Fair cryptosystems and methods of use
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 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q20/00—Payment architectures, schemes or protocols

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q20/00—Payment architectures, schemes or protocols
 G06Q20/02—Payment architectures, schemes or protocols involving a neutral party, e.g. certification authority, notary or trusted third party [TTP]

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q20/00—Payment architectures, schemes or protocols
 G06Q20/38—Payment protocols; Details thereof
 G06Q20/382—Payment protocols; Details thereof insuring higher security of transaction
 G06Q20/3829—Payment protocols; Details thereof insuring higher security of transaction involving key management

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q20/00—Payment architectures, schemes or protocols
 G06Q20/38—Payment protocols; Details thereof
 G06Q20/389—Keeping log of transactions for guaranteeing nonrepudiation of a transaction

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q20/00—Payment architectures, schemes or protocols
 G06Q20/38—Payment protocols; Details thereof
 G06Q20/40—Authorisation, e.g. identification of payer or payee, verification of customer or shop credentials; Review and approval of payers, e.g. check credit lines or negative lists
 G06Q20/403—Solvency checks

 G—PHYSICS
 G07—CHECKINGDEVICES
 G07F—COINFREED OR LIKE APPARATUS
 G07F17/00—Coinfreed apparatus for hiring articles; Coinfreed facilities or services
 G07F17/32—Coinfreed apparatus for hiring articles; Coinfreed facilities or services for games, toys, sports or amusements, e.g. casino games, online gambling or betting
 G07F17/3241—Security aspects of a gaming system, e.g. detecting cheating, device integrity, surveillance

 G—PHYSICS
 G07—CHECKINGDEVICES
 G07F—COINFREED OR LIKE APPARATUS
 G07F7/00—Mechanisms actuated by objects other than coins to free or to actuate vending, hiring, coin or paper currency dispensing or refunding apparatus
 G07F7/08—Mechanisms actuated by objects other than coins to free or to actuate vending, hiring, coin or paper currency dispensing or refunding apparatus by coded identity card or credit card or other personal identification means
 G07F7/10—Mechanisms actuated by objects other than coins to free or to actuate vending, hiring, coin or paper currency dispensing or refunding apparatus by coded identity card or credit card or other personal identification means together with a coded signal, e.g. in the form of personal identification information, like personal identification number [PIN] or biometric data
 G07F7/1016—Devices or methods for securing the PIN and other transactiondata, e.g. by encryption

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
 H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
 H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
 H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
 H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communication including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, nonrepudiation, key authentication or verification of credentials
 H04L9/321—Cryptographic mechanisms or cryptographic arrangements for secret or secure communication including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, nonrepudiation, key authentication or verification of credentials involving a third party or a trusted authority
Abstract
Description
The present invention relates generally to cryptosystems and more particularly to methods for enabling a given entity to monitor communications of users suspected of unlawful activities while protecting the privacy of lawabiding users.
In a singlekey cryptosystem a common secret key is used both to encrypt and decrypt messages. Thus only two parties who have safely exchanged such a key beforehand can use these systems for private communication. This severely limits the applicability of singlekey systems.
In a doublekey cryptosystem, the process of encrypting and decrypting is instead governed by different keys. In essence, one comes up with a pair of matching encryption and decryption keys. What is encrypted using a given encryption key can only be decrypted using the corresponding decryption key. Moreover, the encryption key does not "betray" its matching decryption key. That is, knowledge of the encryption key does not help to find out the value of the decryption key. The advantage of doublekey systems is that they can allow two parties who have never safely exchanged any key to privately communicate over an insecure communication line (i.e., one that may be tapped by an adversary). They do this by executing an online, private communication protocol.
In particular, Party A alerts Party B that he wants to talk to him privately. Party B then computes a pair of matching encryption and decryption keys (E_{B}, D_{B}). B then sends A key E_{B}. Party A now encrypts his message m, obtaining the ciphertext c=E_{B} (m), and sends c to B over the insecure channel. B decrypts the ciphertext by computing m=D_{B} (c). If an adversary eavesdrops all communication between A and B, he will then hear both B's encryption key, E_{B}, and A's ciphertext, c. However, since the adversary does not know B's decryption key, D_{B}, he cannot compute m from c.
The utility of the above protocol is still quite limited since it suffers from two drawbacks. First, for A to send a private message to B it is necessary also that B send a message to A, at least the first time. In some situations this is a real disadvantage. Moreover, A has no guarantee (since the line is insecure anyway) that the received string D_{B} really is B's encryption key. Indeed, it may be a key sent by an adversary, who will then understand the subsequent, encrypted transmission.
An ordinary publickey cryptosystem ("PKC") solves both difficulties and greatly facilitates communication. Such a system essentially consists of using a doublekey system in conjunction with a proper key management center. Each user X comes up with a pair of matching encryption and decryption keys (E_{X}, D_{X}) of a doublekey system. He keeps D_{X} for himself and gives E_{X} to the key management center. The center is responsible for updating and publicizing a directory of correct public keys for each user, that is, a correct list of entries of the type (X, E_{X}). For instance, upon receiving the request from X to have E_{X} as his public key, the center properly checks X's identity, and (digitally) signs the pair (X, E_{X}), together with the current date if every encryption key has a limited validity. The center publicizes E_{X} by distributing the signed information to all users in the system. This way, without any interaction, users can send each other private messages via their public, encryption key that they can look up in the directory published by the center. The identity problem is also solved, since the center's signature of the pair (X, E_{X}) guarantees that the pair has been distributed by the center, which has already checked X's identity.
The convenience of a PKC depends on the key management center. Because setting up such a center on a grand scale requires a great deal of effort, the precise protocols to be followed must be properly chosen. Moreover, publickey cryptography has certain disadvantages. A main disadvantage is that any such system can be abused, for example, by terrorists and criminal organizations who can use their own PKC (without knowledge of the authorities) and thus conduct their illegal business with great secrecy and yet with extreme convenience.
It would therefore be desirable to prevent any abuse of a public key cryptosystem while maintaining all of its lawful advantages.
It is an object of the present invention to provide methods for enabling a given entity, such as the government, to monitor communications of users suspected of unlawful activities while at the same time protecting the privacy of lawabiding users.
It is a further object of the invention to provide such methods using either public or private key cryptosystems.
