Abstract: The invention proposes a novel type of infective countermeasure against fault injection attacks. Instead of determining the injected error before amplifying it, the novel countermeasure applies the same diffusion function to two intermediate ciphers obtained by executing a cryptographic operation on an input. The error is therefore amplified within the same intermediate ciphers, referred to as infective ciphers after diffusion. It is then possible to use diffusion functions which do not map the cipher 0 as an output equal to 0. A cipher recomposed from bits of undiffused ciphers is also generated. These infective and recomposed ciphers are XOR-combined to provide an output cipher. This approach makes it possible to adapt, by simple duplication of the pairs and associated specific diffusion functions, the protection offered by the countermeasure to a desired number of injected faults.

Abstract: The invention proposes a novel type of infective countermeasure against fault injection attacks. Instead of determining the injected error before amplifying it, the novel countermeasure applies the same diffusion function to two intermediate ciphers obtained by executing a cryptographic operation on an input. The error is therefore amplified within the same intermediate ciphers, referred to as infective ciphers after diffusion. It is then possible to use diffusion functions which do not map the cipher 0 as an output equal to 0. A cipher recomposed from bits of undiffused ciphers is also generated. These infective and recomposed ciphers are XOR-combined to provide an output cipher. This approach makes it possible to adapt, by simple duplication of the pairs and associated specific diffusion functions, the protection offered by the countermeasure to a desired number of injected faults.

Abstract: A cryptographic processing method transforming an input byte into an output byte comprises the following steps: converting a plurality of words, each comprising at least one bit of the input byte, into input cryptograms by application, to each of said words, of a homomorphic encryption function from a first group to a second group provided with an operation; obtaining output cryptograms as a function of the input cryptograms, this obtaining step including at least one processing during which said operation is applied to two intermediate cryptograms, this processing producing a cryptogram that is an image by the homomorphic encryption function of a word including a Boolean logic combination of two bits comprised respectively in two words that are arguments, for the homomorphic encryption function, of said two intermediate cryptograms; determining bits of the output byte by applying respectively to the output cryptograms, an inverse function of the homomorphic encryption function.

Abstract: In a method for determining the modular inverse of a number, successive iterations are applied to two pairs each including a first variable and a second variable, such that at the end of each iteration and for each pair, the product of the second variable and of the number is equal to the first variable modulo a given module. Each iteration includes at least one division by two of the first variable of a first pair or of a second pair, or a combination of the first variable of the first pair and of the first variable of the second pair by addition or subtraction. At least some of the iterations including a combination by addition or subtraction include a step of storing the result of the combination in the first variable of a pair determined randomly from among the first pair and the second pair. An associated cryptographic processing device is also described.

Abstract: In a method for determining the modular inverse of a number, successive iterations are applied to two pairs each including a first variable and a second variable, such that at the end of each iteration and for each pair, the product of the second variable and of the number is equal to the first variable modulo a given module. Each iteration includes at least one division by two of the first variable of a first pair or of a second pair, or a combination of the first variable of the first pair and of the first variable of the second pair by addition or subtraction. At least some of the iterations including a combination by addition or subtraction include a step of storing the result of the combination in the first variable of a pair determined randomly from among the first pair and the second pair. An associated cryptographic processing device is also described.