Cryptology ePrint Archive: Report 2017/064

Fast Montgomery-like Square Root Computation over $GF(2^m)$ for All Trinomials

Yin Li and Yu Zhang

Abstract: This letter is concerned with an extension of square root computation over $GF(2^m)$ defined by irreducible trinomials. We introduce a new type of Montgomery-like square root formulae, which is more efficient compared with classic square root operation. By choosing proper Montgomery factor regarding to different types of trinomials, the space and time complexities of our proposal outperform or match the best results. Furthermore, a practical application of the Montgomery-like square root in exponentiation computation is also presented.

Category / Keywords: foundations / finite field, square root

Date: received 30 Jan 2017, last revised 9 Aug 2017

Contact author: yunfeiyangli at gmail com

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Version: 20170809:231215 (All versions of this report)

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