Protection of a modular calculation

A device, comprising:

• one or more memories;
• and
• processing circuitry, which, in operation, performs a modular calculation on a first number and a second number, the performing the modular calculation including:
• combining the second number with a third number to obtain a fourth number;
• executing the modular calculation on the first and fourth numbers, storing the result in a first memory location;
• initializing a second memory location;
• and
• successively, for each bit of the third number at a first state:
• if a corresponding bit of the fourth number is at a first state, a content of the second memory location is multiplied by an inverse of the first number and the result is stored in the first memory location;
• and
• if the corresponding bit of the fourth number is at a second state, the content of the second memory location is multiplied by the first number and the result is stored in the first memory location.

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 modular calculation on a first number and a second number, the performing the modular calculation including:
• combining the second number with a third number, obtaining a fourth number;
• executing the modular calculation on the first and fourth numbers, storing a result in a first memory location;
• initializing a second memory location;
• and
• successively, for each bit of the third number at a first state:
• if a corresponding bit of the fourth number is at a first state, multiplying a content of the second memory location by an inverse of the first number and storing the result in the first memory location;
• and
• if the corresponding bit of the fourth number is at a second state, multiplying the content of the second memory location by the first number and storing the result in the first memory location.

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

• performing a modular calculation on a first number and a second number, the performing the modular calculation including:
• combining the second number with a third number, obtaining a fourth number;
• executing the modular calculation on the first and fourth numbers, storing a result in a first memory location;
• initializing a second memory location;
• and
• successively, for each bit of the third number at a first state:
• if a corresponding bit of the fourth number is at a first state, multiplying a content of the second memory location by an inverse of the first number and storing the result in the first memory location;
• and
• if the corresponding bit of the fourth number is at a second state, multiplying the content of the second memory location by the first number and storing the result in the first memory location.