It is a still further object of the invention to provide socalled "fair" cryptosystems wherein an entity can monitor communications of suspect users only upon predetermined occurrences, e.g., the obtaining of a court order.
It is another object to describe methods of constructing fair cryptosystems for use in such communications techniques.
In one embodiment, these and other objects of the invention are provided in a method, using a publickey cryptosystem, for enabling a predetermined entity to monitor communications of users suspected of unlawful activities while protecting the privacy of lawabiding users, wherein each user is assigned a pair of matching secret and public keys. According to the method, each user's secret key is broken into shares. Then, each user provides a plurality of "trustees" pieces of information. The pieces of information provided to each trustee enable that trustee to verify that such information includes a "share" of a secret key of some given public key. Further, each trustee can verify that the pieces of information provided include a share of the secret key without interaction with any other trustee or by sending messages to the user. Upon a predetermined request or condition, e.g., a court order authorizing the entity to monitor the communications of a user suspected of unlawful activity, the trustees reveal to the entity the shares of the secret key of such user to enable the entity to reconstruct the secret key and monitor the suspect user's communications.
The method can be carried out whether or not the identity of the suspect user is known to the trustees, and even if less than all of the shares of the suspect user's secret key are required to be revealed in order to reconstruct the secret key. The method is robust enough to be effective if a given minority of trustees have been compromised and cannot be trusted to cooperate with the entity. In addition, the suspect user's activities are characterized as unlawful if the entity, after reconstructing or having tried to reconstruct the secret key, is still unable to monitor the suspect user's communications.
According to another more generalized aspect of the invention, a method is described for using a publickey cryptosystem for enabling a predetermined entity to monitor communications of users suspected of unlawful activities while protecting the privacy of lawabiding users. The method comprises the step of "verifiably secret sharing" each user's secret key with a plurality of trustees so that each trustee can verify that the share received is part of a secret key of some public key.
The foregoing has outlined some of the more pertinent objects of the present invention. These objects should be construed to be merely illustrative of some of the more prominent features and applications of the invention. Many other beneficial results can be attained by applying the disclosed invention in a different manner or modifying the invention as will be described. Accordingly, other objects and a fuller understanding of the invention may be had by referring to the following Detailed Description of the preferred embodiment.
For a more complete understanding of the present invention and the advantages thereof, reference should be made to the following Detailed Description taken in connection with the accompanying drawings in which:
FIG. 1 is a simplified diagram of a communications system over which a government entity desires to monitor communications of users suspected of unlawful activities;
FIG. 2 is a block diagram of a preferred hierarchy of entities that may use the methods of the present invention to monitor communications of users suspected of unlawful activities.
FIG. 1 represents a simple communications system 10 comprising a telephone network connected between a calling station 12 and a called station 14. One or more local central offices or telephone switches 16 connect telephone signals over the network in a wellknown fashion. Referring now also to FIG. 2, assume that a government entity, such as local law enforcement agency 18, desires to monitor communications to and/or from calling station 12 because the user of such calling station is suspected of unlawful activity. Assume further that the user of the calling station 12 communicates using a PKC. Following accepted legal practices, the agency 18 obtains a court order from court 20 to privately monitor the line 15. According to the present invention, the agency's is able to monitor the line 15 while at the same time the privacy rights of other lawabiding users of the network are maintained. This is accomplished as will be described by requiring that each user "secret share" the user's secret key (of the PKC) with a plurality of trustees 22a . . . 22n.
According to the invention, a "fair" PKC is a special type of publickey cryptosystem. Every user can still choose his own keys and keep secret his private one; nonetheless, a special agreedupon party (e.g., the government), and solely this party, under the proper circumstances envisaged by the law (e.g., a court order), and solely under these circumstances, is authorized to monitor all messages sent to a specific user. A fair PKC improves the security of the existing communication systems (e.g., the telephone service 10) while remaining within the constraints of accepted legal procedures.
In one embodiment, fair PKC's are constructed in the following general way. Referring now to FIGS. 12, it is assumed that there are five (5) trustees 22a . . . 22e and that the government desires, upon receiving a court order, to monitor the telephone communications to or from the calling station 12. Although the abovedescription is specific, it should be appreciated that users of the communications system and trustees may be people or computing devices. It is preferable that the trustees are chosen to be trustworthy. For instance, they may be judges (or computers controlled by them), or computers specially set up for this purpose. The trustees, together with the individual users, play a crucial role in deciding which encryption keys will be published in the system.
Each user independently chooses his own public and secret keys according to a given doublekey system (for instance, the public key consists of the product of two primes, and the secret key one of these two primes). Since the user has chosen both of his keys, he can be sure of their "quality" and of the privacy of his decryption key. He then breaks his secret decryption key into five special "pieces" (i.e., he computes from his decryption key 5 special strings/numbers) possessing the following properties:
(1) The private key can be reconstructed given knowledge of all five, special pieces;
(2) The private key cannot be guessed at all if one only knows (any) 4, or less, of the special pieces;
(3) For i1, . . . 5, the ith special piece can be individually verified to be correct.
Given all 5 special pieces or "shares", one can verify that they are correct by checking that they indeed yield the private decryption key. According to one feature of the invention, property (3) insures that each special piece can be verified to be correct (i.e., that together with the other 4 special pieces it yields the private key) individually, i.e., without knowing the secret key at all and without knowing the value of any of the other special pieces.
The user then privately (e.g., in encrypted form) gives trustee 22i his own public key and the ith piece of its associated secret key. Each trustee 22 individually inspects his received piece, and, if it is correct, approves the public key (e.g. signs it) and safely stores the piece relative to it. These approvals are given to a key management center 24, either directly by the trustees, or (possibly in a single message) by the individual user who collects them from the trustees. The center 24, which may or may not coincide with the government, itself approves (e.g., signs) any public key that is approved by all trustees. These centerapproved keys are the public keys of the fair PKC and they are distributed and used for private communication as in an ordinary PKC.
Because the special pieces of each decryption key are privately given to the trustees, an adversary who taps the communication line of two users possesses the same information as in the underlying, ordinary PKC. Thus if the underlying PKC is secure, so is the fair PKC. Moreover, even if the adversary were one of the trustees himself, or even a cooperating collection of any four out of five of the trustees, property (2) insures that the adversary would still have the same information as in the ordinary PKC. Because the possibility that an adversary corrupts five out of five judges is absolutely remote, the security of the resulting fair PKC is the same as in the underlying PKC.
