Realizing arbitrary-precision modular multiplication with a fixed-precision multiplier datapath

Within the context of cryptographic hardware, the term scalability refers to the ability to process operands of any size, regardless of the precision of the underlying data path or registers. In this paper we present a simple yet effective technique for increasing the scalability of a fixed-precision Montgomery multiplier. Our idea is to extend the datapath of a Montgomery multiplier in such a way that it can also perform an ordinary multiplication of two n-bit operands (without modular reduction), yielding a 2n-bit result. This conventional (nxn->2n)-bit multiplication is then used as a “sub-routine” to realize arbitrary-precision Montgomery multiplication according to standard software algorithms such as Coarsely Integrated Operand Scanning (CIOS). We show that performing a 2n-bit modular multiplication on an n-bit multiplier can be done in 5n clock cycles, whereby we assume that the n-bit modular multiplication takes n cycles. Extending a Montgomery multiplier for this extra functionality requires just some minor modifications of the datapath and entails a slight increase in silicon area

Low-Cost Double-Size Modular Exponentiation or How to Stretch Your Cryptoprocessor

Public-key implementers often face strong hardware-related constraints. In particular, modular operations required in most cryptosystems generally constitute a computational bottleneck in smart-card applications. This paper adresses the size limitation of arithmetic coprocessors and introduces new techniques that virtually increase their computational capacities. We suspect our algorithm to be nearly optimal and challenge the cryptographic community for better results

Low-Cost Double-Size Modular Exponentiation or How to Stretch Your Cryptoprocessor

This paper adresses the size limitation of arithmetic coprocessors and introduces new techniques that virtually increase their computational capacities. We suspect our algorithm to be nearly optimal and challenge the cryptographic community for better results. 1.1 Introductio