Protection of a modular exponentiation calculation

A device, comprising:

• one or more memories;
• and
• processing circuitry, which, in operation, performs a modular exponentiation calculation on a first number and an exponent, modulo a first modulo by, for each bit of the exponent:
• generating a random number;
• performing a modular multiplication of content of a first memory location by content of a second memory location, and placing a result in one of the first and second memory locations selected according to a state of the bit of the exponent;
• and
• performing a modular squaring of the content of one of the first and second memory locations selected according to the state of the exponent, and placing the result in this selected register or memory location, the multiplication and squaring being performed modulo a product of the first modulo and said random number.

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 exponentiation calculation on a first number and an exponent, modulo a first modulo by, for each bit of the exponent:
• generating a random number;
• performing a modular multiplication of content of a first memory location by content of a second memory location, and placing a result in one of the first and second memory locations selected according to a state of the bit of the exponent;
• and
• performing a modular squaring of the content of one of the first and second memory locations selected according to the state of the exponent, and placing the result in this selected register or memory location, the multiplication and squaring being performed modulo a product of the first modulo and said random number.

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 exponentiation calculation on a first number and an exponent, modulo a first modulo by, for each bit of the exponent:
• generating a random number;
• performing a modular multiplication of content of a first memory location by content of a second memory location, and placing a result in one of the first and second memory locations selected according to a state of the bit of the exponent;
• and
• performing a modular squaring of the content of one of the first and second memory locations selected according to the state of the exponent, and placing the result in this selected register or memory location, the multiplication and squaring operations being performed modulo a product of the first modulo and said random number.