Consecutive Operand-Caching Method for Multiprecision Multiplication, Revisited

Multiprecision multiplication is the most expensive operation in public key-based cryptography. Therefore, many multiplication methods have been studied intensively for several decades. In Workshop on Cryptographic Hardware and Embedded Systems 2011 (CHES2011), a novel multiplication method called 'operand caching' was proposed. This method reduces the number of required load instructions by caching the operands. However, it does not provide full operand caching when changing the row of partial products. To overcome this problem, a novel method, that is, 'consecutive operand caching' was proposed in Workshop on Information Security Applications 2012 (WISA2012). It divides a multiplication structure into partial products and reconstructs them to share common operands between previous and next partial products. However, there is still room for improvement; therefore, we propose a finely designed operand-caching mode to minimize useless memory accesses when the first row is changed. Finally, we reduce the number of memory access instructions and boost the speed of the overall multiprecision multiplication for public key cryptography.