the server computer may decrypt the encrypted client public key using the first shared secret to obtain the client public key  524 . In some embodiments, the server computer may decrypt the encrypted client blinding factor remainder using the first shared secret to obtain the client blinding factor remainder. 
     At  508 , the server computer  560  may verify the blinded client public key received from the client computer  520 . The server computer  560  may verify the blinded client public key by generating a generated blinded client public key using the client public key  524  (e.g., the client public key  524  of the client certificate  532 ) and the client blinding factor  528  and comparing the generated client blinded public key to the client blinded public key received from the client computer  520 . In some embodiments, the server computer  560  may generate the generated blinded client public key using the client public key  524 , the client blinding factor remainder, and a counter value of the counter stored at the server computer  560 . The server computer  560  may authenticate the client computer  520  based on verifying the client blinded public key. At  509 , the server computer  560  may verify the counter value received from the client computer  520  by comparing it to the counter value of the counter stored at the server computer  560 . The server computer  560  may authenticate the client computer  520  based on verifying the counter value received from the client. 
     At  510 , in response to authenticating the client computer  520 , the server computer  560  may generate a server blinding factor  568 . The server blinding factor  568  may be a cryptographic nonce. In some embodiments, the server computer  560  may generated the server blinding factor  568  based on the counter value of the counter stored at the server computer  560 . A server blinding factor bit-length of the server blinding factor  568  may be shorter than a server public key bit-length of the server public key  564 . At  511 , the server computer  560  may generate a server blinded public key using the server public key  564  and the server blinding factor  568 . For example, the server computer  560  may perform a multiplication operation on the server public key  564  and the server blinding factor  468 . In some embodiments, where the server blinding factor  568  is based on the counter value, the server computer  560  may determine a server blinding factor remainder based on the server blinding factor  568  and the counter value. Accordingly, the server blinding factor  568  may be determined based on the server blinding factor remainder and the counter value. 
     At  512 , the server computer  560  may generate a second shared secret using the client blinded public key, the server private key  566 , and the server blinding factor  568 . The second shared secret may be different than the first shared secret. The server computer  560  may derive a second session key for encrypting data using the second shared secret. At  512 , the server computer  560  may encrypt server data using the second shared secret to obtain encrypted server data. In some embodiments, the server computer  560  may encrypt the server blinding factor  568  using the second session key to obtain an encrypted server blinding factor. In some embodiments, the server computer  560  may encrypt the server blinding factor  568  using the second session key derived from the second shared secret to obtain an encrypted server blinding factor. In some embodiments, the server computer  560  may encrypt the server certificate  572  using the second session key derived from the second shared secret to obtain an encrypted server certificate. In some embodiments, the server computer  560  may encrypt the counter value of the counter stored at the server computer  560  using the second session key derived from the second shared secret to obtain an encrypted counter value. In some embodiments, the server computer  560  may encrypt the server public key  564  using the second shared secret to obtain an encrypted server public key. In some embodiments, the server computer  560  encrypt the server blinding factor remainder to obtain an encrypted server blinding factor remainder. In some embodiments, the server computer  560  may sign the server data and encrypt the signature using the second shared secret to obtain an encrypted signature. 
     At  514 , the server computer  560  may send the server blinded public key and encrypted server data to the client computer  520 . The encrypted server data may include one or more of the encrypted client blinding factor, the encrypted counter value, the encrypted signature, the encrypted server public key, and the encrypted client certificate. In some embodiments, the encrypted server data sent to the client computer  520  may include the encrypted server blinding factor remainder but not the encrypted server blinding factor or the encrypted counter value. 
     The client computer  520  may receive the server blinded public key and the encrypted server data from the server computer  560 . At  515 , the client computer  520  may generate the second shared secret using the client private key, the client blinding factor  528 , and the server blinded public key. The second shared secret generated by the client computer  520  may be the same as the second shared secret generated by the server computer  560 . The client computer  520  may derive the second session key for encrypting data using the second shared secret. The second session key generated by the client computer  520  may be the same as the second session key generated by the server computer  560 . 
     At  516 , the client computer  520  may decrypt the encrypted server data using the second shared secret (e.g., using the second session key derived from the second shared secret). In some embodiments, at  513 , the client computer  520  may decrypt the encrypted server blinding factor using the second shared secret to obtain the server blinding factor. In some embodiments, at  513 , the client computer  520  may decrypt the encrypted server public key using the second shared secret to obtain the server public key  564 . In some embodiments, at  513 , the client computer  520  may decrypt the encrypted signature using the second shared secret to obtain the signature. In some embodiments, at  513 , the client computer  520  may decrypt the encrypted server certificate using the second shared secret to obtain the server certificate. In some embodiments, at  513 , the client computer  520  may decrypt the encrypted counter value using the second shared secret to obtain the counter value of the server computer. In embodiments, the client computer  520  may decrypt the encrypted server blinding factor remainder using the second shared secret to obtain the server blinding factor remainder. 
     At  517 , the client computer  520  may verify the blinded server public key received from the server computer  560 . The client computer  520  may verify the blinded server public key by generating a generated blinded server public key using the server public key  564  (e.g., of the server certificate  572 ) and the server blinding factor  568  and comparing the generated server blinded public key to the server blinded public key received from the server computer  560 . The client computer may authenticate the server computer based on verifying the server blinded public key. In some embodiments, the client computer may verify the signature using the server public key  564 . The client computer  520  may authenticate the server computer  560  based on the verification of the signature. In some embodiments, the client computer  520  may generate the generated blinded server public key using the server public key  564  (e.g., of the server certificate), the server blinding factor remainder, and the counter value of the counter stored at the client computer  520 . 
     In some embodiments, at  518 , the client computer  520  may verify the counter value received from the server computer  560  by comparing it to the counter value of the counter stored at the client computer  520 . The client computer  520  may authenticate the server computer  560  based on verifying the counter value received from the server computer. 
     As such, the client computer  520  and the server computer  560  may mutually authenticated each other based on the information received through confidential communications. In particular, the client computer  520  and the server computer  560  may mutually authenticate one another using the only the communication sent from the client computer  520  to the server computer  560  at  505  and the communication sent from the server computer  560  to the client computer  520  at  514 . The client computer and the server computer may encrypt further communications for each other using the second shared secret. 
