Abstract: The invention features a public key cryptography method based on the discrete logarithm which computes a value Gkmod p. Two solutions are proposed to reduce the number of multiplications, one consisting in generating “hollow” k exponents with a few bits of value 1, but of sufficient length to maintain the total security of the system, and the other consisting of performing calculations of the powers of g in parallel while combining the exponents with each other in order to prevent repeating the same power computations twice for a given exponent. The invention is useful for generating digital signatures, authentication and encryption.

Abstract: A method for implementing private key protocols between two processing devices of which at least one is a portable storage medium. The devices are fitted with a digital processing circuit for performing modular calculation operations with a view to executing operations such as modular multiplication, the processing circuit is used to implement a private key encryption function consisting of a series of reversible operations comprising at least a combination of two operations, i.e. a modular calculation operation and a binary logic operation, and said function is applied either for encrypting or signing messages to be transmitted, or for decrypting received messages.

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: The invention relates to a process for generating digital signatures from portable apparatuses (A1, A2, . . . Ai . . . An) of the microprocessor-based card type, including means for computation, communication and retention of data, which means comprise at least one electrically programmable non-volatile memory, consisting in preparing enciphered data constituting coupons and loading these coupons into the non-volatile memories so as later to use these coupons in order to sign a message sent by a verifier device. According to the process, the preparation of the coupons is carried out by a certified central authority B or by the card itself.

Abstract: A system comprises at least, two parts, connected to each other by the means of a common communication interface wherein a first communicating apparatus A, having data processing means, communication means, memory means and random or pseudo-random generation means relies of the computational power of a second communicating apparatus B having data processing means, communication means and memory means in order to compute the inverse of a first number x modulo a second number n and use the resulting modular inverse in an encryption, decryption, key exchange, identification or digital signature cryptographic protocol.

Abstract: The process concerns a system, comprising communication devices A1, A2, . . . A.alpha. connected to a central verification device B by the means of communication interfaces wherein each device Ai, having data processing means, communication means, memory means and random or pseudo-random generation means, transmits to the device B, having data processing means, communication means and memory means, a set of DSS digital signatures. Once all the signatures has been received by device B, device B verifies them simultaneously by performing few calculations for verifying a great same number of signatures sequentially.