Protection of a modular exponentiation calculation by addition of a random quantity

A method, comprising:

• receiving a digital value, the digital value being a message to be used in a calculation;
• protecting the calculation with a modular exponentiation of the digital value, the protecting including:
• initializing a first variable with a sum of a random value and 1;
• initializing a second variable with a product of the digital value and the random value;
• initializing a third variable with the digital value;
• and
• performing a plurality of iterations, each of the plurality of iterations comprising updating the first variable, the updating comprising:
• multiplying a first value of the first variable by a value of the third variable, and
• subtracting from a result of step (a) a value of the second variable and adding the random value to a result of the subtracting;
• and
• performing the calculation using the result of the modular exponentiation of the digital value to obfuscate secret data.

An electronic circuit, comprising:

• circuitry configured to receive a digital value, the digital value being a message to be used in cryptographic operations;
• circuitry configured to generate at least one random value;
• circuitry configured to iterate;
• circuitry to protect the cryptographic operations using a modular exponentiation of the digital value, the circuitry to protect the cryptographic operations configured to:
• initialize a first variable with a sum of the random value and 1;
• initialize a second variable with a product of the digital value and the random value;
• initialize a third variable with the digital value;
• and
• perform a plurality of iterations, each of the plurality of iterations comprising updating the first variable, the updating comprising:
• multiplying a first value of the first variable by a value of the third variable, and
• subtracting from a result of step (a) a value of the second variable and adding the random value;
• and
• circuitry configured to obfuscate secret data with a cryptographic operation using the result of the modular exponentiation of the digital value.