Abstract: Method and device for generating factors of a RSA modulus N with a predetermined portion Nh, the RSA modulus comprising at least two factors. A first prime p is generated; a value Nh that forms a part of modulus N is obtained; a second prime q is generated in an interval dependent from p and Nh so that pq is a RSA modulus that shares Nh; and information enabling the calculation of the modulus/V is outputted.

Abstract: A method for generating a compressed RSA modulus, allowing up to two thirds of the bits of a modulus N to be fixed. N has a predetermined portion NH, which comprises two parts Nh and Nm. A candidate RSA modulus that shares the Nh part is generated, and the candidate is then modified using Euclidian-type computations until it shares both Nh and Nm. Also provided is an apparatus for calculating compressed RSA moduli according to the method and a computer program product.

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 cryptographic operation includes calculating a multiplication of an element of an additively denoted group by a scalar. After two registers R0+R1, are initialized iterations are carried out over the components Ki of the scalar K. If Ki of the scalar equals 0, then the value in register R1 is replaced by 2(R0+R1) If Ki equals 1, the value in register R0 is replaced by 2(R0+R1). At the end of the algorithm, the value of the register R0 is returned as the calculated result This method poses the advantage of carrying out a calculation of multiplying by a scalar by carrying out only doubling and adding operations of the type 2(A+B).

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: 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: A method for the secure application of a cryptographic algorithm of the RSA type in an electronic component obtains the value of a public exponent e from a given set of probable values, without a priori knowledge of that value. Having determined the value for the public exponent e, the application of countermeasures using the value of e, to block error attacks and side channel attacks, particularly of the DPA and SPA type, are carried out on the application of a private operation of the cryptographic algorithm.

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 method for secure and compact exponentiation. The inventive method can be applied in the field of cryptology where cryptographic algorithms are used in electronic devices such as chip cards.

Abstract: A method for the secure application of a cryptographic algorithm of the RSA type in an electronic component obtains the value of a public exponent e from a given set of probable values, without a priori knowledge of that value. Having determined the value for the public exponent e, the application of countermeasures using the value of e, to block error attacks and side channel attacks, particularly of the DPA and SPA type, are carried out on the application of a private operation of the 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: The invention relates to a method for countermeasuring in an electronic component while using a public key cryptographic algorithm. The invention involves the use of a public key cryptographic algorithm containing an exponentiation calculation y=gˆd, in which g and y are elements of specified group G noted in a multiplicative manner and d is a predetermined number.

Abstract: The invention relates to a cryptographic method wherein a random number generator producing random numbers Si whose size N is fixed between 0 and W-1 is used to produce a random number R between 0 and a predefined limiter K. According to the invention: E31: a random variable Si is produced, ranging from 0-W-1, E32: if the random variable Si is strictly lower than a coefficient Ki of the limiter K in base W, the coefficient Ri of order i of the random number R is equal to the random number Si then, for all orders j which are lower than i, a random variable Sj of 0-W-1 is produced and Rj=Sj. E33: unless, if said random variable is greater than coefficient Ki of position i of the limiter K is base W, whereupon said coefficient Ri is determined on the basis of the random variable Si of order i according to a predetermined function, then a coefficient Ri-1 is determined for the random number R of order i-1 which is immediately lower by repeating stages E31-E33.

Abstract: The invention relates to a method for countermeasuring in an electronic component while using a public key cryptographic algorithm. The invention is characterized in that the method comprises an exponentiation calculation with a left-to-right exponentiation algorithm y=gˆd, in which g and y are elements of the specified group G noted in a multiplicative manner and d is a predetermined number. The inventive method is also characterized by comprising a random selection step at the beginning of or during the execution of said exponentiation algorithm in a deterministic or probabilistic manner for masking the accumulator A.

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 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 method for the secure application of a cryptographic algorithm of the RSA type in an electronic component obtains the value of a public exponent e from a given set of probable values, without a priori knowledge of that value. Having determined the value for the public exponent e, the application of countermeasures using the value of e, to block error attacks and side channel attacks, particularly of the DPA and SPA type, are carried out on the application of a private operation of the cryptographic algorithm.

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 relates to a cryptographic method involving an integer division of type q=a div b and r=a mod b, wherein a is a number of m bits, b is a number of n bits, with n being less than or equal to m, and bn?1 being non-null and the most significant bit of b. In addition, each iteration of a loop subscripted by i, which varies between 1 and m?n+1, involves a partial division of a word A of n bits of number a by number b in order to obtain one bit of quotient q. According to the invention, the same operations are performed with each iteration, regardless of the value of the quotient bit obtained. In different embodiments of the invention, one of the following is also performed with each iteration: the addition and subtraction of number b to/from word A; the addition of number b or a complementary number /b of b to word A; or a complement operation at 2n of an updated datum (b or /b) or a dummy datum (c or /c) followed by the addition of the datum updated with word A.

Abstract: A method for universal calculation on the points of an elliptic curve defined by a quartic equation uses identical programmed calculating devices for operating an addition of points, a doubling of points and an addition of a neutral point. The calculating device is a central unit associated with a memory. The invention also concerns a cryptographic method using such a universal method. The invention further concerns a component for implementing the universal calculation method and/or the cryptographic method. For example, the invention is applicable to smart cards.