Patent Application: US-92050497-A

Abstract:
a method is provided for an escrow cryptosystem that is overhead - free , does not require a cryptographic tamper - proof hardware implementation , is publicly verifiable , and cannot be used subliminally to enable a shadow public key system . a shadow public key system is an unescrowed public key system that is publicly displayed in a covert fashion . the keys generated by the method are auto - recoverable and auto - certifiable . the arc cryptosystem is based on a key generation mechanism that outputs a public / private key pair , and a certificate of proof that the key was generated according to the algorithm . each generated public / private key pair can be verified efficiently to be escrowed properly by anyone . the verification procedure does not use the private key . hence , the general public has an efficient way of making sure that any given individual &# 39 ; s private key is escrowed properly , and the trusted authorities will be able to access the private key if needed . since the verification can be performed by anyone , there is no need for a special trusted entity , known in the art as a “ trusted third party ”. furthermore , the system is designed so that its internals can be made publicly scrutinizable . this differs from many schemes which require that the escrowing device be tamper - proof hardware . the system has a novel feature that the system parameters can be generated very efficiently and at the same time provide a very high level of security . another novel feature is a method for making the certificates of recoverability publishable . the system is applicable for law - enforcement , file systems , e - mail systems , certified e - mail systems , and any scenario in which public key cryptography can be employed and where private keys or information encrypted under public keys need to be recoverable .

Description:
the following is a description of the prefered embodiment of the present invention . variations on the prefered embodiment will accompany the description of the prefered embodiment wherever applicable . for convenience in the presentation , the hashing algorithm selected is sha ( schneier 2nd edition , pages 442 - 445 ), though any cryptographic hashing algorithm will suffice in its place . in the prefered embodiment , parameters are chosen uniformly at random from their respective groups . alternate embodiments include alterations of the probability distributions from which such values are chosen . such choices based on random number generators or pseudo - random generators are available in the art . the system setup of the prefered embodiment shown in fig1 initiates the cryptosystem . in the prefered embodiment , the escrow authorities share an integer n = qr , where q and r are prime . when n is generated , it is made sure that gcd ( 3 ,( q − 1 )( r − 1 ))= gcd ( 5 ,( q − 1 )( r − 1 ))= 1 . the generation continues by computing p = 2tn + 1 , where t is drawn from the first , say 256 strong primes starting from 23 , inclusive . if p is found to be prime using one of these values for t , then the values for n and p have been found . if none of the values for t causes p to be prime , this entire process is repeated as many times as necessary . note that if t is a strong prime , then t = 2t ′+ 1 where t ′ is prime . since we insist that t & gt ; 11 , we are guaranteed that gcd ( 3 , 2t ′( q − 1 )( r − 1 ))= gcd ( 5 , 2t ′( q − 1 )( r − 1 ))= 1 . let m denote the number of escrow authorities . once n and p are found , the escrow authorities generate the private shares d 1 , d 2 , . . . , d m corresponding to the public exponent e = 3 . the method described in ( a . de santis , y . desmedt , y . frankel , m . yung , “ how to share a function securely ”, acm stoc &# 39 ; 94 , pages 522 - 533 , 1994 ) can be used to employ such shared values . ideally , q and r are strong primes , to thwart known attacks . a value g which is chosen uniformly at random from z 2tn * is chosen such that g has an order that is at least as large as the smallest of q and r , in the field z p ( recall that the factorization of n is not known ). the values t , n , and g are made public . the twin primes 3 and 5 will act as public key encryption exponents . fig2 is a diagram showing the process of how a user &# 39 ; s system generates a public / private key pair and a certificate of recoverability . having obtained ( and verified as much as possible ) the signal t , n , and g that is made available to users by the escrow authorities , the user system proceeds to generate a public key ( y , g , p ) for the user . note that this key is an elgamal public key in every respect , except that g may have order q or r modulo p . the signal t , n , and g may a priori have been included in the invention . the invention proceeds by choosing a value x ′ in z 2tn * randomly . this is depicted by step 2004 in fig2 . in step 2005 , the invention computes c = x ′ 3 mod 2tn and in step 2006 the invention computes the user &# 39 ; s private key x such that x = x ′ 2 mod 2tn . the invention also computes y to be g x mod p . the system then proceeds to step 2007 and computes a certificate that can be used by any interested party to verify that the user &# 39 ; s “ private key ” is properly encrypted within c . the certificate contains the value c . the system also processes three non interactive zero - knowledge proofs as they are called in the art and includes them in the certificate . let n denote the number of repetitions in each non - interactive proof . the proofs are based on a cryptographic hash function , as they are called in the art . in the prefered embodiment , n is set to be 40 . the first proof is designed so that the user can prove that he or she knows x ′ in c . the second proof is designed so that the user can prove that he or she knows x ′ in y . the last proof is designed so that the user can prove that he or she knows x ′ in ( y raised to the c power mod p ). by saying “ the user knows value x ′” we mean that the system has the value x ′ in its state . the last two proof systems prove knowledge of the root of the logarithm of a value . for example , in the second proof , this value is y . the square root of the log of y is x ′ in a properly generated certificate . in more detail , to construct the non - interactive proofs , the system proceeds as follows . it chooses the values a 1 , 1 , a 1 , 2 , . . . , a 1 , n , a 2 , 1 , a 2 , 2 , a 2 , 3 , . . . , a 2 , n and a 3 , 1 , a 3 , 2 , a 3 , 3 , . . . , a 3 , n in z 2tn * randomly . for i ranging from 1 to n , the system sets i 1 , i to be a 1 , i 3 mod 2tn . for i ranging from 1 to n , the invention sets i 2 , i to be y raised to the ( a 2 , i 2 mod 2tn ) power mod p . for i ranging from 1 to n , the invention sets i 3 , i to be ( y c mod p ) raised to the ( a 3 , i 5 mod 2tn ) power mod p . the invention then computes the value rnd to be the sha hash of the set formed by concatenating together the tuples ( i 1 , i , i 2 , i , i 3 , i ) for i ranging from 1 to n . note that rnd is a function of all of the i values , using a suitably strong cryptographic hash function . in alternate embodiments , the hash function can have an effective range of size different than 160 bits . a greater range of the hash function allows for significantly larger values for n . the system sets each of the bit - sized values b 1 , 1 , b 1 , 2 , . . . , b 1 , n , b 2 , 1 , b 2 , 2 , . . . , b 2 , n , b 3 , 1 , b 3 , 2 , . . . , b 3 , n to be each of the corresponding 3n least significant bits of rnd . there are a multitude of ways in which an embodiment can securely assign the bits of rnd to the values for b . the values for b are the challenge bits , and this method of finding them is known as the fiat - shamir heuristic . the system then proceeds to compute the responses to these challenge bits . for i ranging from 1 to 3 and for j ranging from 1 to n , the invention sets z i , j to be ( a i , j times ( x ′ raised to the b i , j power )) mod 2tn . this completes the description of step 2007 of fig2 . the system proceeds to step 2008 . in step 2008 , the invention outputs the parameters c , y , ( i 1 , i , i 2 , i , i 3 , i ), and ( z 1 , i , z 2 , i , z 3 , i ) for i ranging from 1 to n . in an alternate embodiment the value x ′ is output by the invention to the user . the user then has the option to later interactively prove that his or her private key x is recoverable by the escrow authorities . this will be addressed in more detail later . also , the values b can be made a part of the certificate . this step is however , not necessary , since the values for b can be derived from the values for i alone . the description of the embodiment has thus far explained how the system is setup for use by the ca and authorities , and how the system is used by users ( potential receivers ) to generate public / private key pairs and certificates of recoverability . these certificates are strings showing to anyone presented with them that the key generated has the publicly specified properties . the following describes how the invention is used by the user to prove to a verifier that x is recoverable from c . this process is depicted in fig3 . the verifier can be the ca , an escrow authority , or anyone else who knows the system parameters . the verification process of fig3 is as follows . in step 3009 , the user generates a public / private key pair , and a certificate using the invention as described above . in step 3010 , the user transmits a signal containing these parameters to a verifier . in step 3011 the verifier uses this signal to verify whether or not the user &# 39 ; s private key is recoverable by the escrow authorities . to do so , the verifier uses the user &# 39 ; s public key , the corresponding certificate , and the escrowing public key 2tn . the way in which the users signal is processed will now be described in detail . the verifying system outputs a 0 if the public key and / or certificate are invalid , and a 1 otherwise . the invention may take subsequent action and indicate to the verifier that the public key is invalid in the event that 0 is returned . similarly , the verifying system may inform the verifier of a validation that passes . to perform the verification , the verifying system verifies the three non - interactive proofs contained within the certificate of the user . the invention computes ( b 1 , i , b 2 , i , b 3 , i ) for i ranging from 1 to n in the same way as performed during the certificate generation process . recall that this process was described in regards to fig2 . for the first non - interactive proof , the verifying system checks that i 1 , i c = z 1 , i 3 mod 2tn if b 1 , i = 1 , for i ranging from 1 to n . the verifying system also checks that i 1 , i = z 1 , i 3 mod 2tn if b 1 , i = 0 , for 1 ranging from 1 to n . if any of these equalities fails , then the verifying system returns a value of 0 . this completes the verification of the first non - interactive proof . for the second non - interactive proof , the verifying system checks that i 2 , i = g