Abstract
Hardware and algorithmic optimization techniques are presented to
the left-shift, right-shift, and the traditional Euclidean-modular
inverse algorithms. Theoretical arguments and extensive
simulations determined the resulting expected running time. On
many computational platforms these turn out to be the fastest
known algorithms for moderate operand lengths. They are based on
variants of Euclidean-type extended GCD algorithms. On the
considered computational platforms for operand lengths used in
cryptography, the fastest presented modular inverse algorithms
need about twice the time of modular multiplications, or
even less. Consequently, in elliptic curve cryptography delaying
modular divisions is slower (affine coordinates are the best) and
the RSA and ElGamal cryptosystems can be accelerated.