Abstract

Two algorithms for modular multiplication with very large moduli are analyzed, in particular 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 non-standard system employing reductions modulo a power of the base. The emphasis is on situations -- like 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 bits. 1 Introduction Modular multiplication is a fundamental operation in the implementation of modular exponentiation as needed in many cryptosystems, e.g. the RSA two-key system [6] and in the recently proposed digital signature standard DSS [3]. In such applications very large moduli are needed to safeguard the information, which makes modular exponentiation a very ...

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