Abstract: The present disclosure provides a method for performing modular exponentiation. The method may include generating a first remainder (xp) based on an encrypted message (X) modulo a first prime number (p) and generating a second remainder (xq) based on the encrypted message (X) modulo a second prime number (q). The method may further include generating a third remainder (v1) based on the first remainder (xp) raised to a first private key number (d1) modulo the first prime number (p) and simultaneously generating a fourth remainder (v2) based on the second remainder (xq) raised to a second private key number (d2) modulo the second prime number (q). The method may also include subtracting the fourth remainder (v2) from the third remainder (v1) to yield a result (v1?v2) and multiplying the result (v1?v2) by a constant (c) to produce a second result.

Abstract: The present disclosure provides a system and method for performing carry/borrow handling. A method according to one embodiment may include generating a first result having a first carry or borrow from a first mathematical operation and storing the first carry or borrow and a first pointer address in a temporary register. The method may further include generating a second result having a second carry or borrow from a second mathematical operation and calling a subroutine configured to perform carry and borrow handling. The method may also include copying the first pointer address from the temporary register into a global variable. Of course, many alternatives, variations and modifications are possible without departing from this embodiment.