When presented with a court order, for example, the trustees 22 reveal to the government 20 the pieces of a given decryption key in their possession. According to the invention, the trustees may or may not be aware of the identity of the user who possesses the given decryption key. This provides additional security against "compromised" trustees who might otherwise tip off the suspect user once a request for that user's decryption key share is received by the trustee.
Upon receiving the shares, the government reconstructs the given decryption key. By property (3), each trustee previously verified whether he was given a correct special piece of a given decryption key. Moreover, every public key was authorized by the key management center 24 only if it was approved by all trustees 22. Thus, the government is guaranteed that, in case of a court order, it will be given all special pieces of any decryption key. By property (1), this is a guarantee that the government will be able to reconstruct any given decryption key if necessary to monitor communications over the network.
Several types of fair PKC's are now described in more detail.
The Diffie and Hellman publickey cryptosystem is known and is readily transformed into a fair PKC by the present invention. In the Diffie and Hellman scheme, each pair of users X and Y succeeds, without any interaction, in agreeing upon a common, secret key S_{xy} to be used as a conventional singlekey cryptosystem. In the ordinary DiffieHellman PKC, there are a prime p and a generator (or highorder element) g common to all users. User X secretly selects a random integer Sx in the interval 1, p1! as his private key and publicly announces the integer Px=g^{Sx} mod p as his public key. Another user, Y, will similarly select Sy as his private key and announce Py=g^{Sy} mod p as his public key. The value of this key is determined as S_{xy} =g^{SxSy} mod p. User X computes Sxy by raising Y's public key to his private key mod pX, and user Y by raising X's public key to his secret key mod p. In fact:
(g.sup.Sx).sup.Sy =g.sup.SxSy =Sxy=g.sup.SySx =(g.sup.Sy).sup.Sx mod p.
While it is easy, given g, p and x, to compute y=g^{x} mod p, no efficient algorithm is known for computing, given y and p, x such that g^{x} =y mod p when g has high enough order. This is the discrete logarithm problem. This problem has been used as the basis of security in many cryptosystems. The Diffie and Hellman's PKC is transformed into a fair one in the following manner.
Each user X randomly chooses 5 integers Sx1, . . . Sx5 in the interval 1, p1! and lets Sx be their sum mod p. It should be understood that all following operations are modulo p. User X then computes the numbers:
t1=g.sup.Sx 1. . . , t5=g.sup.Sx5 and Px=g.sup.Sx.
Px will be User X's public key and Sx his private key. The ti's will be referred to as the public pieces of Px, and the Sxi's as the private pieces. It should be noted that the product of the public pieces equals the public key Px. In fact:
t1. . . t5=g.sup.Sx1. . . g.sup.Sx5 =g.sup.(Sx1+. . .+Sx5) =g.sup.Sx.
Let T1, . . . T5 be the five trustees. User X now gives Px, the public pieces and Sx1 to trustee T1, Px, the public pieces and Sx2 to trustee T2, and so on. Piece Sxi is privately given to trustee Ti. Upon receiving public and private pieces ti and Sxi, trustee Ti verifies whether g^{Sxi} =Ti. If so, the trustee stores the pair (Px, Sxi), signs the sequence (Px,t1,t2,t3,t4,t5) and gives the signed sequence to the key management center 24 (or to user X, who will then give all of the signed public pieces at once to the key management center). Upon receiving all the signed sequences relative to a given public key Px, the key management center verifies that these sequences contain the same subsequence of public pieces t1 . . . t5 and that the product of the public pieces indeed equals Px. If so, center 24 approves Px as a public key and distributes it as in the original scheme (e.g., signs it and gives it to user X). The encryption and decryption instructions for any pair of users X and Y are exactly as in the Diffie and Hellman scheme (i.e., with common, secret key Sxy).
This way of proceeding matches the previouslydescribed way of constructing a fair PKC. A still fair version of the DiffieHellman scheme can be obtained in a simpler manner by having the user give to each trustee Ti just the public piece ti and its corresponding private piece Sxi, and have the user give the key management center the public key Px. The center will approve Px only if it receives all public pieces, signed by the proper trustee, and the product of these public pieces equals Px. In this way, trustee Ti can verify that Sxi is the discrete logarithm of public piece ti. Such trustee cannot quite verify that Sxi is a legitimate share of Px since the trustee has not seen Px or the other public pieces. Nonetheless, the result is a fair PKC based on the DiffieHellman scheme because properties (1)(3) described above are still satisfied.
Either one of the abovedescribed fair PKC has the same degree of privacy of communication offered by the underlying DiffieHellman scheme. In fact, the validation of a public key does not compromise the corresponding private key. Each trustee Ti receives, as a special piece, the discrete logarithm, Sxi, of a random number, ti. This information is clearly irrelevant for computing the discrete logarithm of Px. The same is actually true for any 4 of the trustees taken together, since any four special pieces are independent of the private decryption key Sx. Also the key management center does not possess any information relevant to the private key; i.e., the discrete logarithm of Px. All the center has are the public pieces respectively signed by the trustees. The public pieces simply are 5 random numbers whose product is Px. This type of information is irrelevant for computing the discrete logarithm of Px; in fact, any one could choose four integers at random and setting the fifth to be Px divided by the product of the first four. The result would be integral because division is modulo p. As for a trustee's signature, this just represents the promise that someone else has a secret piece.
Even the information in the hands of the center together with any four of the trustees is irrelevant for computing the private key Sx. Thus, not only is the user guaranteed that the validation procedure will not betray his private key, but he also knows that this procedure has been properly followed because it is he himself that computes his own keys and the pieces of his private one.
Second, if the key management center validates the public key Px, then its private key is guaranteed to be reconstructable by the government in case of a court order. In fact, the center receives all 5 public pieces of Px, each signed by the proper trustee. These signatures testify that trustee Ti possesses the discrete logarithm of public piece ti. Since the center verifies that the product of the public pieces equals Px, it also knows that the sum of the secret pieces in storage with the trustees equals the discrete logarithm of Px; i.e, user X's private key. Thus the center knows that, if a court order were issued requesting the private key of X, the government is guaranteed to obtain the needed private key by summing the values received by the trustees.
