Abstract:
An improved encryption and digital signature system and method in accordance with the invention reuses an encryption ephemeral key pair from an encryption process in a digital signature process. The reuse of the encryption ephemeral key pair in the digital signature process advantageously results in reduced byte size of the digital signature and reduction of costly computation overhead. In a preferred embodiment, the invention is based on the El Gamal encryption scheme and the Nyberg-Rueppel signature scheme. The present invention is particularly useful for operation in conjunction with small communication devices having limited processing and storage, wherein such devices may communicate via bandwidth sensitive RF links.

Description:
RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 12/724,950, entitled “Public Key Encryption With Digital Signature Scheme,” filed on Mar. 16, 2010, which in turn, claims the benefit of and is a continuation of U.S. patent application Ser. No. 09/594,368, (now U.S. Pat. No. 7,707,420), entitled “Public Key Encryption With Digital Signature Scheme,” filed on Jun. 15, 2000, which in turn claims priority to and the benefit of the U.S. Provisional Application No. 60/140,564, filed Jun. 23, 1999, entitled “Public Key Encryption With Digital Signature Scheme.” All of these are hereby incorporated into the present application by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    This invention relates to the field of public-key cryptography. More specifically, it is directed to a combined and improved public key encryption and digital signature scheme. 
         [0004]    2. Background of the Invention 
         [0005]    Cryptography essentially provides confidentiality, authentication, integrity and non-repudiation for communication between different parties over public communication channels. 
         [0006]    In a public-key scheme, each user has a key pair consisting of a public key that is made publicly available, and a private key that is kept secret. The two keys are related by a hard one-way function, so as to make it infeasible to determine the private key from the public key. The public-key scheme allows a signature in the form of a digital signature to accompany a message. 
         [0007]    In the public-key environment, there are preferably three major processes. First, there is the certification process. A certificate authority creates a certificate that binds a user identity to the public key. A certificate repository provides a database of certificates where the public can access and retrieve the public key information of participants. In addition, there is a registration authority that acts as an assistant to the certificate authority. In essence, the registration authority is used to validate the binding. The second process is the encryption scheme that essentially converts a plaintext message into a ciphertext message. The third process is a digital signature process. The present invention relates specifically to the latter process and how it may be combined with the encryption process. 
         [0008]    A digital signature is a cryptographic primitive that provides a means for a user or an entity to bind its identity to a piece of information. A digital signature of a message is a sequence of bytes dependent on some secret known only to the signer, and, additionally, on the content of the message being signed. Such signatures must be verifiable, if a dispute arises as to whether a party signed a document. The process of signing entails transforming the message and a key unique to a particular user into a tag called a digital signature. A digital signature may be used to prove the identity of the sender and the integrity of data. To verify the digital signature, a recipient of a digitally signed message can use a verification rule associated with the digital signature scheme. Any attempt to modify the contents of the message or forge a signature will be detected when the signature is verified. 
         [0009]    Each of the above stages requires a certain degree of undesirable computational processing and a certain degree of byte-size overhead associated in the transmission of a communication to make the overall public-key process secure. 
         [0010]    Therefore, there remains an on going desire to reduce the additional byte and processing overhead associated with the public-key system while at the same time, not reducing the effectiveness of the public-key system. 
       SUMMARY OF THE INVENTION 
       [0011]    It is an object of the invention to reduce some of the drawbacks of the prior art public-key systems. 
         [0012]    It is an object of the invention to reduce computational processing associated with public-key schemes. 
         [0013]    It is an object of the invention to reduce byte-size overhead associated with the transmission of the digital signature. 
         [0014]    It is a further object of the present invention to provide a public key scheme with an improved encryption and digital signature scheme. The improved encryption and signature scheme can work in any finite cyclic group, such as a group of points on an elliptic curve over a finite field. 
         [0015]    More specifically, in the present invention, there is provided an improved encryption and digital signature scheme that reuses an ephemeral key pair from the encryption process in the signature process. Advantageously, the reuse of the ephemeral key allows the digital signature to be reduced in byte size. Another advantage is that costly computation may be avoided. 
         [0016]    According to the invention, a public-key encryption process comprises the steps of encrypting a plaintext message into a ciphertext message, the encrypting step includes the step of producing an ephemeral key pair, and signing a digital signature using the ephemeral key pair. 
         [0017]    In another inventive aspect, a public-key encryption system comprises means for encrypting a plaintext message into a ciphertext message, the encrypting means producing an ephemeral key pair, and means for signing a digital signature using the ephemeral key pair. 
