Abstract: An authentication method of a first module by a second module includes the steps of generating a first random datum by the second module to be sent to the first module, generating a first number by the first module starting from the first datum and by way of a private key, and generating a second number by the second module to be compared with the first number, so as to authenticate the first module. The step of generating the second number is performed starting from public parameters and is independent of the step of generating the first number.

Abstract: A method of processing information to be confidentially transmitted from a first module to a second module provides that a first scalar multiplication may be carried out in order to obtain a first result [r]P. This first scalar multiplication comprises a plurality of generation steps of ordered factors from which a plurality of first partial sums are required to be built. The method also comprises the carrying out of a second scalar multiplication in order to obtain a second result. This second multiplication provides that a plurality of second partial sums may be built. A piece of encrypted information is obtained by processing the information based on the results of the scalar multiplications. The second partial sums of the second scalar multiplication use the same ordered factors obtained by the generation step of the first scalar multiplication.

Abstract: An authentication method of a first module by a second module includes the steps of generating a first random datum by the second module to be sent to the first module, generating a first number by the first module starting from the first datum and by way of a private key, and generating a second number by the second module to be compared with the first number, so as to authenticate the first module. The step of generating the second number is performed starting from public parameters and is independent of the step of generating the first number.

Abstract: A method for decrypting the encrypted messages sent by a transmission device to a first electronic device associated with a first trusted authority and to a second electronic device (ME). In one embodiment, first and second tokens are generated and exchanged, respectively, by the first and second electronic devices, which then generate a joint decryption key in order to decrypt the encrypted message.

Abstract: A computing method and circuit for computing a modular operation with at least one operand having a binary representation. Iteratively for each bit of this operand, doubling the value of an intermediate result stored in a first memory element by shifting the bits of the intermediate result towards the most significant bit and, while the most significant bit of the intermediate result is one, updating this intermediate result by subtracting a modulus stored in a second memory element.

Abstract: Cryptographic methods are known that involve the computation of a non-degenerate bilinear mapping of first and second elements one of which comprises a secret of a first entity. For a mapping implemented as, for example, a Tate pairing, the mapping is computable by applying a predetermined function to the first and second elements and then exponentiating the result with a known exponent. Improvements in respect of computational loading, size of output, and security are enabled for the first party by arranging for the first entity to carry out only part of the mapping, a second entity being used to complete computation of the mapping. Cryptographic applications using these improvements are also disclosed.

Abstract: A method decrypts the encrypted messages sent by a transmission device to a first electronic device associated with a first trusted authority and to a second electronic device. In one embodiment, first and second tokens are generated and exchanged, respectively, by the first and second electronic devices, which then generate a joint decryption key in order to decrypt the encrypted message.

Abstract: A method for decrypting the encrypted messages sent by a transmission device to a first electronic device associated with a first trusted authority and to a second electronic device (ME). In one embodiment, first and second tokens are generated and exchanged, respectively, by the first and second electronic devices, which then generate a joint decryption key in order to decrypt the encrypted message.

Abstract: A method establishes a communication between a first electronic device associated with a first trusted authority and a second electronic device. The method includes: making a first key available to the first device for the communication between the first authority and the first device. A second trusted authority, associated with the second device and distinct and autonomous with respect to the first authority, generates a second key in order to communicate with the second device. Furthermore, the method includes: making the second key available to the second device; and providing the first and second devices with a communication key, to be used communication between the first and second devices, through at least one of the first and second authorities.

Abstract: A method of establishing an encrypted communication by using keys between a first electronic device associated with a first trusted authority and a second electronic device, including generating a first secret key associated with the first device for the management of the communication, generating, at least in part by the first authority, a second secret key associated with the second device for the management of the communication. The method includes generating the first key at least in part by a second trusted authority associated with the second device that is distinct and autonomous from the first authority. Alternatively, the generation of the first key is performed, at least in part, by the second device passing through the second trusted authority.

Abstract: Cryptographic methods are known that involve the computation of a non-degenerate bilinear mapping of first and second elements one of which comprises a secret of a first entity. For a mapping implemented as, for example, a Tate pairing, the mapping is computable by applying a predetermined function to the first and second elements and then exponentiating the result with a known exponent. Improvements in respect of computational loading, size of output, and security are enabled for the first party by arranging for the first entity to carry out only part of the mapping, a second entity being used to complete computation of the mapping. Cryptographic applications using these improvements are also disclosed.

Abstract: A computing method and circuit for computing a modular operation with at least one operand having a binary representation. Iteratively for each bit of this operand, doubling the value of an intermediate result stored in a first memory element by shifting the bits of the intermediate result towards the most significant bit and, while the most significant bit of the intermediate result is one, updating this intermediate result by subtracting a modulus stored in a second memory element.

Abstract: A method of processing information to be confidentially transmitted from a first module to a second module provides that a first scalar multiplication may be carried out in order to obtain a first result [r]P). This first scalar multiplication comprises a plurality of generation steps of ordered factors from which a plurality of first partial sums are required to be built. The method also comprises the carrying out of a second scalar multiplication in order to obtain a second result. This second multiplication provides that a plurality of second partial sums may be built. A piece of encrypted information is obtained by processing the information based on the results of said scalar multiplications. The second partial sums of the second scalar multiplication use the same ordered factors obtained by the generation step of the first scalar multiplication.

Abstract: An authentication method of a first module by a second module includes the steps of generating a first random datum by the second module to be sent to the first module, generating a first number by the first module starting from the first datum and by way of a private key, and generating a second number by the second module to be compared with the first number, so as to authenticate the first module. The step of generating the second number is performed starting from public parameters and is independent of the step of generating the first number.

Abstract: A method for decrypting the encrypted messages sent by a transmission device to a first electronic device associated with a first trusted authority and to a second electronic device (ME). In one embodiment, first and second tokens are generated and exchanged, respectively, by the first and second electronic devices, which then generate a joint decryption key in order to decrypt the encrypted message.

Abstract: A method establishes a communication between a first electronic device associated with a first trusted authority and a second electronic device. The method includes: making a first key available to the first device for the communication between the first authority and the first device. A second trusted authority, associated with the second device and distinct and autonomous with respect to the first authority, generates a second key in order to communicate with the second device. Furthermore, the method includes: making the second key available to the second device; and providing the first and second devices with a communication key, to be used communication between the first and second devices, through at least one of the first and second authorities.

Abstract: A method of establishing an encrypted communication by means of keys between a first electronic device associated with a first trusted authority and a second electronic device, including generating a first secret key associated with the first device for the management of the communication, generating, at least in part by means of the first authority, a second secret key associated with the second device for the management of the communication. The method includes generating the first key at least in part by a second trusted authority associated with the second device that is distinct and autonomous from the first authority. Alternatively, the generation of the first key is performed, at least in part, by the second device passing through the second trusted authority.