The following describes a fair PKC based on the known RSA function. In the ordinary RSA PKC, the public key consists of an integer N product of two primes and one exponent e (relatively prime with f(N), where F is Euler's quotient function). No matter what the exponent, the private key may always be chosen to be N's factorization. By way of brief background, the RSA scheme has certain characteristics that derive from aspects of number theory:
Fact 1. Let Z_{N} * denote the multiplicative group of the integers between 1 and N and relatively prime with N. If N is the product of two primes N=pq (or two prime powers: N=p^{a} p^{b}), then
(1) a number s in Z_{N} * is a square mod N if and only if it has four distinct squareroots mod N: x, x mod N, y, and y mod N (i.e., x^{2} =y^{2} =s mod N). Moreover, from the greatest common divisor of +x+y and N, one easily computes the factorization of N. Also;
(2) one in four of the numbers in Z_{N} * is a square mod N.
Fact 2. Among the integers in Z_{N} * is defined a function, the Jacobi symbol, that evaluates easily to either 1 or 1. The Jacobi symbol of x is denoted by (s/N). The Jacobi symbol is multiplicative; i.e., (x/N)(Y/N)=(xy/N). If N is the product of two primes N=pq (or two prime powers: N=p^{a} p^{b}), the p and 1 are congruent to 3 mod 4. Then, if +x and +y are the four square roots of a square mod N (s/N)=(x/N)=+1 and (y/N)=(y/N)=1. Thus, because of Fact 1, if one is given a Jacobi symbol 1 root and a Jacobi symbol 1 root of any square, he can easily factor N.
With this background, the following describes how the RSA cryptosystem can be made fair in a simple way. For simplicity again assume there are five trustees and that all of them must collaborate to reconstruct a secret key, while no four of them can even predict it. The RSA cryptosystem is easily converted into a fair PKC by efficiently sharing with the trustee's N's factorization. In particular, the trustees are privately provided information that, perhaps together with other given common information, enables one to reconstruct two (or more) square roots x and y (x different from ±y mod N) of a common square mod N. The given common information may be the 1 Jacobi symbol root of X^{2}, which is equal to y.
A user chooses P and Q primes congruent to 3 mod 4, as his private key and N=PQ as his public key. Then he chooses 5 Jacobi 1 integers X_{1}, X_{2}, X_{3}, X_{4} and X_{5} (preferably at random) in Z_{N} * and computes their product, X, and X_{i} ^{2} mod N for all i=1, . . . , 5. The product of the last 5 squares, Z, is itself a square. One square root of Z mod N is X, which has Jacobi symbol equal to 1 (since the Jacobi symbol is multiplicative). The user computes Y, one of the Jacobi 1 roots mod N. X_{1}, . . . X_{5} will be the public pieces of public key N and the X_{i} 's the private pieces. The user gives trustee Ti private piece X_{i} (and possibly the corresponding public piece, all other public pieces and Px, depending on whether it is desired that the verification of the shares so as to satisfy properties (1)(3) is performed by both trustees and the center, or the trustees alone). Trustee Ti squares Xi mod N, gives the key management center his signature of X_{i} ^{2}, and stores X_{i}.
The center first checks that (1/N)=1, i.e., for all x: (x/N)=(x/N). This is partial evidence that N is of the right form. Upon receiving the valid signature of the public pieces of N and the Jacobi 1 value Y from the user, the center checks whether mod N the square of Y equals the product of the five public pieces. If so, it checks, possibly with the help of the user, that N is the product of two prime powers. If so, the center approves N.
The reasoning behind the scheme is as follows. The trustees' signatures of the X_{i} ^{2} 's (mod N) guarantee the center that every trustee Ti has stored a Jacobi symbol 1 root of X_{i} ^{2} mod N. Thus, in case of a court order, all these Jacobi symbol 1 roots can be retrieved. Their product, mod N, will also have Jacobi symbol 1, since this function is multiplicative, and will be a root of X^{2} mod N. But since the center has verified that Y^{2} =X^{2} mod N, one would have two roots X and Y of a common square mod N. Moreover, Y is different from X since it has different Jacobi symbol, and Y is also different from x, since (x/N)=(s/N) because (a) (1/N) has been checked to be 1 and (b) the Jacobi symbol is multiplicative. Possession of such square roots, by Facts 1 and 2, is equivalent to having the factorization of N, provided that N is product of at most two prime powers. This last property has also been checked by the center before it has approved N.
Verification that N is the product of at most two prime powers can be performed in various ways. For instance, the center and user can engage in a zeroknowledge proof of this fact. Alternatively, the user may provide the center with the square root mod N for roughly 1/4 of the integers in a prescribed and random enough sequence of integers. For instance, such a sequence could be determined by oneway hashing N to a short seed and then expanding it into a longer sequence using a psuedorandom generator. If a dishonest user has chosen his N to be the product of three or more prime powers, then it would be foolish for him to hope that roughly 1/4of the integers in the sequence are squares mod N. In fact, for his choice of N, at most 1/8 of the integers have square roots mod N.
The above schemes can be modified in many ways. For instance, the proof that N is product of two prime powers can be done by the trustees (in collaboration with the user), who then inform the center of their findings. Also, the scheme can be modified so that the cooperation of the majority of the trustees is sufficient for reconstructing the secret key, while any minority cannot gain any information about the secret key. Also, as with all fair cryptosystems, one can arrange that when the government asks a trustee for his piece of the secret key of a user, the trustee does not learn about the identity of the user. The variations are discussed in more detail below.
In particular, the schemes described above are robust in the sense that some trustees, accidentally or maliciously, may reveal the shares in their possession without compromising the security of the system. However, these schemes rely on the fact that the trustees will collaborate during the reconstruction stage. In fact, it was insisted that all of the shares should be needed for recovering a secret key. This requirement may be disadvantageous, either because some trustees may reveal to be untrustworthy and refuse to give the government the key in their possession, or because, despite all file backups, the trustee may have genuinely lost the information in its possession. Whatever the reason, in this circumstance the reconstruction of a secret key will be prevented. This problem is also solved by the present invention.
