Protection of a modular reduction calculation

A system, comprising:

• one or more processing cores, which in operation, process digital data;
• and
• cryptographic circuitry, coupled to the one or more processing cores, wherein the cryptographic circuitry, in operation:
• performs a cryptographic operation by performing a modular reduction calculation using a first number and a second number, the performing the modular reduction calculation including:
• calculating a first intermediate modular reduction result B;
• adding, to the first intermediate modular reduction value B, a first value corresponding to an integer multiple of the second number, generating a second intermediate modular reduction result B′;
• and
• subtracting, from the second intermediate modular reduction result B′, a second value corresponding to the second number multiplied by a most significant word m of the second intermediate modular reduction result B′ plus 1, generating a third intermediate modular reduction result B″.

A non-transitory computer-readable medium having contents which cause one or more processing devices to perform a method, the method comprising:

• performing a cryptographic operation, the performing the cryptographic operation including performing a modular reduction calculation using a first number and a second number, the performing the modular reduction calculation including:
• calculating a first intermediate modular reduction result B;
• adding a value corresponding to an integer multiple of the second number to the first intermediate modular reduction result B, generating a second intermediate modular reduction result B′;
• subtracting, from the second intermediate modular reduction result B′, a value corresponding to the second number multiplied by a most significant word m of the second intermediate modular reduction result B′ plus 1, generating a third intermediate modular reduction result B″;
• and
• generating a result of the modular reduction calculation using the third intermediate modular reduction result B″.

A method, comprising:

• performing, using cryptographic circuitry, a cryptographic operation, wherein the performing the cryptographic operation includes performing a modular reduction calculation on a first number and a second number, the performing the modular reduction calculation including:
• calculating a first intermediate modular reduction result B;
• adding, to the first intermediate modular reduction result B, a first value corresponding to an integer multiple of the second number, generating a second intermediate modular reduction result B′;
• subtracting, from the second intermediate modular reduction result B′, a second value corresponding to the second number multiplied by a most significant word m of the second intermediate modular reduction result B′ plus 1, generating a third intermediate modular reduction result B″;
• and
• generating a result of the modular reduction calculation using the third intermediate modular reduction result B″.