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An Efficient FPGA Implementation of ECC Modular Inversion over F256

Published: 16 March 2018 Publication History

Abstract

Elliptic Curve Cryptography (ECC) provides high security levels with shorter keys than other public-key cryptosystems such as RSA. Usually modular inversion operation is a choke point in realizing the public-key cryptosystem. Based on the Extended Euclidean Algorithm, this work proposes an efficient FPGA implementation of ECC modular inversion over F256. According to this proposed algorithm, one modular inversion requires 320 clock cycles with a maximum clock frequency of 144.011MHz on a Xilinx Virtex-7 FPGA device which gives a computation time of 2.22μs. On the other words, our scenario can perform 450 thousand times division operations in one second approximately. Compared to other available literature, our scheme presented in this paper provides a high performance FPGA implementation of 256-bit modular inversion over F256. This makes the elliptic curve cryptography have important practical value in hardware implementation.

References

[1]
N. Koblitz, A. Menezes, and S. Vanstone, "The state of elliptic curve cryptography,"Designs, Codes Cryptography, vol.19, pp.173--193,2000.
[2]
S. Ghosh, D. Mukhop adhyay, and D. Roychowdhury, "Petrel: Power and timing attack resistant elliptic curve scalar multiplier based on programmable GF(p) arithmetic unit,"Circuits and Systems I: Regular Papers, IEEE Transactions on, vol. 58, no. 8, pp. 1798--1812, Aug. 2011.
[3]
W. Dong-Mei, "A fast implementation of modular inversion over GF (2m) based on FPGA," 2010 2nd IEEE International Conference on Information Management and Engineering, Chengdu, 2010, pp. 465--468.
[4]
Gang Chen and Guoqiang Bai, "A high-performance el1iptic curve crypto graphic processor for general curves over GF(p) based on a Systolic arithmetic unit," IEEE Transactions on Circuits and Systems,vol. 54, no.5, May 2007.
[5]
J. W. Lee, S. C. Chung, H. C. Chang and C. Y. Lee, "Efficient Power-Analysis-Resistant Dual-Field Elliptic Curve Cryptographic Processor Using Heterogeneous Dual-Processing-Element Architecture," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 22, no. 1, pp. 49--61, Jan. 2014.
[6]
Suwen Yi, Wei Li and Zibin Dai, "A scalable and efficient hardware architecture for Montgomery modular division in dual field," 2016 10th IEEE International Conference on Anti-counterfeiting, Security, and Identification (ASID), Xiamen, 2016, pp. 34--38.
[7]
Z. Liu, D. Liu and X. Zou, "An Efficient and Flexible Hardware Implementation of the Dual-Field Elliptic Curve Cryptographic Processor," in IEEE Transactions on Industrial Electronics, vol. 64, no. 3, pp. 2353--2362, March 2017.
[8]
M. Kaihara and N. Takagi, "A Hardware algorithm for modular multiplication/division based on the extended Euclidean algorithm",IEICE Trans. Fundamentals, vol. E88-A, no. 12, pp.3610--3617, Dec.2005.
[9]
Chester Rebeiro, Debdeep Mukhopadhyay, "High speed compact elliptic curve cryptoprocessor for FPGA platforms", International Conference on Cryptology in India, pp. 376--388, 2008.
[10]
M. S. Hossain and Y. Kong, "High-Performance FPGA Implementation of Modular Inversion over F_256 for Elliptic Curve Cryptography," 2015 IEEE International Conference on Data Science and Data Intensive Systems, Sydney,NSW, 2015, pp. 169--174.
[11]
B.S. Kaliski, "The Montgomery inverse and its applications," in IEEE Transactions on Computers, vol. 44, no.8, pp.1064--1065, Aug 1995.
[12]
L. Li and S. Li, "High-Performance Pipelined Architecture of Elliptic Curve Scalar Multiplication Over GF(2m)," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 24, no. 4, pp. 1223--1232, April 2016.
[13]
Darrel Hankerson, Alfred J. Menezes, and Scott Vanstone. 2003. Guide to Elliptic Curve Cryptography. Springer-Verlag New York, Inc., Secaucus, NJ, USA.
[14]
Szu-Chi Chung, Jen-Wei Lee, Hsie-Chia Chang, and Chen- Yi Lee,. "A High-Performance Elliptic Curve Cryptographic Processor over GF(p) with SPA Resistance", 2012 IEEE International Symposium on Circuits and Systems. IEEE, 2012.
[15]
N. Shylashree, V. Sridhar and D. Patawardhan, "FPGA based efficient Elliptic curve cryptosystem processor for NIST 256 prime field," 2016 IEEE Region 10 Conference (TENCON), Singapore, 2016, pp. 194--199.
[16]
P. Choi, M. K. Lee, J. H. Kim and D. K. Kim, "Low-Complexity Elliptic Curve Cryptography Processor based on Configurable Partial Modular Reduction over NIST Prime Fields," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. PP, no. 99, pp. 1--1.
[17]
Huai. Yi-Hsu, An-Yeu. Wu and Jih-Chiang Yeo, "Area- etlicient VLSI design of Reed-Solomon decorder for IOGBase-LX4 optical communication systems," IEEE Transactions on Circuits and Systems-lI: Express Briefs,vo1.53, no.13, pp. 1245--1249, November 2006.

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  1. An Efficient FPGA Implementation of ECC Modular Inversion over F256

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    ICCSP 2018: Proceedings of the 2nd International Conference on Cryptography, Security and Privacy
    March 2018
    187 pages
    ISBN:9781450363617
    DOI:10.1145/3199478
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    • Wuhan Univ.: Wuhan University, China
    • University of Electronic Science and Technology of China: University of Electronic Science and Technology of China

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    Published: 16 March 2018

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    Author Tags

    1. Elliptic Curve Cryptography
    2. Extended Euclidean Algorithm
    3. FPGA
    4. modular inversion

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    • (2024)Protecting FPGA-Based Cryptohardware Implementations from Fault Attacks Using ADCsSensors10.3390/s2405159824:5(1598)Online publication date: 29-Feb-2024
    • (2023)Optimizing ECC Implementations Based on SoC-FPGA with Hardware Scheduling and Full Pipeline Multiplier for IoT PlatformsIntelligence of Things: Technologies and Applications10.1007/978-3-031-46573-4_28(299-309)Online publication date: 20-Oct-2023
    • (2022)Lightweight Architecture for Elliptic Curve Scalar Multiplication over Prime FieldElectronics10.3390/electronics1114223411:14(2234)Online publication date: 17-Jul-2022
    • (2021)A new DNA coding and hyperchaotic system based asymmetric image encryption algorithmMathematical Biosciences and Engineering10.3934/mbe.202119418:4(3887-3906)Online publication date: 2021
    • (2021)Design of a BIST implemented AES crypto-processor ASICPLOS ONE10.1371/journal.pone.025995616:11(e0259956)Online publication date: 16-Nov-2021
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    • (2021)Efficient FPGA Design of Exception-Free Generic Elliptic Curve CryptosystemsApplied Cryptography and Network Security10.1007/978-3-030-78372-3_15(393-414)Online publication date: 9-Jun-2021
    • (2020)Breaking Trivium Stream Cipher Implemented in ASIC Using Experimental Attacks and DFASensors10.3390/s2023690920:23(6909)Online publication date: 3-Dec-2020
    • (2020)An efficient hardware implementation of the elliptic curve cryptographic processor over prime field,International Journal of Circuit Theory and Applications10.1002/cta.275948:8(1256-1273)Online publication date: Mar-2020

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