         [0018]    A further aspect of the invention involves a software program on a computer-readable storage medium, which when executed by a processor performs a public-key encryption process comprising the steps of encrypting a plaintext message into a ciphertext message, the encrypting step includes the step of producing an ephemeral key pair, and signing a digital signature for the ciphertext message using the ephemeral key. 
         [0019]    In a preferred embodiment described herein, the invention is based on the El Gamal encryption and Nyberg-Rueppel signature schemes. Other encryption and digital signature schemes are all well within the scope of the invention. 
         [0020]    In the inventive process, system or software program, the ephemeral key pair may be produced by generating an encryption ephemeral private key x and calculating an encryption ephemeral public key X=xG, where G is a generator. According to a further preferred embodiment, the digital signature comprises a first value r and a second value s, and the encryption ephemeral public key X the ciphertext message and the second value s of the digital signature are transmitted from a sender to a receiver. At the receiver, the transmitted ciphertext message is decrypted, the first value r of the digital signature is calculated using the decrypted message and the transmitted encryption ephemeral public key X and the digital signature is validated based on the calculated first value r and the transmitted second value s. 
         [0021]    With respect to the notation adopted herein and described below, the improved digital signature scheme uses the value of x, an encryption ephemeral key, for the value of z, a signature ephemeral key, instead of generating a random value for z, as in the prior art. Consequently, the transmitted digital signature of the present invention comprises a value s. A value of r, which according to conventional methods must be transmitted with the message, is instead reconstructed on the recipient end based on given values in the sender&#39;s transmission. In this improved scheme the overall combined El Gamal encryption scheme and the Nyberg-Rueppel digital signature scheme is optimized for faster computation time and lower overhead bandwidth. In particular, the computation of Z=zG is avoided by the sender in the digital signature stage and the byte-size overhead associated with the digital signature transmission is reduced. 
         [0022]    The present invention is preferably configured to operate in conjunction with small devices having limited processing and storage such as those disclosed in co-pending U.S. patent application Ser. No. 09/106,585 titled “Hand-Held Electronic Device With a Keyboard Optimized for Use With The Thumbs”, the disclosure of which is hereby incorporated into this disclosure by reference. Other systems and devices in which the invention may be implemented include, but are not limited to, wireless communication systems, wireless hand-held communication devices, personal digital assistants (PDAs), cellular phones and two-way pagers. 
         [0023]    The present invention addresses specific dilemmas faced in electronic communication devices that are both bandwidth and computation load sensitive. 
         [0024]    Further features of the invention will be described or will become apparent in the course of the following detailed description. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0025]    In order that the invention may be more clearly understood, the preferred embodiment thereof will now be described in detail by way of example, with reference to the accompanying drawings, in which: 
           [0026]      FIG. 1  is a functional diagram of a prior art El Gamal public-key encryption scheme; 
           [0027]      FIG. 2  is a functional diagram of a prior art Nyberg-Rueppel digital signatures scheme; 
           [0028]      FIG. 3  is a functional diagram of a prior art public-key system combining the schemes illustrated in  FIGS. 1 and 2 ; 
           [0029]      FIG. 4  is a functional diagram of the present invention&#39;s public-key system with an improved digital signature scheme; and 
           [0030]      FIG. 5  is a block diagram of a communication system in which the invention could be implemented. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Notation Explanation 
       [0031]    For clarity of the detailed description, the notation used herein is now defined. In the improved encryption and digital signature scheme to be described, any finite cyclic group, such as the group of points on an elliptic curve over a finite field is suitable for its application. In the preferred embodiment described herein, the present invention is based on combining the El Gamal encryption scheme and the Nyberg-Rueppel digital signature scheme. Other encryption and digital signature schemes are all well within the scope of the invention. 
         [0032]    Upper case letters, such as A, B, G, K, Q, X, Z, denote group elements. An upper case G throughout this description is a generator of the group and has order n. Lower case letters, such as a, b, h, r, s, x, z, denote integers modulo (mod) n. An upper case letter with an asterisk, such as. Z*, denotes the conversion of a corresponding group element, i.e. Z, to an integer. For elliptic curves, Z=(x,y) and Z* is usually derived from the x of Z. The group operation is denoted by ‘+’ and aA=A+A+ . . . +A, a times. In addition, ciphertext=encrypt (K, message) denotes a symmetric key encryption function that encrypts a plaintext message using a key derived from a group element K and returns the corresponding ciphertext. Likewise, message=decrypt (K, ciphertext) denotes a symmetric key decryption function that decrypts a ciphertext using a key derived from a group element K and returns the corresponding plaintext message. Finally, h=hash (message) denotes a cryptographically secure hash function that hashes a message to an integer modulo n. 
