Inside Secure

Eshard

Benoît Feix

Christophe Clavier

Pascal Paillier

Hugues Thiebeauld De La Crouee

Gary Chew

Georges Gagnerot

Loïc Thierry

Vincent Verneuil

Mylène Roussellet

Bruno Benteo

Bernard Vian

Sébastien Nerot

Mylène Rousselet

Sébastian Nerot

In a general aspect, a test method can include: acquiring a plurality of value sets, each comprising values of a physical quantity or of logic signals, linked to the activity of a circuit to be tested when executing distinct cryptographic operations applied to a same secret data, for each value set, counting occurrence numbers of the values of the set, for each operation and each of the possible values of a part of the secret data, computing a partial result of operation, computing sums of occurrence numbers, each sum being obtained by adding the occurrence numbers corresponding to the operations which when applied to a same possible value of the part of the secret data, provide a partial operation result having a same value, and analyzing the sums of occurrence numbers to determine the part of the secret data.

Testing resistance of a circuit to a side channel analysis

A cryptographic data processing method, implemented in an electronic device including a processor, the method including steps of providing a point of an elliptic curve in a Galois field, and a whole number, and of calculating a scalar product of the point by the number, the coordinates of the point and the number having a size greater than the size of words that may be processed directly by the processor, the scalar multiplication of the point by the number including steps of: storing scalar multiples of the point multiplied-by the number 2 raised to a power belonging to a series of whole numbers, setting a resulting point for each non-zero bit of the first number, adding the resulting point and one of the stored multiple points, and providing at the output of the processor the resulting point as result of the scalar product.

Cryptography method comprising an operation of multiplication by a scalar or an exponentiation

This disclosure relates to methods for generating a prime number, which can be implemented in an electronic device. An example method can include calculating a candidate prime number using a formula Pr=2P&#xb7;R+1, where P is a prime number and R is an integer. The method can also include applying the Pocklington primality test to the candidate prime number and rejecting the candidate prime number if it fails the Pocklington test. The integer can be generated from an invertible number belonging to a set of invertible elements modulo the product of numbers belonging to a group of small prime numbers greater than 2, where the candidate prime number is not divisible by any number of the group. The prime number P having a number of bits equal to within one bit, to half or a third of the number of bits of the candidate prime number.

Method of generating prime numbers proven suitable for chip cards

The invention relates to a method for generating a prime number, implemented in an electronic device, the method including steps of generating a prime number from another prime number using the formula Pr=2P&#xb7;R+1, where P is a prime number having a number of bits lower than that of the candidate prime number, and R is an integer, and applying the Pocklington primality test to the candidate prime number, the candidate prime number being proven if it passes the Pocklington test. According to the invention, the size in number of bits of the candidate prime number is equal to three times the size of the prime number, to within one unit, the generated candidate prime number being retained as candidate prime number only if the quotient of the integer division of the integer by the prime number is odd.

Method of generating proven prime numbers suitable for being implemented in a smart card

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Aubagne, France

Benoît Feix