High-radix modular multiplication for cryptosystems

Two algorithms for modular multiplication with very large moduli are analyzed specifically for their applicability when a high radix is used for the multiplier. Both algorithms perform modulo reductions interleaved with the addition of partial products; one algorithm is using the standard residue system, whereas the other utilizes a nonstandard system using reductions modulo a power of the base. The emphasis is on situations, as in cryptosystems, where modular exponentiation is to be realized by many repeated modular multiplications on very large operands, e.g., for cryptosystems with key lengths of 500-1000 b