Cryptology ePrint Archive: Report 2021/185

No Silver Bullet: Optimized Montgomery Multiplication on Various 64-bit ARM Platforms

Hwajeong Seo and Pakize Sanal and Wai-Kong Lee and Reza Azarderakhsh

Abstract: In this paper, we firstly presented optimized implementations of Montgomery multiplication on 64-bit ARM processors by taking advantages of Karatsuba algorithm and efficient multiplication instruction sets for ARM64 architectures. The implementation of Montgomery multiplication improved the performance of public key cryptography (e.g. CSIDH, ECC, and RSA) implementations on ARM64 architectures, directly. Last but not least, the performance of Karatsuba algorithm does not ensure the fastest speed record, while it is determined by the clock cycles per multiplication instruction of target ARM architectures. In particular, recent Apple processors based on ARM64 architecture show lower cycles per instruction of multiplication than that of ARM Cortex-A series. For this reason, the schoolbook method shows much better performance than the sophisticated Karatsuba algorithm on Apple processors. With this observation, we can determine the proper approach for multiplication of cryptography library (e.g. MS-SIDH) on Apple processors and ARM Cortex-A processors.

Category / Keywords: implementation / Montogmery Multiplication, ARM64, Public Key Cryptography , Software Implementation

Date: received 19 Feb 2021

Contact author: hwajeong84 at gmail com,psanal2018@fau edu,waikonglee@gachon ac kr,razarderakhsh@fau edu

Available format(s): PDF | BibTeX Citation

Version: 20210220:174110 (All versions of this report)

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