raised to the ( z 2 , i 2 mod 2tn ) power mod p if b 2 , i = 1 , for i ranging from 1 to n . the verifying system also checks that i 2 , i = y raised to the ( z 2 , i 2 mod 2tn ) power mod p if b 2 , i = 0 , for i ranging from 1 to n . if any of these equalities fail , then the verifying system returns a value of 0 . this completes the verification of the second non - interactive proof . for the third non - interactive proof , the invention checks that i 3 , i = g raised to the ( z 3 , i 5 mod 2tn ) power mod p if b 3 , i = 1 , for i ranging from 1 to n . the invention also checks that i 3 , i =( y c mod p ) raised to the ( z 3 , i 5 mod 2tn ) power mod p if b 3 , i = 0 , for i ranging from 1 to n . if any of these equalities fails , then the verifying system returns a value 0 . if all of the verifications pass , then the value 1 is output by the verifying system . in fig4 the user certifies his or her public key with the ca . in step 4012 of this process , the user generates his or her public key and certificate of recoverability , as previously described . the user transmits this signal to the ca . this corresponds to step 4013 of fig4 . in step 4014 the ca acts as a verifier and verifies that the user &# 39 ; s private key is recoverable by the escrow authorities . so far , steps 4012 through 4014 are identical to steps 3009 through 3011 in the key verification process of fig3 . however the ca , in addition , will make keys that pass the verification process available to others upon request and / or certify them . if the user &# 39 ; s public key fails the verification process , then either the certification attempt is ignored , or alternatively the user is notified of the failed certification attempt . depending on the demands of the environment in which the invention is used , users may be required to submit extra information in order to register a public key and to certify that they know the private key portion without divulging it . such information could be a password , social security number , previously used private key , etc . in the case that the ca is a trusted entity , the ca can simply digitally sign the user &# 39 ; s public key together with the user &# 39 ; s name and additional information , and make the key along with the ca &# 39 ; s signature on this information available on request . if the ca is not trusted , then the certificate should be stored in the public file and the certificate together with the certificate of recoverability should be given to the escrow authorities , who in turn can insure recoverability . this completes the description of the public key certification process . the last process to describe is the private key recovery process . this process is depicted in fig5 . in this process , the invention is used by the m escrow authorities to recover the user &# 39 ; s private key based on c . in this process , all m of the escrow authorities obtain c , as depicted in step 5015 of fig5 . in an alternate embodiment the ca transmits c and / or other parameters to one or more of the authorities . thus they are already in possession of c . at this point escrow authorities use a subset of their shares d 1 , d 2 , . . . , d m to decrypt c to get x ′. given x ′, x is found by computing x = x ′ 2 mod 2tn . there are alternative methods in the art for computing x ′ so that x ′ is represented distributively among the authorities . what has been described is an auto - recoverable and auto - certifiable ( arc ) cryptosystem where the system parameters can be generated very easily . the users of such a cryptosytem employ the public key system in a way that is identical to a typical pki for secure communications . this is demonstrated schematically in fig6 and 7 . fig6 is a typical public key cryptosystem in a pki environment . the following are the steps that are followed by the users . ( 1 ) the user first reads the ca &# 39 ; s information and address . ( 2 ) the user generates a public / private key pair and sends the public key to the ca . the registration of the authority in the ca verifies the identity of the user , and publishes the public key together with the ca certificate on that key , identifying the user as the owner of that key . ( 3 ) for another user to send a message to that user , the public key is read from the ca &# 39 ; s database and the certificate is verified . ( 4 ) then , the message is encrypted under new the public key and sent . fig7 schematically describes the arc cryptosystem . the additional operations are as follows . ( 0 ) the authority generates the escrowing public key and gives it to the ca . steps 1 and 2 are analogous , except that a proof is sent along with the public key . steps 3 and 4 are the operation of the system and are identical . steps 5 and 6 describe the case in which keys are recovered from escrow . ( 5 ) the escrow authority gets information from the ca . ( 6 ) the escrow authority recovers the user &# 39 ; s private key . the authorities can require that that the certificate of recoverability be sent along with the public key and encryption so that the user &# 39 ; s parameters can first be verified using the verification process . this completes the description of the private key recovery process . in another embodiment , the interactive versions of the three non - interactive proofs can be used . such an embodiment requires that the system output x ′ to the user during key generation . this value x ′ is used during the interactive protocol , so that the verifier can be convinced that the user &# 39 ; s