     C. Authentication Using a Challenge 
       FIG. 6  shows a message flow diagram  600  of a client computer  620  and a server computer  660  performing dually confidential mutual authentication using a challenge, in accordance with some embodiments. The message flow diagram  600  may be used between any first computer and any second computer. The client/server distinction is of  FIG. 6  is exemplary and made to improve readability. In some embodiments, the client computer  620  may perform the operations described as being performed by the server computer  660 . In some embodiments, the server computer  660  may perform the operations described as being performed by the client computer  620 . 
     Prior to the message flow, the client computer  620  may store a client key pair  622  including a client public key  624  and a client private key  626  corresponding to the client public key  624 . The client key pair  622  may be a static key pair. The client computer  620  may also store a client certificate  632  including the client public key  624 . The client computer  620  may also store a server certificate including a server public key. The client computer may have previously obtained the server certificate  672  obtained using the process described above with reference to  FIG. 2  or the initialization process described above with respect to  FIG. 4 . 
     Prior to the message flow, the server computer  560  may store a server key pair  662  including a server public key  664  and a server private key  666  corresponding to the server public key  664 . The server computer  660  may also store the server certificate  672  including the server public key  664 . The server computer  660  may also store the client certificate  632  including the client public key  624 . The server computer  660  may have previously obtained the client certificate  632  through an initialization process. 
     At  601 , the server computer  660  may generate a server blinding factor  668 . The server blinding factor  668  may be a cryptographic nonce. A server blinding factor bit-length of the server blinding factor  668  may be shorter than a server public key bit-length of the server public key  664 . At  602 , the server computer  660  may generate a server blinded public key using the server public key  664  and the server blinding factor  668 . For example, the server computer  660  may perform a multiplication operation on the server public key  664  and the server blinding factor  668  to obtain the serer blinded public key. 
     At  603 , the server computer  660  may generate a first shared secret using the server blinding factor  668 , the server private key  666 , and the client public key  624  (e.g., of the client certificate  632 ). The server computer  660  may derive a first session key for encrypting data using the first shared secret. At  604 , the server computer may encrypt server data for the client computer using the first session key. In some embodiments, the server computer  660  may encrypt the server blinding factor  668  using the first shared secret (e.g., using the first session key derived from the first shared secret) to obtain an encrypted server blinding factor. In some embodiments, the server computer  660  may encrypt the server certificate  672  using the first shared secret to obtain an encrypted server certificate. In some embodiments, the server computer  660  may encrypt the server public key  664  using the first shared secret to obtain an encrypted server public key. In some embodiments, the server computer  660 , may generated a challenge to use for authentication of the client computer  620  and encrypt the challenge using the first shared secret to obtain an encrypted challenge. At  605 , the server computer may send the server blinded public key and encrypted server data to the client computer  620 . The encrypted server data may include one or more of the encrypted server blinding factor, the encrypted server certificate, the encrypted server public key, the encrypted signature, and the encrypted challenge to the client computer. 
     The client computer  620  may receive the server blinded public key and the encrypted server data from the server computer  660 . At  606 , the client computer  620  may generate the first shared secret using the server blinded public key and the client private key  626 . The first shared secret generated by the client computer  620  may by the same as the first shared secret generated by the server computer  660 . The client computer  620  may derive the first session key from the first shared secret. The first session key derived by the client computer  620  may be the same as the first session key derived by the server computer  660 . At  607 , the client computer  620  may decrypt the encrypted server data using the first shared secret (e.g., using the first session key derived from the first shared secret). In some embodiments, the client computer  620  may decrypt the encrypted server blinding factor using the first shared secret to obtain the server blinding factor. In some embodiments, the client computer  620  may decrypt the encrypted challenge using the first shared secret to obtain the challenge. In some embodiments, the client computer  620  may decrypt the encrypted server certificate using the first shared secret key to obtain the server certificate  672 . In some embodiments, the client computer  620  may decrypt the encrypted server public key using the first shared secret key to obtain the server public key  664 . In some embodiments, the client computer  620  may decrypt the encrypted signature using the first shared secret key to obtain the signature signed by the server computer  660 . 
     At  608 , the client computer  620  may verify the blinded server public key received from the server computer  660 . The client computer  620  may verify the blinded server public key by generating a generated blinded server public key using the server public key  664  (e.g., of the server certificate  672 ) and the server blinding factor  668  and comparing the generated server blinded public key to the server blinded public key received from the server computer  660 . The client computer  620  may authenticate the server computer  660  based on verifying the server blinded public key. The client computer  620  may also verify the signature signed by the server computer  660  using the server public key  664 . the client computer  620  may authenticate the server based on verifying the signature. 
     At  609 , in response to authenticating the server computer  660 , the client computer  620  may sign the challenge received from the server computer  660  using the client private key  626 . 
     At  610 , the client computer  620  may generate a client blinding factor  628 . The client blinding factor  628  may be a cryptographic nonce. A client blinding factor bit-length of the client blinding factor  628  may be shorter than a client public key bit-length of the client public key  624 . At  611 , the client computer  620  may generate a client blinded public key using the client public key  624  and the client blinding factor  628 . For example, the client computer  620  may perform a multiplication operation on the client public key  624  and the client blinding factor  628 . 
     At  612 , the client computer  620  may generate a second shared secret using the server blinded public key, the client private key  626 , and the client blinding factor  628 . The second shared secret may be different than the first shared secret. The client computer  620  may derive a second session key for encrypting data using the second shared secret. The client computer  620  may encrypt client data using the second shared secret to obtain encrypted client data. In some embodiments, the client computer  620  may encrypt the client blinding factor  628  using the second shared secret to obtain an encrypted server blinding factor. In some embodiments, the client computer  620  may encrypt the client blinding factor  628  using the second shared secret to obtain an encrypted client blinding factor. In some embodiments, the client computer  620  may encrypt the client certificate  632  using the second shared secret to obtain an encrypted client certificate. In some embodiments, the client computer  620  may encrypt the client public key  624  using the second shared secret to obtain an encrypted client public key. In some embodiments, the client computer  620  may sign the client data using the client private key  626  to obtain a signature and the client computer may encrypt the signature using the second shared secret to obtain an encrypted signature. In some embodiments, the client computer  620  may encrypt the signed challenge using the second shared secret to obtain an encrypted signed challenge. 