By way of background, "secret sharing" (with parameters n,T,t) is a prior cryptographic scheme consisting of two phases: in phase one a secret value chosen by a distinguished person, the dealer, is put in safe storage with n people or computers, the trustees, by giving each one of them a piece of information. In phase two, when the trustees pool together the information in their possession, the secret is recovered. Secret sharing has a major disadvantageit presupposes that the dealer gives the trustees correct shares (pieces of information) about his secret value. "Verifiable Secret Sharing" (VSS) solves this "honesty" problem. In a VSS scheme, each trustee can verify that the share given to him is genuine without knowing at all the shares of other trustees of the secret itself. Specifically, the trustee can verify that, if T verified shares are revealed, the original secret will be reconstructed, no matter what the dealer or dishonest trustees might do.
The abovedescribed fair PKC schemes are based on a properly structured, noninteractive verifiable secret sharing scheme with parameters n=5, T=5 and t=4. According to the present invention, it may be desirable to have different values of these parameters, e.g., n=5, T=3 and t=2. In such case, any majority of the trustees can recover a secret key, while no minority of trustees can predict it all. This is achieved as follows (and be simply generalized to any desired values of n, T and t in which T>t).
After choosing a secret key Sx in 1, p1!, user X computes his public key Px=g^{Sx} mod p (with all computations below being mod p). User X now considers all triplets of numbers between 1 and 5: (1,2,3), (2,3,4) etc. For each triplet (a,b,c), user X randomly chooses three integers S1abc, . . . S3abc in the interval 1, p1! so that their sum mod p equals Sx. Then he computes the numbers:
t1abc=g.sup.S1abc, t2abc=g.sup.S2abc, t3abc=g.sup.S3abc
The tiabc's will be referred to as public pieces of Px, and the Siabc's as private pieces. Again, the product of the public pieces equals the public key Px. In fact,
t1abct2abct3abc=g.sup.S1abc ·g.sup.S 2abc·gS3abc=g (.sup.S1abc ++.sup.S3abc)=g.sup.Sx =Px
User X then gives trustee Ta t1abc and S1abc, trustee Tb t2abc and S2abc, and trustee Tc t3abc and S3abc, always specifying the triplet in question. Upon receiving these quantities, trustee Ta (all other trustees do something similar) verifies that t1abc=g^{S1abc}, signs the value (Px, t1abc, (a,b,c)) and gives the signature to the management center.
The key management center, for each triple (a,b,c), retrieves the values t1abc, t2abc and t3abc from the signed information received from trustees, Ta, Tb and Tc. If the product of these three values equals Px and the signatures are valid, the center approves Px as a public key.
The reason the scheme works, assuming that at most 2 trustees are untrustworthy, is that all secret pieces of a triple are needed for computing (or predicting) a secret key. Thus no secret key in the system can be retrieved by any 2 trustees. On the other hand, after a court order at least three trustees reveal all the secret pieces in their possession about a given public key. The government then has all the necessary secret pieces for at least one triple, and thus can compute easily the desired secret key.
Alternatively, each trustee is replaced by a group of new trustees. For instance, instead of a single trustee Ta, there may be three trustees: Ta1, Ta2 and Ta3. Each of these trustees will receive and check the same share of trustee Ta. In this way it is very unlikely that all three trustees will refuse to surrender their copy of the first share.
After having insured that a few potentially malicious trustees cannot prevent reconstruction of the key, there are still further security issues to address, namely, a trusteerequested by a court order to surrender his share of a given secret keymay alert the owner of that key that his communications are about to be monitored. This problem is also solved by the invention. A simple solution arises if the cryptosystem used by the trustees possess certain algebraic properties. This is illustrated for the DiffieHellman case, though the same result occurs for the RSA scheme. In the following discussion, for simplicity it is assumed that all trustees collaborate in the reconstruction of the secret key.
Assume that all trustees use deterministic RSA for receiving private messages. Thus, let Ni be the public RSA modulus of trustee Ti and ei his encryption exponent (i.e., to send Ti a message m in encrypted form, one would send m^{ei} mod Ni).
User U prepares his public and secret key, respectively Px and Sx (thus Px=g^{Sx} mod p), as well as his public and secret pieces of the secret key, respectively ti and Sxi's (thus Px=t1, t2 . . . t5 mod p and ti=g^{Sxi} mod p for all i). Then, the user gives to the key management center Px, all of the ti's and the n values Ui=(Sxi)^{3} mod Ni; i.e., he encrypts the ith share with the public key of trustee Ti. Since the center does not know the factorization of the Ni's, this is not useful information to predict Sx, nor can the center verify that the decryption of the n ciphertexts are proper shares of Sx. For this, the center will seek the cooperation of the n trustees, but without informing them of the identity of the user as will be described.
The center stores the values tj's and Uj's relative to user U and then forwards Ui and ti to trustee Ti. If every trustee Ti verified that the decryption of Ui is a proper private piece relative to ti, the center approves Px.
Assume now that the judicial authority decides to monitor user U's communications. To lawfully reconstruct secret key Sx without leaking to a trustee the identity of the suspected user U, a judge (or another authorized representative) randomly selects a number Ri mod Ni and computes yi=Ri ^{ei} mod Ni. Then, he sends trustee Ti the value zi=Uiyi mod Ni, asking with a court order to compute and send back wi, the eith root of zi mod Ni. Since zi is a random number mod Ni, no matter what the value of Ui is, trustee Ti cannot guess the identity of the user U in question. Moreover, since zi is the product of Ui and yi mod Ni the eith root of zi is the product mod Ni of the eith root of Ui (i.e., Sxi) and the eith root of yi (i.e., Ri). Thus, upon receiving wi, the judge divides it by yi mod Ni, thereby computing the desired Sxi. The product of these Sxi's equals the desired Sx.
In other variations of the invention, in case of a court order, the government is only authorized to understand the messages concerning a given user for a limited amount of time. The collective approval of all trustees may stand for the government approval. Also, trustees need not store their piece of the private key. The encryption of this piecein the trustee's public key and signed by the trusteecan be made part of the user's public key. In this way, the public key carries the proof of its own authenticity and verification. In the latter case it may be advantageous to break the trustee's private keys into pieces.
If the user is an electronic device, such as an integrated circuit chip, the basic process of key selection and publickey validation can be done before the device leaves the factory. In this case, it may be advantageous that a "copy" of the trustee can be maintained within the factory. A copy of a trustee is a physically secure chipone whose data cannot be readcontaining a copy of the trustee's decryption key. The trustee (i.e., the party capable of giving the piece of a private key under a court order) need not necessarily coincide with this device.
