Abstract: The invention concerns a cryptographic method which includes integer division of the type q=a div b and/or a modular reduction of the type r=a mod b, with q being a quotient, a being a number of m bits, b being a number of n bits, n being not more than m and bn?1 being the most significant bit of the number b. The number a is masked by a random number p before performing the integer division and/or the modular reduction. The invention also concerns an electronic component for implementing the method. The invention is applicable for making smart cards secure against hidden channel attacks, and in particular differential attacks.

Abstract: A method of generating electronic keys for a public-key cryptography method using an electronic device. In a first of two separate calculating steps, pairs of prime numbers (p, q) are calculated and stored independent of knowledge of the pair of values (e,l), in which e is the public exponent and l is the length of the key of the cryptography method. The second step is very quick and can be executed in real time by the device, in which a key d is calculated from the results of the first step and knowledge of the pair (e,l).

Abstract: The invention relates to a cryptographic method secured against a covert channel attack. According to the invention, in order to carry out a selected block of instructions as a function of an input variable amongst N predefined instruction blocks, a common block is carried out on the predefined N instruction blocks, a predefined number of times, the predefined number being associated with the selected instruction block.

Abstract: A method for converting in a binary representation of a number based on a left-to-right processing of bits of the binary representation, to obtain a signed representation equivalent to the so-called Reitwiesner representation. The use of such a conversion method with left-to-right arithmetic processing improves hardware implementation of the method.

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 a universal calculation method that is applied to points on an elliptical curve which is defined by a Weierstrass equation. According to the invention, identical programmed computing means are used to perform an operation involving the addition of points and an operation involving the doubling of points. The computing means comprise, in particular, a central unit which is connected to a storage unit.

Abstract: A countermeasure method in an electronic component uses a public key cryptographic algorithm on a specific elliptic curve E on a body IK. An exponential computation of Q=d.P type is carried out, where P and Q are points of the specific elliptic curve E, and d is a predetermined number. A non-null random number u is selected which is an element of the finite body IK, to define randomly an isomorphic elliptic curve Eu′. Co-ordinates of a point P′ on the isomorphic elliptic curve Eu′ are calculated which are an image of the point P. An exponentiation algorithm is applied to the point image P′ on the isomorphic elliptic curve Eu′, to obtain a resulting point Q′. Co-ordinates on the specific elliptic curve E of point Q, which is a pre-image of the resulting point Q′, are then computed.

Abstract: The invention concerns a method for converting in a signed binary representation (r′m, r′0) of a number r based on a left-to-right processing of bits of the binary representation (r′m, r′0) and enabling to obtain a representation equivalent to the so-called Reitwiesner representation. The use of such a conversion method with left-to-right arithmetic processing enables to improve their hardware implementation.

Abstract: The invention concerns a secure method for performing an exponentiation operation which consists in carrying out an operation of type U=V{circumflex over ( )}W modulo X. U, V, X are integers, W is an integer used in the form of a number W* masked by a fractional masking parameter randomly selected at each execution of the method. The invention is applicable to smart cards.

Abstract: The invention concerns a method for breaking down and performing with an electronic circuit, a computing operation based on a digital factor (N) expressed in integral base (r) by a series of integers (pn−1, p2, p1, p0). The invention provides steps which consists in: breaking down the series of integers into elementary multiplets, each elementary multiplet (Mj) comprising part of the series of integers (mji+1, mji, mj0), wherein each pair of successive numbers (mi, mi−1) has a sum equal in value to the base decreased by one unit (mi+mi1=r−1) and transforming each elementary multiplet (Mj) into a modified multiplet (Sj) comprising a series of sign digits (sji,sj−1, ,sj1)such that the concatenation of modified multiplets constitute a series of sign digits containing a minimum of non-null digits and representing the value of the digital factor (N) in a relative base ({−(r−1), ,−1,0,1, ,r−1}).

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 table establishes correspondence between first sets of at least one number, expressed in accordance with a signed code where each number may have the value of 0, 1 or −1, and second sets of at least one number, expressed according to a simple form where each number may have the value 0 or 1. An input sequence of numbers is decomposed into sets of numbers present in the correspondence table. For each set of numbers derived from the decomposition, a corresponding set of numbers is given by the correspondence table. A sequence of numbers is compiled from the sets retrieved from the table. The invention is in particular useful in various algorithms, such as in cryptography, for example to store values in signed binary mode, in compact non-adjacent form with only the numbers 0, 1 and/or for rapidly producing random numbers in the non-adjacent form.

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.