Uniform Montgomery multiplier

Abstract

As the importance of the modular arithmetic in public-key systems remains, the pursuits of sophisticated cryptographic engineering continue in designing improved architectures for realizing modular arithmetic. This sophistication does not only involve the high-performance, low-power or area-aware optimizations, but also includes secure or hardened realizations, immune against the so-called side-channel attacks. Among these, simple power analysis attack (SPA) requiring only one or a few power traces of the cryptographic activity is considered as the most dangerous treat for security. This study concentrates on implementing SPA-resistant Montgomery multipliers which are the key ingredients in designing substantial cryptosystems. We introduce new encoding schemes that allow multiplication with the operands having no zero digits. Naturally, such encodings result in a homogeneous multiplication in which accumulation needs equivalent computational work. Moreover, in order to layout more secure and timing-independent multipliers, we impose the I/O requirements that resulting Montgomery multipliers do not need extra final reduction. Finally, as proposed methods allow architectures suitable for word serial processing, a memory performance trade-off is possible for constraint environments.