     At  614 , the client computer  620  may send the client blinded public key and the encrypted client data to the server computer  660 . The encrypted client data may include one or more of the encrypted client blinding factor, the encrypted client certificate, the encrypted signature, the encrypted client public key, and the encrypted signed challenge. 
     The server computer  660  may receive the client blinded public key and the encrypted client data from the client computer  620 . At  615 , the server computer  660  may generate the second shared secret using the server private key  666 , the server blinding factor  668 , and the client blinded public key. The second shared secret generated by the server computer  660  may be the same as the second shared secret generated by the client computer  620 . The server computer  660  may derive the second session key for encrypting data using the second shared secret. The second session key generated by the server computer  660  may be the same as the second session key generated by the client computer  620 . 
     At  616 , the server computer may decrypt the encrypted client data using the second shared secret (e.g., using the second session key derived from the second shared secret). In some embodiments, at  616 , the server computer  660  may decrypt the encrypted client blinding factor using the second shared secret to obtain the client blinding factor. In some embodiments, at  616 , the server computer  660  may decrypt the encrypted client certificate using the second shared secret to obtain the client certificate  632 . In some embodiments, at  616 , the server computer  660  may decrypt the encrypted signed challenge using the second shared secret to obtain the signed challenge. In some embodiments, at  616 , the server computer  660  may decrypt the encrypted client public key using the second shared secret to obtain the client public key  624 . In some embodiments, at  616 , the server computer  660  may decrypt the encrypted signature using the second shared secret to obtain the signature generated by the client computer  620 . 
     At  617 , the server computer  660  may verify the blinded client public key received from the client computer  620 . The server computer  660  may verify the blinded client public key by generating a generated blinded client public key using the client public key  624  (e.g., of the client certificate  632 ) and the client blinding factor  628  and comparing the generated client blinded public key to the client blinded public key received from the client computer  620 . The server computer  660  may authenticate the client computer based on verifying the client blinded public key. In some embodiments, the server computer  660  may verify the signature using the client public key  624  and the server computer  660  may authenticate the client computer  620  based on verifying the signature. 
     At  618 , the server computer  660  may verify the signed challenge. The server computer  660  may verify the signed challenge using the client public key  624  (e.g., of the client certificate). In some embodiments, the server computer  660  may verify the signed challenge based on the challenge generated by the server computer  660 . The server computer  660  may authenticate the client computer  620  based on verifying the signed challenge. 
     As such, the client computer  620  and the server computer  660  may mutually authenticated each other based on the information received through confidential communications. In particular, the client computer  620  and the server computer  660  may mutually authenticate one another using the only the communication sent from the server computer  660  to the client computer  620  at  6505  and the communication sent from the client computer  620  to the server computer  660  at  614 . The client computer  620  and the server computer  660  may encrypt further communications for each other using the second shared secret. 
     IV. Methods for Secure and Confidential Communication 
     Methods for secure and confidential communications are described below with reference to  FIG. 7  and  FIG. 8 . The message flows described herein may incorporate these methods or a portion thereof. 
     A. Method for Confidentially Establishing a Shared Secret by a First Computer 
       FIG. 7  shows a flowchart  700  of a method performed by a first computer for establishing dually confidential communications with a second computer, in accordance with some embodiments. The first computer may operate similar to the client computer and/or the server computer described above. In some embodiments, the method of  FIG. 7  may be performed by the server computer  260  of  FIG. 2 . 
     At  701 , the first computer may receive a second computer blinded public key from a second computer. The second computer blinded public key may be received over an unsecured network. The second computer blinded public key may have been generated by the second computer using a second computer blinding factor and a second computer public key. The second computer public key may be a static public key of a static key pair. The second computer blinding factor may be a cryptographic nonce. The second computer may have generated the second computer blinded public key by multiplying the second computer public key by the second computer blinding factor. As such, the second computer public key is blinded by the second computer blinding factor, resulting in the second computer blinded public key. Since the second computer blinded public key is blinded, it may not be used to track the identity of the second computer since the second computer may use different blinding factors, and thus, different blinded public keys, to create different shared secrets for encrypting different communications. 
     At  702 , the first computer may generate a first computer blinded public key using a first   computer blinding factor and a first computer public key. The first computer public key may be a static public key of a static key pair. The first computer blinding factor may be a cryptographic nonce. The first computer may generate the first computer blinded public key by multiplying the first computer public key by the first computer blinding factor. As such, the first computer public key is blinded by the first computer blinding factor, resulting in the first computer blinded public key. Because the first computer blinded public key is blinded, it may not be used to track the identity of the second computer since the second computer may use different blinding factors, and thus, different blinded public keys, to create different shared secrets for encrypting different communications. 
     At  703 , the first computer may generate a first shared secret using a first computer private key corresponding to the first computer public key, the first computer blinding factor, and the second computer blinded public key. The first computer may also derive a first session key for encrypting data using the first shared secret. 
     At  704  the first computer may send the first computer blinded public key to the second computer. As such, the second computer may generate the same first shared secret as generated by the first computer. The second computer may generate the first shared secret using the first computer blinded public key, the second computer blinding factor, and a second computer private key corresponding to the second computer public key. The second computer may also derive a first session key for encrypting data using the first shared secret. 
     At  705 , the first computer may communicate with the second computer using the first shared secret. The first computer may encrypt communications using the first session key derived from the first shared secret. In some embodiments, the first computer may encrypt the first computer public key or a first computer certificate including the first computer public key and send the encrypted first computer public key or the encrypted first computer certificate to the second computer, thereby enabling the second computer to authenticate the first computer using an authentication process as described herein. 
     B. Method for Confidentially Establishing a Shared Secret by a Second Computer 
