Multiplicative blinding for cryptographic operations

A system comprising:

• a memory;
• and
• a processor of an integrated circuit operatively coupled with the memory and to:
• receive an input for a cryptographic operation;
• generate a random number;
• perform an exponentiation operation corresponding to the random number raised to an exponent value of a public key that is associated with the cryptographic operation;
• receive a second exponent value from a private key that corresponds to the public key;
• decrement the second exponent value from the private key to generate a decremented private key exponent value;
• perform a multiplication operation with the random number raised to the exponent value and the input to generate a first value;
• and
• perform the cryptographic operation based on the first value and the decremented private key exponent value, wherein the cryptographic operation corresponds to a generation or a verification of a cryptographic signature.

A non-transitory computer readable medium including data that, when accessed by a processor of an integrated circuit, cause the processor to perform operations comprising:

• receiving a value corresponding to an input for a cryptographic operation;
• blinding the value by multiplying the value based on an exponentiation of a random number raised to an exponent value that is associated with a public key;
• receiving a second exponent value from a private key that corresponds to the public key;
• decrementing the second exponent value from the private key to generate a decremented private key exponent value;
• and
• performing the cryptographic operation based on the blinded value and the decremented private key exponent value, wherein the cryptographic operation corresponds to an encryption operation or a decryption operation.