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Up to 8k-bit Modular Montgomery Multiplication in Residue Number Systems with Fast 16-bit Residue Channels by Zabihollah Ahmadpour; Ghassem Jaberipur is a Computer Science article available to read on EtoBox.

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Hardware realization of public-key cryptosystems often entails Montgomery modular multiplication (MMM), which is more efficient in residue number systems (RNS). A large pool of co-prime moduli allows for higher number of dynamically changeable moduli-set pairs for the required base extension, leading to ultra-wide key-lengths to accommodate the indispensable resistance to differential power-analysis (DPA) attacks. The moduli are often of the form 2 r -δ, where r denotes the width of residue channels. In a previous relevant RNS MMM design, with r = 64, probability of a successful DPA attack is less than 2 -66 , where efficient arithmetic is obtained only for a limited set of moduli that are insufficient for key-lengths over 1024 bits. Here we propose a free-δ RNS MMM scheme, for up-to 8192-bit key-lengths and fast 16-bit residue channels, based on the proposed δindependent modulo-(2 r -δ) adders and multipliers. Moreover, we propose an especial method for moduli selection that is required for base extension, leading to the same aforementioned DPA-resistance measure and much lower measures for keylengths over 1024. The implementation results show 82%, 69%, 44% less RSA delay, for key

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Author

Zabihollah Ahmadpour; Ghassem Jaberipur

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Published

2021

Language

EN

Field

Computer Science (Physical Sciences)