In another variation, it may be arranged that the trustees each a have piece of the government private key, and that each user's private key is encrypted with the public key of the government.
While the use of a fair PKC in a telecommunications network (and under the authority of the government) has been described, such description is not meant to be taken by way of limitation. A fair PKC can be used in private organizations as well. For example, in a large organization where there is a need for privacy, assume there is an established "superior" but not all employees can be trusted since there are too many of them. The need for privacy requires the use of encryption. Because not all employees can be trusted, using a single encryption key for the whole company is unacceptable, as is using a number of singlekey cryptosystems (since this would generate enormous keydistribution problems). Having each employee use his own doublekey system is also dangerous, since he or she might conspire against the company with great secrecy, impunity and convenience.
In such application of a fair PKC, numerous advantages are obtained. First, each employee is in charge of choosing his own keys. While enjoying the advantages of a more distributed procedure, the organization retains absolute control because the superior is guaranteed to be able to decrypt every employee's communications when necessary. There is no need to change keys when the superior changes because the trustees need not be changed. The trustees' storage places need less surveillance, since only compromising all of them will give an adversary any advantage.
For making fair a private key cryptosystem, but also for a PKC, it is desirable that each trustee first deposits an encrypted version or otherwise committed version of his share, so that, when he is asked to reveal what his share was, he cannot change his mind about its value. Also, it is desirable that the user gives his shares to the trustees signed; such signatures can be relative to a different public key (if they are digital signatures) or to the same new public key if the new key can be used for signing as well. In this way, the share revealed by the trustee clearly proves that it way originated. Better still, the user may sign (with the trustee's key) the encryption of the share given to a trustee, and the signature can be revealed together with the share. This approach insures that one can both be certain that what was revealed was a share approved by the user and also that the trustees and the user cannot collaborate later on in changing its value.
It should be appreciated by those skilled in the art that the specific embodiments disclosed above may be readily utilized as a basis for modifying or designing other techniques and processes for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims.
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Cited By (17)
Publication number  Priority date  Publication date  Assignee  Title 

WO2000074298A1 (en) *  19990526  20001207  Ascom Hasler Mailing Systems, Inc.  Technique for split knowledge backup and recovery of a cryptographic key 
US20020165824A1 (en) *  19951002  20021107  Silvio Micali  Scalable certificate validation and simplified PKI management 
US20040237031A1 (en) *  20030513  20041125  Silvio Micali  Efficient and secure data currentness systems 
US20050010783A1 (en) *  19951024  20050113  Phil Libin  Access control 
US20050154918A1 (en) *  20031119  20050714  David Engberg  Distributed delegated path discovery and validation 
US6973571B2 (en)  20010703  20051206  Bank Of America Corporation  System, apparatus, and method for performing cryptographic validity services 
US7205882B2 (en)  20041110  20070417  Corestreet, Ltd.  Actuating a security system using a wireless device 
US7337315B2 (en)  19951002  20080226  Corestreet, Ltd.  Efficient certificate revocation 
US7353396B2 (en)  19951002  20080401  Corestreet, Ltd.  Physical access control 
US7529928B2 (en)  19951024  20090505  Corestreet, Ltd.  Certificate revocation system 
US7600129B2 (en)  19951002  20091006  Corestreet, Ltd.  Controlling access using additional data 
US7698557B2 (en)  20031222  20100413  Guardtime As  System and method for generating a digital certificate 
US7716486B2 (en)  19951002  20100511  Corestreet, Ltd.  Controlling group access to doors 
US7822989B2 (en)  19951002  20101026  Corestreet, Ltd.  Controlling access to an area 
US7966487B2 (en)  20040109  20110621  Corestreet, Ltd.  Communicationefficient real time credentials for OCSP and distributed OCSP 
US8015597B2 (en)  19951002  20110906  Corestreet, Ltd.  Disseminating additional data used for controlling access 
US8261319B2 (en)  19951024  20120904  Corestreet, Ltd.  Logging access attempts to an area 
Families Citing this family (96)
Publication number  Priority date  Publication date  Assignee  Title 

US6272632B1 (en)  19950221  20010807  Network Associates, Inc.  System and method for controlling access to a user secret using a key recovery field 
US6418424B1 (en)  19911223  20020709  Steven M. Hoffberg  Ergonomic manmachine interface incorporating adaptive pattern recognition based control system 
US8352400B2 (en)  19911223  20130108  Hoffberg Steven M  Adaptive pattern recognition based controller apparatus and method and humanfactored interface therefore 
US7904187B2 (en)  19990201  20110308  Hoffberg Steven M  Internet appliance system and method 
US5903454A (en)  19911223  19990511  Hoffberg; Linda Irene  Humanfactored interface corporating adaptive pattern recognition based controller apparatus 
US5315658B1 (en) *  19920420  19950912  Silvio Micali  Fair cryptosystems and methods of use 
USRE36918E (en) *  19920420  20001017  Certco Llc  Fair cryptosystems and methods of use 
WO1995005712A3 (en) *  19930813  19950427  Frank Thomson Leighton  Secret key exchange 
US5825880A (en)  19940113  19981020  Sudia; Frank W.  Multistep digital signature method and system 
CN1138927A (en) *  19940113  19961225  银行家信托公司  Cryptographic system and method with key escrow feature 
US20020013898A1 (en) *  19970604  20020131  Sudia Frank W.  Method and apparatus for roaming use of cryptographic values 
US5537475A (en) *  19940201  19960716  Micali; Silvio  Efficient digital signature algorithm and use thereof technical field 
US5712913A (en) *  19940208  19980127  Digicash Incorporated  Limitedtraceability systems 
US5481613A (en) *  19940415  19960102  Northern Telecom Limited  Computer network cryptographic key distribution system 
US5748735A (en) *  19940718  19980505  Bell Atlantic Network Services, Inc.  Securing Email communications and encrypted file storage using yaksha split private key asymmetric cryptography 
