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http://dx.doi.org/10.13089/JKIISC.2014.24.1.41

Fault Detection Architecture of the Field Multiplication Using Gaussian Normal Bases in GF(2n  

Kim, Chang Han (Semyung University)
Chang, Nam Su (Sejong Cyber University)
Park, Young Ho (Sejong Cyber University)
Publication Information
Journal of the Korea Institute of Information Security & Cryptology / v.24, no.1, 2014 , pp. 41-50 More about this Journal
Abstract
In this paper, we proposed an error detection in Gaussian normal basis multiplier over $GF(2^n)$. It is shown that by using parity prediction, error detection can be very simply constructed in hardware. The hardware overheads are only one AND gate, n+1 XOR gates, and one 1-bit register in serial multipliers, and so n AND gates, 2n-1 XOR gates in parallel multipliers. This method are detect in odd number of bit fault in C = AB.
Keywords
Finite Fields; Normal Basis; Multiplication; Error Detection;
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1 A.J. Menezes, I.F. Blake, X. Gao, R.C. Muliin, S.A. Vanstone, and T. Yaghoobian, "Applications of Finite Fields," Kluwer Academic Publishers, 1993.
2 R.Lidl and H. Niederreiter, " Introduction to finite fields and their applications," Cambridge University Press, Revised Edition, 1994.
3 National Institute for of Standards and Technology, "Digital Signature Standard," FIPS Publication 186-2, Jan. 2000.
4 IEEE Std. 1363-2000, "IEEE Standard Specifications for Public-key Cryptography," Jan. 2000.
5 E.R. Berlekamp, "Bit-Serial Reed-Solomon Encoders," IEEETrans. on info. Theory, vol. 28, pp. 869-874, Nov. 1982.   DOI
6 M. Joye and M. Tunstall, "Fault Analysis in Cryptography," Springer, 2012.
7 S. Fenn, M. Gossel, M. Benassia, and D. Taylor. "On-Line Error Detection for Bit-Serial Multipliers in $GF(2^m)$," Journal of Electronic Testing : Theory and Applications, vol. 13, pp. 29-40, Aug. 1998.   DOI
8 A. Reyhani-Masoleh and M.H. Hasan, "Fault Detection Architectures for Field Multiplication Using Polynomial Bases," IEEE Trans. computers Vol. 55, no. 9, pp. 1089-1103, Sep. 2006.
9 A. Reyhani-Masoleh, "Efficient Algorithms and Architecture for Finite Multiplication Using Gaussian Normal Bases," IEEE Trans. computers, vol. 55 no. 1, pp. 34-47, Jan. 2006.   DOI   ScienceOn
10 A. Hariri and A. Reyhani-Masoleh, "Fault Detection structures for the Montgomery Multiplication over Binary Extension Fields," 2007 Workshop on Fault and Tolerance in Cryptography, pp. 37-42, Sep. 2007.
11 C.W. Chiou, C.C. Chang, C.Y. Lee, and T.W. Hou, "Concurrent Error Detection and Correction in Gaussian Normal Basis Multiplier over $GF(2^m)$," IEEE Trans. computers Vol. 58, no. 6, pp. 851-857, June. 2009.   DOI
12 C.H. Kim, N.S. Chang and Y.I. Cho, "Modified Sequential Multipliers for Type-k Gaussian Normal Bases," MUE 2011, pp. 220-225, June. 2011.
13 S. Kwon, K. Gaj, C.H. Kim, and C.P. hong, "Efficient Linear Array for Multiplication in $GF(2^m)$ Using a Normal Basis for Elliptic Curve Cryptography," CHES 2004, LNCS 3156, pp. 76-91, 2004.
14 D.J. Yang, C.H. Kim, Y. Park, and J. Lim, "Modified Sequential Normal Basis Multipliers for Type II Optimal Normal Basis," ICCA 2005, LNCS 3481, pp. 647-656, 2005.
15 C.H. Kim, Y. Kim, S.Y. Ji and I. Park, "A New Parallel Multiplier for Type II Optimal Normal Basis," CIS 2006, pp.460-469, 2006.
16 C.H. kim and Y. Kim, "A parallel Architecture for Type k Gaussian Normal Basis Multiplier over $GF(2^n)$," The Workshop of 2005 International Conference on Computational Intelligence and Security, pp. 109-114, Dec. 2005.
17 A. Reyhani-Masoleh and M.H. Hasan, "A New Construction of Massey-Omura Parallel Multiplier over $GF(2^m)$," IEEE Trans. computers, Vol. 51, no. 5, pp. 512-520, May. 2002.
18 C.Y. Lee, C.W. Chiou, and J.M. Lin, "Concurrent Error Detection in a Polynomial Basis Multiplier over $GF(2^n)$," Journal of Electronic Testing: Theory and Applications, vol. 22, no. 2, pp. 143-150, Apr. 2006.   DOI   ScienceOn