Device and method for protecting execution of a cryptographic operation

A computer implementing one or more cryptographic mechanisms, the computer comprising a cryptographic processor device configured to (i) execute a cryptographic operation related to said one or more cryptographic mechanisms and (ii) protect an execution of the cryptographic operation from attacks, said cryptographic operation being implemented by a cryptographic algorithm, said cryptographic operation comprising at least one modular operation between a main base (m) representing a data block and at least one scalar (d) in at least one finite starting group,

• wherein said cryptographic processor device comprises hardware that comprises a group determination unit:
• said group determination unit being configured to determine at least one intermediary group (E′) different from at least one starting group (E), a number of the at least one intermediary group (E′) being equal to a number of said at least one starting group (E);
• and
• said group determination unit being configured to determine at least one final group (E″) from said at least one starting group (E) and said at least one intermediary group (E′);
• said cryptographic processor device being configured such that the main base (m) is mapped to an auxiliary element (x) in said at least one intermediary group (E′) and to an auxiliary base (m″) in said at least one final group (E″), said auxiliary element (x) being determined from a parameter (r), the parameter (r) being at least one of determined randomly, an odd parameter, or a prime parameter;
• and
• wherein said cryptographic processor device further comprises hardware that comprises an execution engine for executing each modular operation, said execution engine comprising:
• a first unit configured to perform a first elementary operation in each final group (E″i), the first elementary operation comprising executing said modular operation between said auxiliary base (m″) and an auxiliary scalar (da) in each at least one final group (E″), which provides at least one result, the auxiliary scalar (da) being determined from the main scalar (d), and
• a second unit configured to perform a second elementary operation in each at least one starting group (E), the second elementary operation comprising executing said modular operation between an additional auxiliary base and an additional auxiliary scalar (d′b) in each at least one starting group, at least one of the additional auxiliary base and of the additional auxiliary scalar (d′b) being determined from the at least one result of the first elementary operation,
• wherein the cryptographic processor device is configured to implement the group determination unit, the first unit, and the second unit in an electronic device, a computer device, and/or a system;
• and
• wherein the cryptographic processor device is configured to protect the execution of the cryptographic operation in the electronic device, the computer device, and/or the system from attacks.