         [0033]    The detailed description now follows with reference to  FIGS. 1-5 . In the functional diagrams of  FIGS. 1-4 , time is represented as increasing from the top to the bottom of the diagrams, as indicated by the “t” arrow at the top of each diagram. 
         [0034]      FIG. 1  is a schematic of the prior art El Gamal public key encryption scheme  10 . An encrypted message exchange between a notional sender, Alice  20 , and a notional recipient, Bob  30  is illustrated therein. In a certification stage  40 , Bob randomly generates private key b and computes public key B=bG, as shown at  12 . For the purposes of this description, it is assumed that Alice has Bob&#39;s authentic public key B. A certification authority, if used, validates a public key by creating and issuing a certificate. Alice may receive Bob&#39;s certificate  14  directly from Bob, or from a publicly accessible public key repository. Alice verifies that the signature on the certificate is correct, and that the certificate has not expired or been revoked. If those conditions are satisfied, then the public key B in the certificate  14  may be trusted. 
         [0035]    In the illustrated encryption process  10 , the sender Alice performs the processing indicated in block  16 . A random integer x, known as an encryption ephemeral private key is generated and an encryption ephemeral public key X=xG is calculated. X and x comprise an encryption ephemeral key pair. Alice then generates a secret encryption key K=xB=xbG and encrypts her plaintext message  18  with secret key K  20 . The encryption ephemeral public key X and ciphertext message  22  are then transmitted to Bob. Bob then calculates secret key K=bX=bxG=xbG=xB and decrypts the ciphertext  22  back into plaintext message  18 . This key agreement scheme is a protocol by which a pair of users, communicating over an insecure channel, may independently calculate the same secret key from publicly communicated values. 
         [0036]      FIG. 2  is a schematic of the prior art Nyberg-Rueppel digital signature scheme  60 . In this scheme, Alice randomly generates private key a and computes public key A=aG (see block  24 ). Similar to the scheme of  FIG. 1 , it is assumed that Bob has obtained Alice&#39;s authentic public key either directly from Alice or through a certificate  26  from a certification authority or public key repository. As shown in  FIG. 2 , a hash value h  32  is created from the message using a hash function. An ephemeral signature key pair (Z, z) is produced by randomly generating ephemeral signature private key z  34  and calculating ephemeral public key Z  36 , where Z=zG. The digital signature  38 , comprising values r=Z*+h mod n and s=z−ar mod n, are calculated and transmitted with message  18  to Bob. 
         [0037]    This scheme requires the message  18  as input into the signature and verification algorithms  42 . The verification portion of the scheme verifies a signature with Alice&#39;s public key A, given the digital signature  38  comprising integers r, s and the message  18 . The recipient verifies the message by creating the hash value h  32  using the same hash function and processing it with Alice&#39;s public key. The verification output is compared with the received signature r, s to determine its validity, as shown in block  42 . 
         [0038]      FIG. 3  is illustrative of a traditional prior art public key encryption scheme using the El Gamal public key encryption scheme and the Nyberg Rueppel digital signature scheme. In this scheme  80 , there are three main stages to a public key encryption scheme. First, there is a preliminary certification scheme  40 , during which Alice and Bob obtain each other&#39;s authentic public key A and B. Second, there is an encryption process  50 . Third, there is a digital signature scheme  70 . As the El Gamal and Nyberg-Rueppel schemes have been described separately above, a detailed description of the combined encryption/signature scheme in  FIG. 3  will not be pursued. However, it is highlighted that the signature ephemeral private key z  34  is randomly generated by the sender, the signature ephemeral public key Z  36  is computed by the sender and the transmitted digital signature  38  comprises the integers r and s. The values of r and s representing the transmitted digital signature  38  are transmitted with the encryption public key X and the ciphertext in the prior art. 
         [0039]    There are, however, some undesirable characteristics associated with this prior art approach. Firstly, computational resources and time are consumed where Z is calculated with large bit numbers. Secondly, the byte-size overhead associated with the public-key transmitted information is undesirably large for bandwidth sensitive devices such as wireless communication devices. The present invention addresses these two undesirable qualities. 
         [0040]      FIG. 4  illustrates an overview of a preferred embodiment of the present invention. Like the prior art, there are three main stages to the preferred embodiment of the present invention, namely the certification  40 ′, encryption  50 ′ and digital signature  70 ′ stage. 