       FIG. 8  shows a flowchart  800  of a method performed by a second computer for establishing dually confidential communications with a first computer, in accordance with some embodiments. The second computer may operate similar to the client computer and/or the server computer described above. In some embodiments, the method of  FIG. 8  may be performed by the client computer  220  of  FIG. 2 . 
     At  801 , the second computer may generate a second computer blinded public using a second computer blinding factor and a second computer public key. The second computer may generate the second computer blinded public key using a second computer blinding factor and a second computer public key. The second computer public key may be a static public key of a static key pair. The second computer blinding factor may be a cryptographic nonce. The second computer may generate the second computer blinded public key by multiplying the second computer public key by the second computer blinding factor. As such, the second computer public key is blinded by the second computer blinding factor, resulting in the second computer blinded public key. Because the second computer blinded public key is blinded, it may not be used to track the identity of the second computer since the second computer may use different blinding factors, and thus, different blinded public keys, to create different shared secrets for encrypting different communications. 
     At  802 , the second computer may send the second computer blinded public key to a first computer. The second computer may send the second computer blinded public key to the first computer over an unsecured network. The first computer may receive the second computer blinded public key from the second computer. The first computer may generate a first computer blinded public key using a first computer blinding factor and a first computer public key. The first computer public key may be a static public key of a static key pair. The first computer blinding factor may be a cryptographic nonce. The first computer may generate the first computer blinded public key by multiplying the first computer public key by the first computer blinding factor. The first computer may send the first computer blinded public key to the second computer over the unsecured network. 
     At  803 , the second computer may receive a first computer blinded public key from the first computer. As discussed above, the first computer may generate the first computer blinded public key and sent it to the second computer. 
     At  804 , the second computer may generate a first shared secret using the first computer blinded public key, the second computer blinding factor, and a second computer private key corresponding to the second computer public key. The second computer may also derive a first session key for encrypting data using the first shared secret. The first computer may generate the same first shared secret using the second computer blinded public key, the first computer blinding factor, and the first computer private key corresponding to the first computer public key. The first computer may also derive the first session key using the first shared secret. 
     At  805 , the second computer may communicate with the first computer using   the first shared secret. The second computer may encrypt communications using the first session key derived from the first shared secret. In some embodiments, the second computer may encrypt the second computer public key or a second computer certificate including the second computer public key and send the encrypted second computer public key or the encrypted second computer certificate to the first computer, thereby enabling the first computer to authenticate the second computer using an authentication process as described herein. 
     V. Methods for Secure and Confidential Mutual Authentication 
     Methods for secure and confidential mutual authentication are described below with reference to  FIG. 9 ,  FIG. 10 , and  FIG. 11 . The message flows described herein may incorporate these methods or a portion thereof. 
     A. Method for Confidential Mutual Authentication Using a Certificate 
       FIG. 9  shows a flowchart of a method performed by a first computer for performing mutual authentication with a second computer using dually confidential communications, in accordance with some embodiments. The first computer may operate similar to the client computer and/or the server computer described above. 
     At  901 , the first computer may obtain a second computer certificate including a second computer public key. The first computer may obtain the second computer certificate through an initialization process as described above. In some embodiments, the first computer may obtain just the second computer public key and not the second computer certificate. 
     At  902 , the first computer may generate a first computer blinded public key using a first   computer blinding factor and a first computer public key. The first computer blinding factor may be a cryptographic nonce. The first computer may perform a multiplication operation on the first computer public key and the first computer blinding factor to obtain the first computer blinded public key 
     At  903 , the first computer may generate a first shared secret using a first computer private key, the first computer blinding factor, and the second computer public key. The first computer may also derive a first session key for encrypting data using the first shared secret. 
     At  904 , the first computer may encrypt a first computer certificate and the first computer blinding factor using the first shared secret. For example, the first computer may encrypt the first computer certificate and the first computer blinding factor using the first session key derived from the first shared secret. 
     At  905 , the first computer may send the first computer blinded public key, the encrypted first computer certificate, and the encrypted first computer blinding factor to the second computer. The second computer may receive the first computer blinded public key, the encrypted first computer certificate, and the encrypted first computer blinding factor from the first computer. 
     At  906 , the first computer may receive a second computer blinded public key, an encrypted second computer blinding factor, and an encrypted second computer certificate. The second computer may have encrypted the encrypted second computer blinding factor and the encrypted second computer certificate using a second shared secret. The second computer may have generated the second shared secret using a second computer private key, a second computer blinding factor, and the first computer blinded public key. 
     At  907 , the first computer may generate the second shared secret using the first computer private key, the first computer blinding factor, and the second computer blinded public key. The second shared secret generated by the first computer may be the same as the second shared secret generated by the second computer. The first computer may derive a second session key from the second shared secret. 
     At  908 , the first computer may decrypt the encrypted second computer blinding factor using the second shared secret to obtain the second computer blinding factor and the first computer may decrypt the encrypted second computer certificate using the second shared secret to obtain the second computer certificate. In some embodiments, the first computer may decrypt the encrypted second computer blinding factor and the encrypted second computer certificate using the second session key derived from the second shared secret. 
     At  909 , the first computer may verify the second computer blinded public key. the first computer may verify the second computer blinded public key by generating a generated second computer blinded public key using the second computer public key (e.g., of the second computer certificate) and the second computer blinding factor, and comparing the generated second computer blinded public key to the second computer blinded public key received from the second computer. 
     At  910 , the first computer may communicate with the second computer using the second shared secret. The first computer and the second computer may communicate in response to mutually authenticating each other. 
     B. Method for Confidential Mutual Authentication Performed by a Second Computer 
       FIG. 10  shows a flowchart  1000  of a computer-implemented method for performing communications between a first computer and second computer for mutual authentication, in accordance with some embodiments. 
