Abstract: The present invention concerns a cryptographic system, combining the so-called discrete logarithm and factorization principles, comprising an encryption and decryption system and a key escrow system, and the associated equipment and devices. It is particularly intended to be used in electronic systems of the type comprising chip cards, PCMCIA cards, badges, contactless cards or any other portable equipment.

Abstract: A method relating to probabilistic digital signatures of a message, between a signatory and a checker, uses an algorithm based on the calculation of a discrete logarithm. For the signatory, at least two signatures are generated for the same unchopped message, these signatures being calculated by the algorithm by means of the same public and private key parameters using respectively distinct random values. For the checker, all the signatures of the message are checked.

Abstract: A process for the identification of a claimant by a verifier. The process is of the public key type, where the public exponent is equal to 3. The claimant draws at random a first exponent .alpha., calculates r=g.sup..alpha. mod n and transmits R=r.sup.3. The verifier draws at random a second exponent .beta., calculates t=g.sup..beta. mod n, calculates T=t.sup.3 mod n and h=H.sub.1 (Z), where H.sub.1 is a hash function, and calculates Z=R.sup.3 mod n. The verifier transmits to the claimant the numbers T and h. The claimant calculates Y=T.sup..alpha. mod n, verifies the result H.sub.1 (Y), calculates H=H.sub.2 (Y), where H.sub.2 is another hash function, calculates z=rS mod n, and transmits z and H. The claimant also has a secret number S equal to the modulo n cubic root of a number I deduced from its identity so that the number S verifies S.sup.3 =I mod n. The verifier verifies that H received is equal to H.sub.2 (Z) and that z.sup.3 is equal to RI mod n.

Abstract: Method of public key cryptography based on the discrete logarithm that makes use of the computation of the variable r=g.sup.k modp where p is a prime number called a modulus, the exponent k is a random number usually with a length of N bits and g is an integer called a base, wherein an entity E carries out operations of authentication and/or of signature, including exchanges of signals with another entity in which this variable comes into play.

Abstract: Encryption circuits and methods, in particular for smart cards, are disclosed. Smart cards without microprocessors may be authenticated very simply by using encryption with a secret card data table on which recursive cycles are executed. During each cycle, a word is read out of the table, said word being at an address that is at least partially defined by the word read out in the previous cycle. The new address preferably consists of several bits from the previous word and a bit from internal card data, external data supplied by a card reader, or a register containing a partial encryption result.

Abstract: The present invention relates to a method of processing a digital signal of dimension k, in a so-called secure communication system, such that the digital signal (y) at output cannot be deduced from the digital signal (x) at input, consisting in dispatching the digital signal (x) to a device effecting a one-way function.The method includes the following steps:the digital signal (x) at the input is dispatched to a circuit C (1, 2) which gives as output a digital signal (x") of dimension n acceptable to the one-way function;the signal (x") from the circuit C (1, 2) is dispatched to the circuit effecting the one-way function giving as output the digital signal (y).The invention applies in particular to so-called secure communication systems.

Abstract: A new procedure for authentication of at least one prover by a verifier, the authentication being based on public and secret key cryptographic techniques and making use of a zero-knowledge protocol. In addition, this protocol is established using the problem of constrained linear equations and finds applications in cryptography. This procedure uses a published matrix M of dimension m.times.n where coefficients are chosen at random from the integers from 0 to d-1, where d is generally a prime number close the square of a number c. The "prover" authenticates itself to a "verifier" by performing hashing functions based on a randomly chosen vector U of dimension m and a randomly chosen vector V of dimension n, the results of which are called commitments and are sent to the prover. The prover then chooses one of several predefined functions and requests that the verifier perform this one predefined function.

Abstract: A a process for the authentication of at least one identification device by a verification device. In this process, authentication is done by a zero knowledge input protocol based on the decoding by syndrome problem. The process consists of setting up a secret vector s with a Hamming weight d, a known matrix M with dimensions n.times.k and a public vector K such that K=Ms, the production of a random vector y and a random permutation p in the identification device, a commitment on parameters dependent on y and/or p and/or s based on use of the cryptographic hashing function H and the matrix M, an exchange of information concerning y, p, s in order to answer questions asked by the verification device without directly or indirectly revealing s to the verification device, and a verification of validity of the hashed commitments using K and/or previously transmitted information.