         [0041]    In the certification stage, Alice generates a long term random private key a and computes public key A, where A=aG. Likewise, Bob randomly generates private key b and computes public key B, where B=bG. As described above in relation to  FIGS. 1-3 , Alice and Bob exchange authentic public keys A and B directly, through a certification authority or through a public key repository 
         [0042]    In the encryption stage  40 ′, Alice generates an encryption ephemeral private key as random integer value x and computes a corresponding encryption ephemeral public key X, where X=xG. As described above, the set (X, x) represents the ephemeral key pair produced in the encryption scheme. With this information, Alice uses Bob&#39;s public key B to compute secret key K  20 , given by K=xB. Alice then encrypts the message producing ciphertext=encrypt (K, message)  22 . 
         [0043]    The present invention outlined in  FIG. 4  deviates from the prior art scheme of  FIG. 3  in several important aspects. The improved digital signature scheme of the present invention uses the encryption ephemeral key pair (X, x) produced in the encryption stage  50 ′ as a substitute for the signature ephemeral key pair (Z, z) required in the digital signature stage  70 ′. The value of signature ephemeral private key z  34 ′ is set to the value of encryption ephemeral private key x from the encryption stage. Consequently, the random generation of z and the computation of Z  36 ′ are not required since signature ephemeral public key Z  36 ′ equals encryption ephemeral public key X  20 . Advantageously, this reduces the computational load on the sender. In essence, the value for x is used for two different purposes. In the first instance, x is used for the encryption process scheme  50 ′. In the second instance, the x is also used in the digital signature scheme  70 ′. 
         [0044]    After transmission of the encryption public key X  20 , ciphertext  22  and signature s  38 ′, Bob may then calculate secret key K=bX and then decrypt the message by message=decrypt (K, ciphertext). The digital signature scheme then preferably hashes the message  40  to calculate h, as indicated in block  42 ′. Two pieces of information for the digital signature still need to be computed, namely integers r and s. The integers are calculated as follows: r=Z*+h mod n=X*+h mod n and s=z−ar mod n=x−ar mod n. However, only s in addition to the encryption ephemeral public key X and the ciphertext must be transmitted to Bob in the inventive scheme  80 ′. Rather than r being transmitted to Bob, r is instead reconstructed at the receive side by calculating r=X*+h mod n. In this manner, the overall byte-size overhead associated with the digital signature  38 ′ is reduced by not transmitting r. In a specific embodiment of the invention, the saving was in the range of twenty-two bytes. In portable two-way wireless communication devices, reducing the transmission by twenty-two bytes is considerably useful and advantageous. 
         [0045]    The inventive encryption and signature scheme outlined in  FIG. 4  would preferably be implemented in software in a communication system. The block diagram in  FIG. 5  represents one such system  100  in which the inventive scheme could be used. In  FIG. 5 ,  110 ,  112  and  114  are communication devices and  116  is certification authority or public key repository. In order for the devices to communicate using the inventive scheme, each device must first exchange authentic public keys with the other device or devices with which communication is desired. As shown in  FIG. 5  and described above, each device may communicate with a certification authority or public key repository  116  or with each other to accomplish public key exchange. Each communication device may incorporate software or hardware to perform the inventive encryption and signature scheme. Communication devices  110 ,  112  and  114  may be wired or wireless communication devices. This invention has particular application in, but not limited to, Personal Digital Assistants, mobile communication devices, cellular phones, two-way pagers and wireless two-way e-mail communication devices. One such illustrative device that may implement the present invention is disclosed in co-pending U.S. patent application Ser. No. 09/106,585, referenced above. In an alternative embodiment of the present invention, a system disclosed in FIG. 2 of PCT/CA99/00494 titled “System and Method for Pushing Information From a Host System to Mobile Data Communication Device”, the specification of which is hereby incorporated by reference into the present disclosure, may implement the present invention. In all such systems, a typical system for which the present invention is particularly useful is a low bandwidth system such as one that utilizes an RF link in the communication path. The system and method of pushing information from a host system to a mobile described in the latter application is only one preferred system and method for the present invention herein; however, it is to be understood other types of systems and methods could be implemented that utilizes the present invention. 
         [0046]    It will be appreciated that the above description relates to a preferred embodiment by way of example only. Many variations on the invention will be obvious to those knowledgeable in the field, and such obvious variations are within the scope of the invention as described and claimed, whether or not expressly described. For instance, the aforementioned process could obviously be extended to include multiple recipients from a single sender.