     At  1001 , the second computer may receive a first message including first computer blinded public key and first encrypted authentication information from the first computer, wherein the first computer blinded public is generated by the first computer using a first computer blinding factor and a first computer public key. In some embodiments, the first computer blinding factor may be a cryptographic nonce. In some embodiments, the encrypted first authentication may be decrypted to obtain first authentication information of the first computer. The first authentication information may include one or more of the first computer public key, the first computer blinding factor, a time stamp (e.g., a trusted time stamp generated by a trusted time server), a signature of the first computer public key, and a signer key identifier. 
     At  1002 , in response to receiving the first message, the second computer may generate a first shared secret using the first computer blinded public key and a second computer private key. 
     At  1003 , the second computer may decrypt the first encrypted authentication information using the first shared secret to obtain first authentication information of the first computer. 
     At  1004 , the second computer may authenticate the first computer using the first authentication information. The second computer may authenticate the first computer based on comparing the first computer public key to one or more stored computer public keys to identify a matching computer public key. The second computer may authenticate the first computer based on comparing the timestamp from the first computer to a second timestamp of the second computer. The second computer may authenticate the first computer based on using the signer key identifier to retrieve (e.g., from a local database) a signer public key and validating the first signature using the signer public key and the first computer public key. The second computer may authenticate the first computer based on applying the first computer blinding factor to the first computer public key to obtain a generated blinded public key and comparing the generated blinded public key to the first computer blinded public key. 
     At  1005 , in response to the authenticating of the first computer, the second computer may encrypt second authentication information of the second computer to obtain second encrypted authentication information, the encrypting of the second authentication information based on the second computer private key and the first computer public key. In some embodiments, the second computer may encrypt the second authentication information using the first shared secret which is based on the first computer blinded public key, thereby enabling the first computer to authenticate the second computer based on the first computer decrypting the second authentication information using the first shared secret. 
     In some embodiments, the second computer may generate a second shared secret using the first computer blinded public key, the second computer private key, and a second computer blinding factor and encrypt the second authentication information using the second shared secret. In some embodiments, the second computer may send, to the first computer, a second computer blinded public key that the second computer generated using a second computer public key corresponding to the second computer private key and the second computer blinding factor. 
     At  1006 , the second computer may send a second message including the second encrypted authentication information to the first computer, thereby enabling the first computer to authenticate the second computer using the second authentication information. 
     C. Method for Confidential Mutual Authentication Performed by a First Computer 
       FIG. 11  shows a flowchart  1100  of a computer-implemented method for performing communications between a first computer and second computer for mutual authentication, in accordance with some embodiments. 
     At  1101 , the first computer may generate a first computer blinded public key using a first computer blinding factor and a first computer public key. In some embodiments, the first computer blinding factor may be a cryptographic nonce. At  1102 , the first computer may generate a first shared secret using a first computer private key corresponding to the first computer public key, the first computer blinding factor, and a second computer public key of the second computer. 
     At  1103 , the first computer may encrypt first authentication information of the first computer using the first shared secret to obtain first encrypted authentication information. The first authentication information may include one or more of the first computer public key, the first computer blinding factor, a time stamp (e.g., a trusted time stamp generated by a trusted time server), a signature of the first computer public key, and a signer key identifier. 
     At  1104 , the first computer may send, to the second computer, a first message including the first computer blinded public key and the first encrypted authentication information, thereby enabling the second computer to generate the first shared secret using the first computer blinded public key and a second computer private key corresponding to the second computer public key, to decrypt the first encrypted authentication information, and to authenticate the first computer using the first authentication information. The second computer may authenticate the first computer based on comparing the first computer public key to one or more stored computer public keys to identify a matching computer public key. The second computer may authenticate the first computer based on comparing the timestamp from the first computer to a second timestamp of the second computer. The second computer may authenticate the first computer based on using the signer key identifier to retrieve a signer public key and validating the first signature using the signer public key and the first computer public key. The second computer may authenticate the first computer based on applying the first computer blinding factor to the first computer public key to obtain a generated blinded public key and comparing the generated blinded public key to the first computer blinded public key. 
     At  1105 , the first computer may receive a second message from the second computer, the second message including second encrypted authentication information. At  1106 , in response to receiving the second message, the first computer may decrypt the second encrypted authentication information based on the first computer private key and the second computer public key to obtain second authentication information of the second computer. In some embodiments, the second message may include a second computer blinded public key and the first computer may generate a second shared secret using the first computer private key, the first computer blinding factor, and the second computer blinded public key. The first computer may decrypt the second encrypted authentication information using the second shared secret. In some embodiments, the second authentication information may include a second computer blinding factor. In some embodiments, the second authentication information may include the second computer public key. 
     At  1107 , the first computer may authenticate the second computer using the second authentication information. In some embodiments, authenticating the second computer may include verifying the second computer blinded public key using the second computer blinding factor and the second computer public key. In some embodiments, authenticating the second computer may include comparing the second computer public key to one or more stored computer public keys to identify a matching computer public key. In some embodiments, authenticating the second computer may include applying the second computer blinding factor to the second computer public key to obtain a generated blinded public key and comparing the generated blinded public key to the second computer blinded public key. In some embodiments, authenticating the second computer may include using a signer key identifier to retrieve a signer public key and validating a signature of the second computer using the signer public key and the second computer public key. The first computer may communicate further with the second computer based on the authenticating of the second computer. 
     VI. Detailed Methods for Mutual Authentication Using Secure and Confidential Communication 
     Embodiments of the invention may utilize methods for secure communication. Some embodiments of the invention may establish secure communications according to the methods described below with respect to  FIG. 12  and  FIG. 13 . Table 1, below, includes definitions of terms. 
     
