Abstract: A method for executing an operation by a circuit, may include using a first mask set of mask parameters including a same number of occurrences of all possible values of a word of an input data in relation to a size thereof, using an input set including for each mask parameter in the first mask set a data obtained by applying XOR operations to the input data and to the mask parameter and providing an output set including all data resulting from the application of the operation to a data in the input set. The output data may be obtained by applying XOR operations to any of the data in the output set and to a respective second mask parameter in a second mask set including a same number of occurrences of all possible values of the second mask parameters in relation to a size of thereof.

Abstract: A method for executing by a circuit a substitution operation such that an output data may be selected in a substitution table using an input data as an index. The substitution operation may be performed using a new masked substitution table. The input data may be combined by XOR operations with a new value of a first mask parameter, and the output data may be combined by XOR operations with a new value of a second mask parameter. The new masked substitution table may be generated by computing the new value of the first mask parameter by applying XOR operations to a previous value of the first mask parameter and to a first input mask, computing the new value of the second mask parameter by applying XOR operations to a previous value of the second mask parameter and to a second input mask, and generating the new masked substitution table using a previous masked substitution table and the first and second input masks.

Abstract: The present invention relates to a test method of a circuit, comprising: acquiring a plurality of value sets comprising values of a physical quantity linked to the activity of a circuit to be tested when the circuit executes an operation of a set of distinct cryptographic operations applied to a secret data, selecting at least a first subset in each value set, for each value set, counting by a processing unit occurrence numbers of values transformed by a first surjective function applied to the values of the first subset of the value set, to form an occurrence number set for the value set, for each operation of the operation set, and each of the possible values of a part of the secret data, computing a partial operation result, computing cumulative occurrence number sets by adding the occurrence number sets corresponding to the operations of the operation set, which when applied to a same value or equivalent value of the possible values of the part of the secret data, provide a partial operation result having

Abstract: A method for executing an operation by a circuit, may include using a first mask set of mask parameters including a same number of occurrences of all possible values of a word of an input data in relation to a size thereof, using an input set including for each mask parameter in the first mask set a data obtained by applying XOR operations to the input data and to the mask parameter and providing an output set including all data resulting from the application of the operation to a data in the input set. The output data may be obtained by applying XOR operations to any of the data in the output set and to a respective second mask parameter in a second mask set including a same number of occurrences of all possible values of the second mask parameters in relation to a size of thereof.

Abstract: A method for executing by a circuit a substitution operation such that an output data may be selected in a substitution table using an input data as an index. The substitution operation may be performed using a new masked substitution table. The input data may be combined by XOR operations with a new value of a first mask parameter, and the output data may be combined by XOR operations with a new value of a second mask parameter. The new masked substitution table may be generated by computing the new value of the first mask parameter by applying XOR operations to a previous value of the first mask parameter and to a first input mask, computing the new value of the second mask parameter by applying XOR operations to a previous value of the second mask parameter and to a second input mask, and generating the new masked substitution table using a previous masked substitution table and the first and second input masks.

Abstract: 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.

Abstract: The present invention relates to a test method of a circuit, comprising: acquiring a plurality of value sets comprising values of a physical quantity linked to the activity of a circuit to be tested when the circuit executes an operation of a set of distinct cryptographic operations applied to a secret data, selecting at least a first subset in each value set, for each value set, counting by a processing unit occurrence numbers of values transformed by a first surjective function applied to the values of the first subset of the value set, to form an occurrence number set for the value set, for each operation of the operation set, and each of the possible values of a part of the secret data, computing a partial operation result, computing cumulative occurrence number sets by adding the occurrence number sets corresponding to the operations of the operation set, which when applied to a same value or equivalent value of the possible values of the part of the secret data, provide a partial operation result having

Abstract: 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·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.

Abstract: 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·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.

Abstract: The present invention relates to a method for performing an iterative calculation of exponentiation of a large datum, the method being implemented in an electronic device (DV1) and comprising calculations of squaring and multiplying large variables performed in parallel, by squaring (SB1) and multiplication (SM1) blocks, the method comprising steps of: while a temporary storage buffer memory is not full of unused squares, triggering a calculation by the squaring block for a bit of the exponent, when the squaring block is inactive, storing each square provided by the squaring block in the buffer memory, if the bit of the corresponding exponent is on 1, and while the buffer memory contains an unused square, triggering a calculation by the multiplication block concerning the unused square, when the multiplication block is inactive.

Abstract: 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.

Abstract: 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·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.

Abstract: The invention relates to a method for generating a prime number, implemented in an electronic device, the method including steps of calculating a candidate prime number having a number of bits, using the formula: Pr=2P·R+1, where P is a prime number and R is an integer, applying the Pocklington primality test to the candidate prime number, rejecting the candidate prime number if it fails the Pocklington test, generating the integer 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, so that 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.

Abstract: The present invention relates to a method for performing an iterative calculation of exponentiation of a large datum, the method being implemented in an electronic device (DV1) and comprising calculations of squaring and multiplying large variables performed in parallel, by squaring (SB1) and multiplication (SM1) blocks, the method comprising steps of: while a temporary storage buffer memory is not full of unused squares, triggering a calculation by the squaring block for a bit of the exponent, when the squaring block is inactive, storing each square provided by the squaring block in the buffer memory, if the bit of the corresponding exponent is on 1, and while the buffer memory contains an unused square, triggering a calculation by the multiplication block concerning the unused square, when the multiplication block is inactive.

Abstract: A method and a device protected against hidden channel attacks includes a calculation of the result of the exponentiation of a data m by an exponent d. The method and the device are configured to execute only multiplications of identical large variables, by breaking down any multiplication of different large variables x, y into a combination of multiplications of identical large variables.

Abstract: In an electronic component using a secret key cryptographic algorithm, one operation utilizes a first table for supplying output data from input data. The output data, and/or derived data, is manipulated by critical instructions. A countermeasure method involves the use of other tables such that the output data and the derived data are unpredictable. The other tables are obtained from the first table by an exclusive-OR operation with a random value, or a derived random value, on one and/or the other of the input and output data of the first table.

Abstract: The invention concerns a countermeasure method in an electronic component using a secret key K cryptographic algorithm with sixteen computing cycles to supply an encrypted message (C) from an input message (M), each cycle using first means TC0 to supply an output information from an input information, Said method consists in applying by selection a sequence with the first means or another sequence with other means TC1, TC2 to a group G1 comprising the first three cycles at least and another group G4 comprising the last three cycles at least. Whatever the sequence, the output result of the last cycle of each group is the same for the same input message (M).