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Paper 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.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Preprint. MINOR revision.
Keywords
Quantum ComputersMontgomery MultiplicationBinary Field
Contact author(s)
hwajeong84 @ gmail com,starj1023 @ gmail com,waikonglee @ gachon ac kr,huzhi_math @ csu edu cn
History
2021-07-22: received
Short URL
https://ia.cr/2021/980
License
Creative Commons Attribution
CC BY
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