Protecting the input/output of modular encoded white-box RSA/ECC

A computer system implemented method of obscuring an input and output of a modular exponentiation function, the method comprising:

• receiving, by a processor of the computer system, modular exponentiation parameters including an exponent e having N bits and a modulus m;
• generating randomly, by the processor, a pre-multiplier;
• calculating, by the processor, a post-multiplier y=x−emod m, where y is the post-multiplier, x is the pre-multiplier, and the exponent e is a secret key,
• multiplying, by the processor, the input to the modular exponentiation function by the pre-multiplier;
• performing, by the processor, the modular exponentiation function;
• and
• multiplying, by the processor, the output of the modular exponentiation function by the post-multiplier,
• wherein the pre-multiplier and the post-multiplier are both split variable encoded values, wherein starting the modular exponentiation function with a pre-multiplier and ending the modular exponentiation function with a post-multiplier prevents the exponent e from appearing in isolation in a white-box implementation in the computer system, making the computer system more secure, and wherein multiplying the input to the modular exponentiation function by the pre-multiplier, performing the modular exponentiation function, and multiplying the output of the modular exponentiation function by the post-multiplier are split variable operations.