       
         
           
               
             
               
                   
               
               
                 TABLE 1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 ICC 
                 Mobile phone, Integrated Circuit chip or 
               
               
                   
                 server 
               
               
                 IFD 
                 Interface device or client 
               
               
                 enc_c 
                 Encrypted data generated on client (IFD/ 
               
               
                   
                 Mobile) 
               
               
                 enc_s 
                 Encrypted data generated on server (ICC) 
               
               
                 SD_c 
                 Client sensitive Data (payload) 
               
               
                 SD_s 
                 Server sensitive Data (payload) 
               
               
                 sID_s 
                 Server (ICC) identifier for the session. 
               
               
                   
                 Based on Q_bs x_coordinate 
               
               
                 sID_c 
                 Client (IFD or mobile device) identifier. 
               
               
                   
                 Truncated value of Q_ec’s x_coordinate 
               
               
                 C_s 
                 Certificate Chain authenticating the 
               
               
                   
                 Server (ICC) 
               
               
                 C_s_{n} 
                 Certificate Chain authenticating the 
               
               
                   
                 Server (ICC) - nth version 
               
               
                 C_c 
                 Certificate Chain authenticating the 
               
               
                   
                 client (ICC) 
               
               
                 d_bc 
                 Client blinding factor 
               
               
                 d_bs 
                 Server Blinding factor 
               
               
                 seed 
                 Counter or time, etc. verifiable at 
               
               
                   
                 ICC or server and proving that blinding 
               
               
                   
                 factor is fresh. d_bc = PRNG (seed) 
               
               
                 Q_bc 
                 Blinded Client public key 
               
               
                 Q_bs 
                 Blinded server public key 
               
               
                 d_c, Q_c = [d_c]P 
                 Client authentication public key, 
               
               
                   
                 matched with the corresponding private 
               
               
                   
                 key: d_c 
               
               
                 d_s, Q_s = [d_s]P 
                 Server (ICC) authentication public key, 
               
               
                   
                 matched with the corresponding private 
               
               
                   
                 key: d_s 
               
               
                 d_s_{n}, Q_s_{n} 
                 Server (ICC) authentication public and 
               
               
                   
                 private key, nth version. 
               
               
                 d_ec, Q_ec = [d_ec]P 
                 client ephemeral public key, matched 
               
               
                   
                 with the ephemeral private key: d_ec 
               
               
                 sk_1c, sk_c, sk_1s, sk_s 
                 AES Secure Messaging Session Keys 
               
               
                 Z, Z_1 
                 Intermediate Shared secrets (x-coordinate 
               
               
                   
                 of EC-DH shared resulting point) 
               
               
                 AEAD, AEAD-1 (sk, data, 
                 Authenticated Encryption with Associated 
               
               
                 associated data) 
                 Data (AES session key SK, data will 
               
               
                   
                 be encrypted or decrypted. Associated 
               
               
                   
                 data will remain as is, but controlled 
               
               
                   
                 for integrity. 
               
               
                 KDF 
                 Key Derivation Function 800-56C based 
               
               
                   
                 on AES C_MAC. Applied on concatenated 
               
               
                   
                 input 
               
               
                 PRNG 
                 Pseudo random number generator 
               
               
                 zero_key 
                 AES key where all bytes have a zero 
               
               
                   
                 value (see 800-56C) 
               
               
                 PubK (C) 
                 Extract the public key from Cert C 
               
               
                   
               
            
           
         
       
     
