We propose a new algorithm for fast multiplication of large integers having a precision of 2 k computer words, where k is an integer. The algorithm is derived from the Karatsuba-Ofman Algorithm and has the same asymptotic complexity. However, the running time of the new algorithm is slightly better, and it makes one third as many recursive calls.
Practical implementations of cryptographic algorithms are vulnerable to side-channel analysis and fault attacks. Thus, some masking and fault detection algorithms must be incorporated into these implementations. These additions further increase the complexity of the cryptographic devices which already need to perform computationally-intensive operations.… (More)