Recent results on modular multiplications for smart cards

Abstract

In most currently used public-key cryptographic systems, including those based on the difficulty to either factorize large numbers like the RSA [RSA78] or to extract a discrete logarithm of a large number [Elg85,DH76,US 94], the most time consuming part is modular exponentiation. The base of this computation is modular multiplication. We demonstrate the ability to implement very efficiently public-key crypto- graphic algorithms on nearly standard processors. Furthermore, as our study is also oriented to smart cards, we focus on algorithms minimizing the RAM needed for the computations as well as the ROM code.