Computer Science

Computer Science ›› 2024, Vol. 51 ›› Issue (6A): 230900051-6.doi: 10.11896/jsjkx.230900051

• Information Security • Previous Articles     Next Articles

Quantum Circuit Optimization of Camellia Cryptographic Algorithm S-box

LYU Yi1, LUO Qingbin1,2, LI Qiang1, ZHENG Yuanmeng3   

  1. 1 College of Intelligent Science and Engineering,Hubei Minzu University,Enshi,Hubei 445000,China
    2 School of Information and Software,University of Electronic Science and Technology of China,Chengdu 610054,China
    3 School of Mathematics and Statistics,Hubei Minzu University,Enshi,Hubei 445000,China
  • Published:2024-06-06
  • About author:LYU Yi,born in 1997,postgraduate.His main research interests include quantum circuits and security analysis.
    LUO Qingbin,born in 1987,Ph.D.His main research interests include quantum computing and quantum cryptography.
  • Supported by:
    National Natural Science Foundation of China(62262020),Hubei Provincial Natural Science Foundation(2020CFB326) and Hubei Minzu University Graduate Innovation Project(MYK2023074).

PDF (PC)

278

Abstract: S-box is an important nonlinear component of Camellia cryptographic algorithm.In this paper,Toffoli gate,CNOT gate and NOT gate are used to construct the quantum circuit of Camellia cryptographic algorithm S box.In order to reduce the computational complexity,according to the algebraic expression of the S-box,the multiplication inversion operation in the finite domain GF(28)isisomorphic to the operation in the complex domain GF((24)2,and finally the quantum circuit diagram of Camellia cipher algorithm S box is synthesized.In optimization,the affine matrix,isomorphic matrix and a group of matrices corresponding to CNOT gates are first multiplied and then synthesized,and the quantum circuit of multiplication inversion in GF((24)2 is optimized using DORCIS tool,and the quantum circuit of matrix operation is optimized using W-Type algorithm.The resulting quantum circuit of the S-box uses only 20 qubits,52 Toffoli gates,178 CNOT gates,and 13 NOT gates,Toffoli-depth is 40,with a circuit depth of 130.The correctness of the quantum circuit is verified by IBM’s Aer simulator.Compared with the existing results,the quantum resources used in this paper are further reduced.

Key words: Quantum circuit, Camellia, S-box, Composite field

CLC Number: 

