## Cryptology ePrint Archive: Report 2021/980

Binary Field Montgomery Multiplication on Quantum Computers

Kyoungbae Jang and Gyeong Ju Song and Hyunji Kim and Hyeokdong Kwon and Wai-Kong Lee and Zhi Hu and Hwajeong Seo

Abstract: Optimizing arithmetic operations into quantum circuits to utilize quantum algorithms, such as the Shor algorithm and Grover search algorithm for cryptanalysis, is an active research field in cryptography implementation. In particular, reducing quantum resources is important for efficient implementation. In this paper, binary field ($GF(2^n)$) Montgomery multiplication in quantum circuits is presented. We utilize the bit-level Montgomery algorithm to efficiently compute the Montgomery product $C = A \cdot B \cdot r^{-1}$ in the binary field $GF(2^n)$. Additionally, we also present an efficient Montgomery multiplication quantum circuit in the case where the modulus of $GF(2^n)$ is specified.

Category / Keywords: implementation / Quantum Computers, Montgomery Multiplication, Binary Field

Date: received 21 Jul 2021

Contact author: hwajeong84 at gmail com, starj1023 at gmail com, waikonglee at gachon ac kr, huzhi_math at csu edu cn

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/980

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