     A. Methods Assuming a Pre-Loaded Server Certificate 
       FIG. 12  shows a method for secure communication using a client computer that is pre-loaded with a server computer certificate, in accordance with some embodiments. The client computer may maintain data prior to the communication. For example, the client computer can maintain a number (n) server authentication public keys (Q_s_{n}) and server computer certificate chains (C_s_{n}). The client computer can also maintain client sensitive data (SD_c), which may include data usable by a server computer to authenticate the client computer. In addition, the client computer can maintain a client computer certificate chain (C_c) and a client authentication key pair including a client authentication public key (Q_c) and a corresponding client authentication private key (d_c). Furthermore, the client computer can maintain a seed value (seed) that is typically verifiable by the server computer. 
     The server computer may also maintain data prior to the communication. For example, the server computer can maintain a number (n) server computer certificate chains (C_s_{n}), each including a server authentication public key (Q_s_{n}) and the server computer maintaining a corresponding server authentication private key (d_s_{n}). The server computer can also maintain a next server authentication key pair including a next server authentication public key (Q_s_{n+1}) and a next server authentication private key (d_s_{n+1}). The server computer can also maintain an initialization value (IV) and server sensitive data (SD_s), which may include data usable by a client computer to authenticate the server computer. 
     At step  1201 , the client computer generates a client blinding factor (d_bc) using a PRNG function with the seed value as an input. 
     At step  1202 , the client computer generates a blinded client authentication public key (Q_bc) using the client blinding factor, an initialization value (d_iv), and the client authentication public key. 
     At step  1203 , the client computer generates a first shared secret (Z_ 1 ) using the client authentication public key, the client blinding factor, and the server authentication public key corresponding to the server computer for which communication is intended (Q_s_{n}). 
     At step  1204 , a client session identifier is generated using the blinded client authentication public key. 
     At step  1205 , a first client session key is derived using the first shared secret, a server identifier (ID_s), and the client session identifier. 
     At step  1206 , the first client session key is used to encrypt (AEAD) the client sensitive data, the client certificate chain, either the client blinding factor or the seed, some client padding data (PAD_c), and the blinded client authentication public key. The result is encrypted client data (enc_c). 
     At step  1207 , the first shared secret and the first client session key are zeroized (i.e., erased). 
     At step  1208 , the blinded client authentication public key ad the client encrypted data are sent to the server computer. 
     At step  1209 , the server computer validates that the blinded client authentication public key belongs to the correct elliptic curve domain. 
     At step  1210 , the server computer generates the same first shared secret, but using the server authentication private key, the initialization value, and the blinded client authentication public key. 
     At step  1211 , the server computer determines the client session identifier from the blinded client authentication public key. 
     At step  1212 , the server computer derives the first client session key using the first shard secret, the server identifier, and the client session identifier. 
     At step  1213 , the server computer decrypts (AEAD-1) the encrypted client data using the first client session key to obtain the client sensitive data, the client certificate chain, the client blinding factor or seed, and the client padding data. 
     At step  1214 , the server computer zeroizes the first client session key and the first shard secret. 
     At step  1215 , if the client blinding factor was not included in the encrypted client data decrypted at step  1213 , the server computer derives it from the seed using a PRNG function. 
     At step  1216 , the server computer extracts the client authentication public key from the client certificate. The client certificate is also validated. 
     At step  1217 , the blinded client authentication public key received from the client computer is compared to a combination of the client blinding factor and the client authentication public key. If they match, the server computer can authenticate the client computer. 
     At step  1218 , the server computer generates a server blinding factor (d_bs). 
     At step  1219 , a second shared secret (Z) is generated using the second blinding factor, the next server authentication private key, and the blinded client authentication public key. 
     At step  1220 , a blinded server authentication public key (Q_bs) is generated using the server authentication public key and the server blinding factor. 
     At step  1221 , a server session identifier (sID_s) is generated using the blinded server authentication public key. 
     At step  1222 , a server session key (sk_s) and a second client session key (sk_c) are generated using the second shared secret, the server session identifier, and the client session identifier. 
     At step  1223 , the server blinding factor, the next server certificate chain, the server sensitive data, and a server pad (PAD_s) are encrypted using the server session key to generate encrypted server data (enc_s). 
     At step  1224 , the server session key and the second shared secret are zeroized. 
     At step  1225 , the blinded server authentication public key and the encrypted server data are sent to the client computer. 
     At step  1226 , the client computer validates that the blinded server authentication public key belongs to the correct EC domain. 
     At step  1227 , the client computer determines the second shared secret using a combination of the client authentication private key and the client blinding factor, and the blinded server authentication public key. 
     At step  1228 , the client computer determines the server session identifier using the blinded server computer public key. 
     At step  1229 , the client computer derives the server session key and the second client session key using the second shared secret, the server session identifier, and the client session identifier. 
     At step  1230 , the client computer zeroizes the second session key and the client blinding factor. 
     At step  1231 , the client computer decrypts (AEAD-1) the encrypted server data using the server session key to obtain the server blinding factor, the next server certificate chain, the server sensitive data, and the server pad. 
     At step  1232 , the client computer extracts the next server authentication public key from the next server certificate chain. 
     At step  1233 , the client computer validates that the next server certificate chain belongs to the correct elliptic curve domain. 
     At step  1234 , the client computer validates that the combination of the next server authentication public key and the server blinding factor equals the blinded server authentication public key. 
     At step  1235 , the client computer and sever computer can end communication or continue secure messaging using the second client session key and/or the server session key. 
     B. Methods Including Transfer of a Server Certificate 
       FIG. 13  shows a method for secure communication using a client computer that is not pre-loaded with a server computer certificate, in accordance with some embodiments. The client computer may maintain data prior to the communication. For example, the client computer can maintain a client computer certificate chain (C_c) and a client authentication key pair including a client authentication public key (Q_c) and a corresponding client authentication private key (d_c). 
     The server computer may also maintain data prior to the communication. For example, the server computer can maintain a server computer certificate chain (C_s), including a server authentication public key (Q_s) and the server computer maintaining a corresponding server authentication private key (d_s). The server computer can also maintain server sensitive data (SD_s), which may include data usable by a client computer to authenticate the server computer. 
     At step  1301 , the client computer generates a client blinding factor (d_bc). 
     At step  1302 , the client computer combines the blinding factor with the client authentication public key to determine a blinded client authentication public key (Q_bc). 
     At step  1303 , the client computer determines a client session identifier (sID_c) using the blinded client authentication public key. 
     At step  1304 , the client computer sends the blinded client authentication public key to the server computer. 
     At step  1305 , the server computer ensures that the blinded client authentication public key belongs to the correct elliptic curve (EC) domain. 
     At step  1306 , the server computer generates a server blinding factor (d_bs). 
     At step  1307 , the server computer generates a shared secret (Z) using a combination of the server authentication private key and the server blinding factor, and the blinded client authentication public key. 
