Paper 2021/980
Binary Field Montgomery Multiplication on Quantum Computers
Kyoungbae Jang, Gyeong Ju Song, Hyunji Kim, Hyeokdong Kwon, Wai-Kong Lee, 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
-
CC BY
BibTeX
@misc{cryptoeprint:2021/980,
author = {Kyoungbae Jang and Gyeong Ju Song and Hyunji Kim and Hyeokdong Kwon and Wai-Kong Lee and Zhi Hu and Hwajeong Seo},
title = {Binary Field Montgomery Multiplication on Quantum Computers},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/980},
year = {2021},
url = {https://eprint.iacr.org/2021/980}
}
