Abstract: The invention proposes an off-line divisible e-cash scheme where a user can withdraw a divisible coin of monetary value nL (n being for example equal to 2) that he can parceled and spend anonymously and unlinkably. The invention allows to protect the anonymity of honest users and to revoke anonymity only in case of cheat for protocols based on a tree structure without using a trusted third party.

Abstract: A method for encrypting/decrypting a message includes the initial step of generating keys by the sub-steps of generating a public key; generating a decryption key; and generating a derivation key. For a first entity, the message is encrypted using the public key and a cipher. For a second entity, the cipher is decrypted to find the message. A trapdoor associated with said message is generated. The trapdoor corresponds to a derivative of the derivation key specific to the message. A test cipher is tested, using the trapdoor associated with the message, to determine if the test cipher is an encryption of the message using the public key.

Abstract: A method for dynamically authenticating an executable program, that is the continuation of the instructions defined thereby, is performed repeatedly during the very execution of the program. The method for making secure an electronic portable object through execution of a program supplied by another insecure electronic object uses, inter alia, a secret key protocol.

Abstract: There exist numerous public key probabilistic encryption algorithms. Most of these algorithms do not have a maximum security level against someone capable of chosen ciphertext attacks. The disclosed method provides a construct to enhance the security of any public key probabilistic or deterministic encryption algorithm to achieve an optimal security level.

Abstract: The invention concerns a method for implementing in an electronic component a cryptographic algorithm using calculating means. The invention is characterized in that it consists in carrying out the following steps: a) selecting a value e among a specific number of values eI, ei being integers, b) checking if ei verifies a predetermined relationship: if so, then e=ei, and storing e for use in calculating said cryptographic algorithm.

Abstract: The invention relates to method of performing a modular multiplication using numbers with 2n bits. The method includes the steps of breaking the numbers (A, B) down into a 2n base or a U base, U being a suitable integer; and, subsequently, performing MultModDiv—and/or MultModDivlnit-type elementary operations on the numbers with n bits resulting from the first step. The invention also relates to a method of calculating a Euclidean multiplication/division. The invention can be used for cryptographic calculations.

Abstract: A multiply unit includes an extended precision accumulator. Microprocessor instructions are provided for manipulating portions of the extended precision accumulator including an instruction to move the contents of a portion of the extended accumulator to a general-purpose register (“MFLHXU”) and an instruction to move the contents of a general-purpose register to a portion of the extended accumulator (“MTLHX”).

Abstract: A multiply unit includes an extended precision accumulator. Microprocessor instructions are provided for manipulating portions of the extended precision accumulator including an instruction to move the contents of a portion of the extended accumulator to a general-purpose register (“MFLHXU”) and an instruction to move the contents of a general-purpose register to a portion of the extended accumulator (“MTLHX”).

Abstract: A random prime number is generated within a predetermined interval by precalculating and storing a single value that functions as a universal parameter for generating prime numbers of any desired size. The value, ?, is chosen as a product of k prime numbers. A number a is also chosen such that is co-prime with ?. Once the values for ? and a have been determined they can be stored and used for all subsequent iterations of the prime number generating algorithm. To generate a prime number, a random number x is chosen with uniform distribution, and a candidate prime number within the predetermined interval is calculated on the basis of the random number. This candidate is tested for primality, and returned as the result if it is prime. If the candidate is not prime, the random number x is multiplied by a, and used to generate a new candidate. This procedure is repeated, until the candidate is prime. Since a single value, namely ?, needs to be precalculated, economies of storage are achieved.

Abstract: A countermeasure method in an electronic component which uses an RSA-type public key cryptographic algorithm. A first countermeasure method uses a random calculation for each new execution of the decryption algorithm with CRT. The calculations are made modulo p*r and q*t, r and t being random numbers. A second countermeasure makes the recombination random using the CRT theorem.

Abstract: A random number that is co-prime with a set of prime numbers is generated, without having to calculate the greatest common denominator of the numbers. The value of 1?x?(mod ?), where x is a randomly generated value and ? is the Carmichael function, is tested to determine whether it is non-zero. If it equals zero, x is chosen as the random number of interest. Otherwise the value for x is updated, and the procedure is repeated. Due to the minimal amount of computation resources required to select x, the process is particularly well suited for generating cryptographic keys in portable electronic devices, such as smart cards.

