TY - GEN
T1 - Efficient Quantum Circuit of Proth Number Modular Multiplication
AU - Jeon, Chanho
AU - Heo, Donghoe
AU - Lee, Myeong Hoon
AU - Kim, Sunyeop
AU - Hong, Seokhie
N1 - Funding Information:
Acknowledgments. This work was supported by Institute for Information and communications Technology Planning and Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity).
Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - The efficient quantum circuit of Post Quantum Cryptography (PQC) impacts both performance and security because Grover’s algorithm, upon which various attacks are based, also requires a circuit. Therefore, the implementation of cryptographic operations in a quantum environment is considered to be one of the main concerns for PQC. Most lattice-based cryptography schemes employ Number Theoretic Transform (NTT). Moreover, NTT can be efficiently implemented using the modulus p= k· 2 m+ 1, called Proth number, and there is a need to elaborate on the quantum circuit for a modular multiplication over p. However, to the best of our knowledge, only quantum circuits for modular multiplication of the general odd modulus have been proposed, and quantum circuits for specific odd modulus are not presented. Thus, this paper addresses this issue and presents a new optimized quantum circuit for Proth Number Modular Multiplication (PNMM) which is faster than Rines et al.’s modular multiplication circuit. According to the evaluation with commonly used modulus parameters for lattice-based cryptography, our circuit requires an approximately 22%–45% less T-depth than that of Rines et al.’s.
AB - The efficient quantum circuit of Post Quantum Cryptography (PQC) impacts both performance and security because Grover’s algorithm, upon which various attacks are based, also requires a circuit. Therefore, the implementation of cryptographic operations in a quantum environment is considered to be one of the main concerns for PQC. Most lattice-based cryptography schemes employ Number Theoretic Transform (NTT). Moreover, NTT can be efficiently implemented using the modulus p= k· 2 m+ 1, called Proth number, and there is a need to elaborate on the quantum circuit for a modular multiplication over p. However, to the best of our knowledge, only quantum circuits for modular multiplication of the general odd modulus have been proposed, and quantum circuits for specific odd modulus are not presented. Thus, this paper addresses this issue and presents a new optimized quantum circuit for Proth Number Modular Multiplication (PNMM) which is faster than Rines et al.’s modular multiplication circuit. According to the evaluation with commonly used modulus parameters for lattice-based cryptography, our circuit requires an approximately 22%–45% less T-depth than that of Rines et al.’s.
KW - CDKM adder
KW - Lattice
KW - Moduluar multiplication
KW - Number theoretic transform
KW - Proth number
KW - Quantum circuit
UR - http://www.scopus.com/inward/record.url?scp=85135170675&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-08896-4_21
DO - 10.1007/978-3-031-08896-4_21
M3 - Conference contribution
AN - SCOPUS:85135170675
SN - 9783031088957
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 403
EP - 417
BT - Information Security and Cryptology – ICISC 2021 - 24th International Conference, Revised Selected Papers
A2 - Park, Jong Hwan
A2 - Seo, Seung-Hyun
PB - Springer Science and Business Media Deutschland GmbH
T2 - 24th International Conference on Information Security and Cryptology, ICISC 2021
Y2 - 1 December 2021 through 3 December 2021
ER -