private key is recoverable by the escrow authorities . note that by outputing any of the non - interactive zero - knowledge proofs , a shadow public key cryptosystem may result . this follows from the fact that the values for z can be chosen by a malicious user . in yet another embodiment , the ca , or other trusted entity , takes the further action of cryptographicly blinding the certificate of recoverability . blinding is typically done by exponentiating a modular exponentiation by a given factor . it also holds for multiplication . see ( d . chaum , “ blind signatures for untraceable payments ”, crypto &# 39 ; 82 , pages 199 - 203 , springer - verlag , 1982 ) for more on blinding . blinding is done as follows . the user commits to his values . the ca or a third party sends the blinding factors to the user . the non - interactive proofs are then constructed based on the blinded values . this prevents users from exploiting subliminal channels , and the resulting certificate of recoverability can be published . in particular , the certificate of recoverability can be part of the ca &# 39 ; s certificate for the given user , which typically also includes the user name , the user &# 39 ; s public key , and other information . an application of this invention is a multi - escrow authority system where each escrow authority has its own cas and users . when users from two different escrow authorities conduct secure communication the two escrow authorities can retrieve the user &# 39 ; s messages or keys and exchange them through bilateral agreement . this is applicable to international multi - country scenarios . another application of key escrow systems is a secure file system or file repository system with recoverable keys . such a system can be implemented based on the previous embodiments , in particular based on the preceding paragraph . for example , user a can be the owner of the file , user b can be the file server , and the trustees can be file recovery agents . an example of a file could be a password , in which case , the file recovery agents are password recovery agents . yet another application of this invention is a certified electronic mailing system . when the users register into the system , they register an auto - recoverable encryption public key and a certificate of recoverability to the ca , and they also register a signature public key . to send a certified piece of mail , the following is done . the sender sends a packet which includes the following : an encryption of an e - mail key under his own auto - certified public key , the receiver &# 39 ; s name , an encryption of the e - mail message encrypted under the e - mail key , a header indicating a certified e - mail message , his own certified public key , and the ca &# 39 ; s certificate on his certified public key , and other information . the packet is signed using the senders signature private key . both the packet and the signature on the packet are sent to the receiver . the receiver forms a return receipt packet that consists of a fixed return receipt header , the received message ( or the hash of the received message ), and additional information . this packet is signed using the receivers private signature key and is sent to the original sender . the original sender verifies the signature on the return receipt packet . if the signature is valid , the original sender sends the receiver the e - mail key encrypted under the receiver &# 39 ; s certified public key . this message is sent along with a signature on it using the original sender &# 39 ; s private signing key . the receiver verifies the signature on the encrypted e - mail key . if the signature is valid , the receiver decrypts the e - mail key using his private decryption key . the receiver then encrypts the result using the original senders certified public key . if the result matches the ciphertext in the first packet that the original sender sent , then the e - mail key is regarded as authentic . this key is then used to decrypt and obtain the actual information that the original sender sent . if the receiver is for some reason unable to contact the original sender after the first packet is received , the receiver sends the return receipt and the first packet to the escrow authorities . the escrow authorities will recover the e - mail key , provided the packet and return receipts are authentic and provided that the packet contains the corrects receivers name . the escrow authorities retain the return receipt and the packet . provided the checks pass , the e - mail key is sent to the receiver . this constitutes a certified e - mail system based on auto - recoverable keys and signature keys , and where user registration is analogous to user registration in a typical public key system with a ca . also , it is known in the art how to employ certified e - mail systems as above for contract signing between two parties . the above application can be used as such . thus , there has been described a new and improved key escrow system , its variants , and applications . it is to be understood that the prefered embodiment is merely illustrative of some of the many specific embodiments which represent applications of the principles and paradigms of the present invention . clearly , numerous and alternate arrangements can be readily devised by those who are skilled in the art without departing from the scope of the present invention . r . anderson , “ the gchq protocol and its problems ”, eurocrypt &# 39 ; 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