US5838792A (en) *  19940718  19981117  Bell Atlantic Network Services, Inc.  Computer system for centralized session key distribution, privacy enhanced messaging and information distribution using a split private key public cryptosystem 
US5905799A (en) *  19940720  19990518  Bell Atlantic Network Services, Inc.  Programmed computer for identity verification, forming joint signatures and session key agreement in an RSA public cryptosystem 
US5588061A (en) *  19940720  19961224  Bell Atlantic Network Services, Inc.  System and method for identity verification, forming joint signatures and session key agreement in an RSA public cryptosystem 
DE69534192D1 (en) *  19940729  20050616  Canon Kk  Method for sharing a secret information, to generate a digital signature and for performing authentication in a communication system having a plurality of information processing devices and communication system for use of this method 
US5557346A (en) *  19940811  19960917  Trusted Information Systems, Inc.  System and method for key escrow encryption 
US5557765A (en) *  19940811  19960917  Trusted Information Systems, Inc.  System and method for data recovery 
WO1996005674A1 (en) *  19940812  19960222  Frank Thomson Leighton  Failsafe key escrow system 
US5499296A (en) *  19940822  19960312  Micali; Silvio  Natural input encryption and method of use 
US5737419A (en) *  19941109  19980407  Bell Atlantic Network Services, Inc.  Computer system for securing communications using split private key asymmetric cryptography 
US6237096B1 (en)  19950117  20010522  Eoriginal Inc.  System and method for electronic transmission storage and retrieval of authenticated documents 
US7162635B2 (en) *  19950117  20070109  Eoriginal, Inc.  System and method for electronic transmission, storage, and retrieval of authenticated electronic original documents 
US5748738A (en) *  19950117  19980505  Document Authentication Systems, Inc.  System and method for electronic transmission, storage and retrieval of authenticated documents 
US5615268A (en) *  19950117  19970325  Document Authentication Systems, Inc.  System and method for electronic transmission storage and retrieval of authenticated documents 
US7743248B2 (en) *  19950117  20100622  Eoriginal, Inc.  System and method for a remote access service enabling trust and interoperability when retrieving certificate status from multiple certification authority reporting components 
US5564106A (en) *  19950309  19961008  Motorola, Inc.  Method for providing blind access to an encryption key 
US5553145A (en) *  19950321  19960903  Micali; Silvia  Simultaneous electronic transactions with visible trusted parties 
US6134326A (en) *  19961118  20001017  Bankers Trust Corporation  Simultaneous electronic transactions 
US6141750A (en) *  19950321  20001031  Micali; Silvio  Simultaneous electronic transactions with subscriber verification 
JP2000515649A (en) *  19960807  20001121  バンカーズ・トラスト・コーポレーション  Concurrency electronic transaction by a trusted party can be seen 
EP0815671B1 (en) *  19950321  20051221  Silvio Micali  Simultaneous electronic transactions 
US6137884A (en) *  19950321  20001024  Bankers Trust Corporation  Simultaneous electronic transactions with visible trusted parties 
EP0738058A2 (en) *  19950405  19961016  Mordhay Barkan  Method and apparatus for the secure distribution of encryption keys 
DE69638307D1 (en) *  19950605  20110127  Cqrcert Llc  Method and device for digital signature in several steps 
US5978053A (en) *  19950707  19991102  New Mexico State University Technology Transfer Corporation  Characterization of collimation and beam alignment 
US5684545A (en) *  19950707  19971104  New Mexico State University Technology Transfer Corp.  Adaptive optics wave measurement and correction system 
US5631961A (en) *  19950915  19970520  The United States Of America As Represented By The Director Of The National Security Agency  Device for and method of cryptography that allows third party access 
US6026163A (en) *  19951213  20000215  Micali; Silvio  Distributed splitkey cryptosystem and applications 
US5764772A (en) *  19951215  19980609  Lotus Development Coporation  Differential work factor cryptography method and system 
US5787169A (en) *  19951228  19980728  International Business Machines Corp.  Method and apparatus for controlling access to encrypted data files in a computer system 
US5812670A (en) *  19951228  19980922  Micali; Silvio  Traceable anonymous transactions 
US5615269A (en) *  19960222  19970325  Micali; Silvio  Ideal electronic negotiations 
US5768388A (en) *  19960301  19980616  Goldwasser; Shafi  Time delayed key escrow 
US5666414A (en) *  19960321  19970909  Micali; Silvio  Guaranteed partial keyescrow 
US5815573A (en) *  19960410  19980929  International Business Machines Corporation  Cryptographic key recovery system 
US5903651A (en)  19960514  19990511  Valicert, Inc.  Apparatus and method for demonstrating and confirming the status of a digital certificates and other data 
US6901509B1 (en)  19960514  20050531  Tumbleweed Communications Corp.  Apparatus and method for demonstrating and confirming the status of a digital certificates and other data 
US5638447A (en) *  19960515  19970610  Micali; Silvio  Compact digital signatures 
US5901227A (en) *  19960620  19990504  Novell, Inc.  Method and apparatus for implementing partial and complete optional key escrow 
US5796830A (en) *  19960729  19980818  International Business Machines Corporation  Interoperable cryptographic key recovery system 
US6081597A (en) *  19960819  20000627  Ntru Cryptosystems, Inc.  Public key cryptosystem method and apparatus 
US5937066A (en) *  19961002  19990810  International Business Machines Corporation  Twophase cryptographic key recovery system 
US5960084A (en) *  19961213  19990928  Compaq Computer Corporation  Secure method for enabling/disabling power to a computer system following twopiece user verification 
US6400823B1 (en)  19961213  20020604  Compaq Computer Corporation  Securely generating a computer system password by utilizing an external encryption algorithm 
US5949882A (en) *  19961213  19990907  Compaq Computer Corporation  Method and apparatus for allowing access to secured computer resources by utilzing a password and an external encryption algorithm 
US5887131A (en) *  19961231  19990323  Compaq Computer Corporation  Method for controlling access to a computer system by utilizing an external device containing a hash value representation of a user password 
US5953422A (en) *  19961231  19990914  Compaq Computer Corporation  Secure twopiece user authentication in a computer network 
US6581162B1 (en)  19961231  20030617  Compaq Information Technologies Group, L.P.  Method for securely creating, storing and using encryption keys in a computer system 
US5907618A (en) *  19970103  19990525  International Business Machines Corporation  Method and apparatus for verifiably providing key recovery information in a cryptographic system 
