Protection of an iterative calculation

A device, comprising:

• a memory including a plurality of registers;
• and
• cryptographic circuitry coupled to the memory, wherein the cryptographic circuitry, in operation, performs a calculation on a first number and a second number, wherein the performing the calculation includes:
• generating a third number comprising at least the bits of the second number, a number of bits of the third number being an integer multiple of a fourth number;
• dividing the third number into blocks each having a size in bits of the fourth number;
• and
• successively, for each block of the third number:
• performing a first function, the first function using a first operator and having as inputs:
• contents of a first register of the memory, contents of a second register of the memory and the first number, and placing a result of the first function in a third register of the memory;
• and
• for each bit of the current block,
• performing a second function, the second function using a second operator and having as inputs:
• contents of the third register;
• a rank of a current bit of the third number;
• and
• the contents of a selected one of the first and the second register according to a state of said current bit;
• and
• placing a result of the second function in the selected one of the first and second register.

A non-transitory computer-readable medium having contents which cause cryptographic circuitry to perform a calculation on a first number and a second number, wherein the performing the calculation includes:

• generating a third number comprising at least the bits of the second number, a number of bits of the third number being an integer multiple of a fourth number;
• dividing the third number into blocks each having a size in bits of the fourth number;
• and
• successively, for each block of the third number:
• performing a first function, the first function using a first operator and having as inputs:
• contents of a first register of the memory, contents of a second register of the memory and the first number, and placing a result of the first function in a third register of the memory;
• and
• for each bit of the current block,
• performing a second function, the second function using a second operator and having as inputs:
• contents of the third register;
• a rank of a current bit of the third number;
• and
• the contents of a selected one of the first and the second register according to a state of said current bit;
• and
• placing a result of the second function in the selected one of the first and second register.