     At step  1308 , the server computer combines the server authentication public key and the server blinding factor to determine a blinded server authentication public key (Q_bs). 
     At step  1309 , the server computer determines a client session identifier (sID_c) using the blinded client authentication public key. 
     At step  1310 , the server computer determines a server session identifier (sID_s) using the blinded server authentication public key. 
     At step  1311 , the server computer generates a server session key and a client session key using the shared secret, the client session identifier, and the server session identifier. 
     At step  1312 , the server computer encrypts the server blinding factor, the server certificate chain, the server sensitive data, and a server pad (PAD_s) using the server session key to determine server encrypted data (enc_s). 
     At step  1313 , the server session key and the shared secret are zeroized. 
     At step  1314 , the blinded server authentication public key and the server encrypted data are sent to the client computer. 
     At step  1315 , the client computer validates that the blinded server authentication public key belongs to the correct EC domain. 
     At step  1316 , the client computer determines the shared secret using a combination of the client authentication private key and the client blinding factor, and the blinded server authentication public key. 
     At step  1317 , the client computer determines the server session identifier using the blinded server authentication public key. 
     At step  1318 , the client computer determines the server session key and the client session key using the shared secret, the server session identifier, and the client session identifier. 
     At step  1319 , the client computer zeroizes the shared secret and the client blinding factor. 
     At step  1320 , the client computer decrypts the server encrypted data using the server session key to obtain the server blinding factor, the server certificate chain, the server sensitive data, and the server pad. 
     At step  1321 , the client computer extracts the server authentication public key from the server certificate chain. 
     At step  1322 , the client computer validates that the server authentication public key belongs to the correct EC domain. 
     At step  1323 , the client computer verifies the server certificate chain. 
     At step  1324 , the client computer ensures that the combination of the server blinding factor and the server authentication public key is equal to the blinded server authentication public key received from the server computer. 
     At step  1325 , the server blinding factor is zeroized. 
     At step  1326 , if at step  24  the check is successful, the server computer is authenticated at the client computer. 
     At step  1327 , client encrypted data (enc_c) is generated by encrypting the client blinding factor, the client certificate chain, the client sensitive data, and a client pad (PAD_c) using the client session key. 
     At step  1328 , the client computer sends the client encrypted data to the server computer. 
     At step  1329 , the server computer decrypts the client encrypted data using the client session key to obtain the client blinding factor, the client certificate chain, the client sensitive data, and the client pad. 
     At step  1330 , the server computer extracts the client authentication public key from the client certificate chain and validates the client certificate chain. 
     At step  1331 , the server computer ensures that the combination of the client blinding factor and the client authentication public key matches the blinded client authentication public key received from the client computer. If they match, at step  33  the client computer is authenticated by the server computer. 
     At step  1332 , the client blinding factor is zeroized. 
     At step  1334 , the client computer and sever computer can end communication or continue secure messaging using the second client session key and/or the server session key. 
     The above description is illustrative and is not restrictive. Many variations of the invention may become apparent to those skilled in the art upon review of the disclosure. The scope of the invention may, therefore, be determined not with reference to the above description, but instead may be determined with reference to the pending claims along with their full scope or equivalents. 
     It should be understood that any of the embodiments of the present invention can be implemented in the form of control logic using hardware (e.g. an application specific integrated circuit or field programmable gate array) and/or using computer software with a generally programmable processor in a modular or integrated manner. As used herein, a processor includes a single-core processor, multi-core processor on a same integrated chip, or multiple processing units on a single circuit board or networked. Based on the disclosure and teachings provided herein, a person of ordinary skill in the art will know and appreciate other ways and/or methods to implement embodiments of the present invention using hardware and a combination of hardware and software. 
     Any of the software components or functions described in this application may be implemented as software code to be executed by a processor using any suitable computer language such as, for example, Java, C, C++, C#, Objective-C, Swift, or scripting language such as Perl or Python using, for example, conventional or object-oriented techniques. The software code may be stored as a series of instructions or commands on a computer readable medium for storage and/or transmission. A suitable non-transitory computer readable medium can include random access memory (RAM), a read only memory (ROM), a magnetic medium such as a hard-drive or a floppy disk, or an optical medium such as a compact disk (CD) or DVD (digital versatile disk), flash memory, and the like. The computer readable medium may be any combination of such storage or transmission devices. 
     Storage media and computer-readable media for containing code, or portions of code, can include any appropriate media known or used in the art, including storage media and communication media, such as but not limited to volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage and/or transmission of information such as computer-readable instructions, data structures, program modules, or other data, including RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, data signals, data transmissions, or any other medium which can be used to store or transmit the desired information and which can be accessed by the computer. Based on the disclosure and teachings provided herein, a person of ordinary skill in the art will appreciate other ways and/or methods to implement the various embodiments. 
     Such programs may also be encoded and transmitted using carrier signals adapted for transmission via wired, optical, and/or wireless networks conforming to a variety of protocols, including the Internet. As such, a computer readable medium according to an embodiment of the present invention may be created using a data signal encoded with such programs. Computer readable media encoded with the program code may be packaged with a compatible device or provided separately from other devices (e.g., via Internet download). Any such computer readable medium may reside on or within a single computer product (e.g. a hard drive, a CD, or an entire computer system), and may be present on or within different computer products within a system or network. A computer system may include a monitor, printer, or other suitable display for providing any of the results mentioned herein to a user. 
     Any of the methods described herein may be totally or partially performed with a computer system including one or more processors, which can be configured to perform the steps. Thus, embodiments can be directed to computer systems configured to perform the steps of any of the methods described herein, potentially with different components performing a respective steps or a respective group of steps. Although presented as numbered steps, steps of methods herein can be performed at a same time or in a different order. Additionally, portions of these steps may be used with portions of other steps from other methods. Also, all or portions of a step may be optional. Additionally, any of the steps of any of the methods can be performed with modules, units, circuits, or other means for performing these steps. 
     The specific details of particular embodiments may be combined in any suitable manner without departing from the spirit and scope of embodiments of the invention. However, other embodiments of the invention may be directed to specific embodiments relating to each individual aspect, or specific combinations of these individual aspects. 
     The above description of example embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form described, and many modifications and variations are possible in light of the teaching above. 
     A recitation of “a”, “an” or “the” is intended to mean “one or more” unless specifically indicated to the contrary. The use of “or” is intended to mean an “inclusive or,” and not an “exclusive or” unless specifically indicated to the contrary. 
     All patents, patent applications, publications, and descriptions mentioned herein are incorporated by reference in their entirety for all purposes. None is admitted to be prior art.