  • TP309
[1]BENNETT C H.Logical Reversibility of Computation[J].IBM Journal of Research and Development,1973,17(6):525-532.
[2]SARAVANAN P,KALPANA P.Novel Reversible Design ofAdvanced Encryption Standard Cryptographic Algorithm for Wireless Sensor Networks[J].Wireless Personal Communications,2018,100(4):1427-1458.
[3]FIPS 197.Advanced Encryption Standard(AES)[S].Gaithersburg,NIST,2001.
[4]LIN D,XIANG Z,XU R,et al.Optimized Quantum Implementation of AES[J].arXiv:2109.12354,2021.
[5]LI Z,GAO F,QIN S,et al.New record in the number of qubits for a quantum implementation of AES[J].Frontiers in Physics,2023,11:1171753.
[6]JAQUES S.Implementing Grover Oracles for Quantum KeySearch on AES and LowMC[J].arXiv:1910.01700,2019.
[7]LI Z,CAI B,SUN H,et al.Novel quantum circuit implementation of Advanced Encryption Standard with low costs[J].Science China Physics,Mechanics & Astronomy,2022,65(9),290311.
[8]HUANG Z,SUN S.Synthesizing Quantum Circuits of AES with Lower T-depth and Less Qubits[M]//Advances in Cryptology-ASIACRYPT.Cham:Springer,2022:614-644.
[9]FOWLER A G.Time-optimal quantum computation[J].arXiv:1210.4626,2013.
[10]AOKI K,ICHIKAWA T,KANDA M,et al.Camel lia:a 128-bit block cipher suitable for multiple platforms-design and analysis[C]//Proceedings of the 7th Annual International Workshop.Waterloo:Springer,2000:39-56.
[11]ZOU J,WEI Z,SUN S,et al.Some efficient quantum circuit implementations of Camellia[J].Quantum Information Processing,2022,21(4):131.
[12]LI Z Q,GAO F,QIN S J,et al.Quantum circuit for implementing Camellia S-box with low costs[J].Science China Physics,Mechanics & Astronomy,2023,53(4):21-29.
[13]XIANG Z,ZENG X,LIN D,et al.Optimizing Imple mentations of Linear Layers[J].IACR Trans.Symm.Cryptol.,2020(2):120-145.
[14]ROMAN S.Field Extensions[M]//Graduate Texts in Mathematics:Field Theory.New York:Springer,1995:39-59.
[15]LUO Q B,LI X Y,YAGN G W,et al.Quantum Cir cuit Implementation of S-box for SM4 Cryptographic Algorithm Based on Composite Field Arithmetic[J].Journal of University of Electronic Science and Technology of China,2022,50(6):820-826.
[16]LI Z Q,CAI B B,SUN H W,et al.Novel quantum circuit implementation of Advanced Encryption Standard with low costs[J].Chinese Science:Physics,Mechanics and Astronomy,2022(9):65.
[17]ALMAZROOIE M,ABDULLAH R,SAMSUDIN A,et al.Quantum Grover Attack on the Simplified-AES[C]//Proceedings of the 2018 7th International Conference on Software and Computer Applications.Kuantan Malaysia:ACM,2018:204-211.
[18]SARAVANAN P,KALPANA P.Novel Reversible Design ofAdvanced Encryption Standard Cryptographic Algorithm for Wireless Sensor Networks[J].Wireless Personal Communications,2018,100(4):1427-1458.
[19]WANG Z G,WEI S J,LONG G L.A quantum circuit design of AES requiring fewer quantumqubits and gate operations[J].Front Phys,2022,17:41501
[20]BOYAR J,PERALTA R.A New Combinational Logic Minimization Technique with Applications to Cryptology[C]//Experimental Algorithms[M].Berlin:Springer,2010:178-189.
[21]DASU V A,BAKSI A,SARKAR S,et al.LIGHTER-R:Optimized Reversible Circuit Implementation For SBoxes[C]//2019 32nd IEEE International System-on-Chip Conference(SOCC).Singapore:IEEE,2019:260-265.
[22]CHUN M,BAKSI A,CHATTOPADHYAY A.DORCIS:Depth Optimized Quantum Implementation of Substitution Boxes[EB/OL].(2023-02-25).https://eprint.iacr.org/2023/286.
[1] LIU Xiaonan, LIU Zhengyu, XIE Haoshan, ZHAO Chenyan. Solving Graph Coloring Problem Based on Grover Algorithm [J]. Computer Science, 2023, 50(6): 351-357.
[2] ZHAO Geng, GAO Shirui, MA Yingjie, DONG Youheng. Design of Dynamic S-box Based on Anti-degradation Chaotic System and Elementary Cellular Automata [J]. Computer Science, 2023, 50(11): 333-339.
[3] LIU Jian-mei, WANG Hong, MA Zhi. Optimization for Shor's Integer Factorization Algorithm Circuit [J]. Computer Science, 2022, 49(6A): 649-653.
[4] LU Yao, CHEN Kai-yan, WANG Yin-long and SHANG Qian-yi. L3 Cache Attack Against Last Round of Encryption AES Table Lookup Method [J]. Computer Science, 2020, 47(6A): 375-380.
[5] HAN Yu, ZHANG Wen-zheng, DONG Xin-feng. Design and Analysis of Trapdoor S-Box Based on Linear Partition [J]. Computer Science, 2020, 47(11A): 368-372.
[6] LIANG Yan-hui, LI Guo-dong, WANG Ai-yan. Frequency Domain Adaptive Image Encryption Algorithm Based on Fractional Order Chen Hyperchaos [J]. Computer Science, 2019, 46(11A): 488-492.
[7] LIANG Yan-hui, LI Guo-dong. Image Encryption Algorithm of Chaotic Cellular Automata Based on Fractional Hyperchaos [J]. Computer Science, 2019, 46(11A): 502-506.
[8] ZHANG Li, WEI Hong-ru. Improved Higher-order Meet-in-the-Middle Attack on Camellia-256 [J]. Computer Science, 2019, 46(11): 119-122.
[9] DING Jie, SHI Hui, GONG Jing and DENG Yuan-qing. Design and Characteristic Study on Fast Stream Cipher Algorithm Based on Camellia [J]. Computer Science, 2017, 44(8): 146-150.
[10] CAO Xiao-mei, CHEN Hai-shan and WANG Shao-hui. Method to Construct Secure S-boxes Based on Multimap [J]. Computer Science, 2017, 44(7): 107-110.
[11] FAN Fu-you, YANG Guo-wu, ZHANG Yan and YANG Gang. Three-valued Quantum Elementary and Implementation of Quantum Fourier Transform Circuit [J]. Computer Science, 2015, 42(7): 57-61.
[12] QIU Feng-pin and WEI Hong-ru. Impossible Differential Cryptanalysis of CLEFIA-128 [J]. Computer Science, 2015, 42(11): 208-211.
[13] YIN Guang-li and WEI Hong-ru. Impossible Differential Cryptanalysis of CLEFIA [J]. Computer Science, 2014, 41(Z6): 352-356.
[14] FAN Fu-you,YANG Guo-wu,LI Xiao-yu and LUO Qing-bin. Realization of Toffoli Gate Only Using CNOT Gate in Hybrid Multi-value Reversible Logic [J]. Computer Science, 2014, 41(8): 115-117.
[15] LUO Qing-bin,YANG Guo-wu,SHAO Yuan-hua and FAN Fu-you. Judgment of NP-NP Equivalence for 3-bit Reversible Logic Functions via Fixed Polarity Reed-muller Forms [J]. Computer Science, 2013, 40(10): 218-220.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
渝ICP备16013121号-4
Add:18# Honghu West Rd., Yubei ,Chongqing,China    Post Code: 401121
Tel: 023-63500828/023-67039612/023-67039623
E-mail: jsjkx12@163.com
Powered by Beijing Magtech Co., Ltd.