Abstract: A multiply unit includes an extended precision accumulator. Microprocessor instructions are provided for manipulating portions of the extended precision accumulator including an instruction to move the contents of a portion of the extended accumulator to a general-purpose register (“MFLHXU”) and an instruction to move the contents of a general-purpose register to a portion of the extended accumulator (“MTLHX”).

Abstract: An encryption method in which a clear message (m) is formatted with a formatting function (p), and in which the result of the formatting step is exponentiated using a public key (N, e) in accordance with the relationship c=?(m)e mod N, c being an encrypted message, ?(m) being the result of the formatting step, and e and N elements of the public key. The formatting function (?) is the PSS function. The invention is applicable to cryptography, for example of RSA type, for smart cards for instance.

Abstract: The invention concerns a cryptographic method for generating public keys and private keys. Two distinct first numbers p and q, of neighboring value are selected, and the number n equal to the product of p·q is calculated. The lowest common multiple of the numbers (p?1) and (q?1)?(n)=PPCM(p?1, q?1) is then calculated. A number g, 0<g?n2, is then determined which verifies the two following conditions: a) g is invertible modulo n2; and b) ord(g,n2)=0 mod n. The public key is formed by the parameters n and g and its private key is formed by the parameters p, q and ?(n)or by the parameters p and q. An encryption method for a number m representing a message, 0?m<n, involves calculating the cryptogram c=gm mod n2.

Abstract: The invention concerns a method for implementing in an electronic component a cryptographic algorithm using calculating means. The invention is characterized in that it consists in carrying out the following steps: a) selecting a value e among a specific number of values eI, ei being integers, b) checking if ei verifies a predetermined relationship: if so, then e=ei, and storing e for use in calculating said cryptographic algorithm.

Abstract: The invention relates to an identification module comprising an authentication code in a permanent memory, said authentication code resulting from the application of a conversion to secret code function. The module also comprises means for generating said secret code. The invention also relates to a securement method which comprises the steps necessary for the abovementioned identification module to operate.

Abstract: There exist numerous public key probabilistic encryption algorithms. Most of said algorithms do not have a maximum security level against someone capable of chosen ciphertext attacks. The method consists in a construct enabling to enhance the security of any public key probabilistic or deterministic encryption algorithm to achieve optimal security level.

Abstract: A method for generating an electronic key from a prime number q contained in a specific interval of positive integers (wm, wM). The method includes the following operations: a) selecting a positive integer &eegr;, where &eegr; is the product of the first k prime numbers, with k as maximum so that there exist two positive integers &egr;m and &egr;M such that &egr;m is the higher round off of wm/&eegr;, and &egr;M is the lower round off of (wM−wm)/&eegr;, calculating II=&egr;m &eegr;, generating two positive integers a and c belonging to the multiplicative group Z*II of integers modulo II, with c prime with II, calculating q=c+&rgr;; b) testing the primality nature of q; c) if primality is verified, storing q; d) otherwise, updating c by calculating a.c mod II, and repeating the preceding operations from b) with the new value q=c+&rgr;. The invention is applicable to cryptography.

Abstract: A random prime number is generated within a predetermined interval by precalculating and storing a single value that functions as a universal parameter for generating prime numbers of any desired size. The value, &pgr;, is chosen as a product of k prime numbers. A number a is also chosen such that is co-prime with &pgr;. Once the values for &pgr; and a have been determined they can be stored and used for all subsequent iterations of the prime number generating algorithm. To generate a prime number, a random number x is chosen with uniform distribution, and a candidate prime number within the predetermined interval is calculated on the basis of the random number. This candidate is tested for primality, and returned as the result if it is prime. If the candidate is not prime, the random number x is multiplied by a, and used to generate a new candidate. This procedure is repeated, until the candidate is prime. Since a single value, namely &pgr;, needs to be precalculated, economies of storage are achieved.

Abstract: A random number that is co-prime with a set of prime numbers is generated, without having to calculate the greatest common denominator of the numbers. The value of 1−x&lgr;(mod &pgr;), where x is a randomly generated value and &lgr; is the Carmichael function, is tested to determine whether it is non-zero. If it equals zero, x is chosen as the random number of interest. Otherwise the value for x is updated, and the procedure is repeated. Due to the minimal amount of computation resources required to select x, the process is particularly well suited for generating cryptographic keys in portable electronic devices, such as smart cards.