R. Beguenane, Jean-Luc Beuchat, J. Muller, S. Simard
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Public key cryptography often involves modular multiplication of large operands (160 up to 2048 bits). Several researchers have proposed iterative algorithms whose internal data are carry-save numbers. This number system is unfortunately not well suited to today’s Field Programmable Gate Arrays (FPGAs) embedding dedicated carry logic. We propose to perform modular multiplication in a high-radix carry-save number system, where the sum bit of the well-known carry-save representation is replaced by a sum word. Two digits are then added by means of a small Carry-Ripple Adder (CRA). The originality of our approach is to analyze the modulus in order to select the most efficient high-radix carry-save representation.
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