US6260145B1 (en) *  19970214  20010710  Fujitsu Limited  System and method of authentication of digital information 
US5920630A (en) *  19970225  19990706  United States Of America  Method of public key cryptography that includes key escrow 
JP3656688B2 (en) *  19970331  20050608  富士通株式会社  Encrypted data recovery method and a key registration system 
US6335972B1 (en)  19970523  20020101  International Business Machines Corporation  Frameworkbased cryptographic key recovery system 
US6202150B1 (en)  19970528  20010313  Adam Lucas Young  Autoescrowable and autocertifiable cryptosystems 
US6389136B1 (en)  19970528  20020514  Adam Lucas Young  AutoRecoverable and Autocertifiable cryptosystems with RSA or factoring based keys 
US6314190B1 (en)  19970606  20011106  Networks Associates Technology, Inc.  Cryptographic system with methods for usercontrolled message recovery 
US6122742A (en) *  19970618  20000919  Young; Adam Lucas  Autorecoverable and autocertifiable cryptosystem with unescrowed signing keys 
US6058188A (en) *  19970724  20000502  International Business Machines Corporation  Method and apparatus for interoperable validation of key recovery information in a cryptographic system 
US6243466B1 (en)  19970829  20010605  Adam Lucas Young  Autoescrowable and autocertifiable cryptosystems with fast key generation 
US6282295B1 (en)  19971028  20010828  Adam Lucas Young  Autorecoverable and autocertifiable cryptostem using zeroknowledge proofs for key escrow in general exponential ciphers 
US6038317A (en) *  19971224  20000314  Magliveras; Spyros S.  Secret key cryptosystem and method utilizing factorizations of permutation groups of arbitrary order 2l 
FI105987B (en) *  19980113  20001031  Nokia Networks Oy  Transmits short messages and mobile communication system 
WO2000019652A1 (en) *  19981001  20000406  University Of Maryland  Distributed shared key generation and management using fractional keys 
US6535607B1 (en)  19981102  20030318  International Business Machines Corporation  Method and apparatus for providing interoperability between key recovery and nonkey recovery systems 
JP2000165373A (en) *  19981125  20000616  Toshiba Corp  Enciphering device, cryptographic communication system, key restoration system and storage medium 
US6473508B1 (en)  19981222  20021029  Adam Lucas Young  Autorecoverable autocertifiable cryptosystems with unescrowed signatureonly keys 
US6400996B1 (en)  19990201  20020604  Steven M. Hoffberg  Adaptive pattern recognition based control system and method 
US6850252B1 (en) *  19991005  20050201  Steven M. Hoffberg  Intelligent electronic appliance system and method 
US6823070B1 (en)  20000328  20041123  Freescale Semiconductor, Inc.  Method for key escrow in a communication system and apparatus therefor 
US20040073617A1 (en) *  20000619  20040415  Milliken Walter Clark  Hashbased systems and methods for detecting and preventing transmission of unwanted email 
US7181017B1 (en)  20010323  20070220  David Felsher  System and method for secure threeparty communications 
WO2002100022A3 (en) *  20010601  20030605  No Magic Inc  Electronic information and cryptographic key management system 
US7093133B2 (en) *  20011220  20060815  HewlettPackard Development Company, L.P.  Group signature generation system using multiple primes 
US7146009B2 (en) *  20020205  20061205  Surety, Llc  Secure electronic messaging system requiring key retrieval for deriving decryption keys 
US7289629B2 (en) *  20040209  20071030  Microsoft Corporation  Primitives for fast secure hash functions and stream ciphers 
US20080126808A1 (en) *  20060705  20080529  Cms Products, Inc.  Encrypted dataset access by custodians 
EP2078274B1 (en) *  20061102  20150909  NDS Limited  Privacyaware content protection system 
US20100172501A1 (en) *  20090106  20100708  Tian Weicheng  Secure key system 
US20100174653A1 (en) *  20090107  20100708  Tian Weicheng  Secure method and device of financial transaction 
US8856879B2 (en) *  20090514  20141007  Microsoft Corporation  Social authentication for account recovery 
US9124431B2 (en)  20090514  20150901  Microsoft Technology Licensing, Llc  Evidencebased dynamic scoring to limit guesses in knowledgebased authentication 
RU2496239C1 (en) *  20120209  20131020  Государственное казенное образовательное учреждение высшего профессионального образования Академия Федеральной службы охраны Российской Федерации (Академия ФСО России)  Method for steganographic transmission of information through main optical channel and apparatus for implementing said method 
Citations (6)
Publication number  Priority date  Publication date  Assignee  Title 

US4375579A (en) *  19800130  19830301  Wisconsin Alumni Research Foundation  Database encryption and decryption circuit and method using subkeys 
US4933970A (en) *  19880119  19900612  Yeda Research And Development Company Limited  Variants of the fiatshamir identification and signature scheme 
US5005200A (en) *  19880212  19910402  Fischer Addison M  Public key/signature cryptosystem with enhanced digital signature certification 
US5018196A (en) *  19850904  19910521  Hitachi, Ltd.  Method for electronic transaction with digital signature 
US5136643A (en) *  19891013  19920804  Fischer Addison M  Public/key datetime notary facility 
US5150411A (en) *  19901024  19920922  Omnisec  Cryptographic system allowing encrypted communication between users with a secure mutual cipher key determined without user interaction 
Patent Citations (6)
Publication number  Priority date  Publication date  Assignee  Title 

US4375579A (en) *  19800130  19830301  Wisconsin Alumni Research Foundation  Database encryption and decryption circuit and method using subkeys 
US5018196A (en) *  19850904  19910521  Hitachi, Ltd.  Method for electronic transaction with digital signature 
US4933970A (en) *  19880119  19900612  Yeda Research And Development Company Limited  Variants of the fiatshamir identification and signature scheme 
US5005200A (en) *  19880212  19910402  Fischer Addison M  Public key/signature cryptosystem with enhanced digital signature certification 
US5136643A (en) *  19891013  19920804  Fischer Addison M  Public/key datetime notary facility 
US5150411A (en) *  19901024  19920922  Omnisec  Cryptographic system allowing encrypted communication between users with a secure mutual cipher key determined without user interaction 
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Publication number  Publication date  Type 

EP0637413A1 (en)  19950208  application 
KR0151217B1 (en)  19981102  grant 
US5276737B1 (en)  19950912  grant 
DE69332305D1 (en)  20021024  grant 
EP0637413A4 (en)  19970820  application 
EP0637413B1 (en)  20020918  grant 
US5276737A (en)  19940104  grant 
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