Montgomery multiplication and squaring for Optimal Prime Fields. Issue 52 (July 2015)

• Record Type: Journal Article
• Authors: Seo, Hwajeong; Liu, Zhe; Nogami, Yasuyuki; Choi, Jongseok; Kim, Howon
• Is Part Of: Computers & security. Issue 52(2015)
• Page Start: 276
• Page End: 291
• Publication Date: 2015-07
• Subjects: Montgomery multiplication -- Optimal Prime Fields -- Embedded processors -- Public key cryptography -- Operand caching -- Consecutive operand caching -- Sliding block doubling; Computer security -- Periodicals; Electronic data processing departments -- Security measures -- Periodicals; 005.805
• DOI: 10.1016/j.cose.2015.03.005
• Languages: English
• ISSNs: 0167-4048

Abstract

Abstract: Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementations on resource-constraint embedded processors. In this paper, we revisit the efficient modular arithmetic over the special prime fields, and present improved implementations of modular multiplication and squaring for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) and Coarsely Integrated Sliding Block Doubling (OPF-CISBD) methods. The OPF-CIOC and OPF-CISBD methods follow the general ideas of (consecutive) operand caching and sliding block doubling techniques, respectively. The methods have been carefully optimized and redesigned for Montgomery multiplication and squaring in an integrated fashion. We then evaluate the practical performance of proposed methods on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC and OPF-CISBD methods outperform the previous best known results in ACNS'14 by a factor of 8% and 32%. Furthermore, our methods are implemented in a regular way which helps to reduce the leakage of side-channel information.