Abstract
In cryptographic applications, the use of normal bases to represent elements of the finite field GF(2m) is quite advantageous, especially for hardware implementation. In this article, we consider an important field operation, namely, multiplication which is used in many cryptographic functions. We present a class of algorithms for normal basis multiplication in GF(2m). Our proposed multiplication algorithm for composite finite fields requires significantly lower number of bit level operations and hence can reduce the space complexity of cryptographic systems when implemented in hardware.
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References
M. A. Hasan, M. Z. Wang, and V. K. Bhargava, “A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields,” IEEE Transactions on Computers, vol. 42, no. 10, pp. 1278–1280, Oct. 1993. 213, 213, 215, 219, 219
C. K. Koc and B. Sunar, “Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields,” IEEE Transactions on Computers, vol. 47, no. 3, pp. 353–356, March 1998. 219, 219
Chung-Chin Lu, “A Search of Minimal Key Functions for Normal Basis Multipliers,” IEEE Transactions on Computers, vol. 46, no. 5, pp. 588–592, May 1997. 213, 222
S. D. Galbraith and N. P. Smart, “A Cryptographic Application of Weil Descent,” in Proceedings of Cryptography and Coding, LNCS 1764, pp. 191–200, Springer-Verlag, 1999. 220
J. L. Massey and J. K. Omura, “Computational Method and Apparatus for Finite Field Arithmetic,” US Patent No. 4,587,627, 1986. 213
A. J. Menezes, I. F. Blake, X. Gao, R. C. Mullin, S. A. Vanstone, and T. Yaghoobian, Applications of Finite Fields, Kluwer Academic Publishers, 1993. 218
R. C. Mullin, I. M. Onyszchuk, S. A. Vanstone, and R. M. Wilson, “Optimal normal bases in GF(p n),” Discrete Applied Mathematics, vol. 22, pp. 149–161, 1988/1989. 213, 213, 215, 218, 222
A. Reyhani-Masoleh and M. A. Hasan, “A Reduced Redundancy Massey-Omura Parallel Multiplier over GF(2 m),” in Proceedings of the 20 th Biennial Symposium on Communications, pp. 308–312, Kingston, Ontario, Canada, May 2000. 213, 213, 217, 217, 217, 217, 217, 219, 219, 223, 223
J. E. Seguin, “Low complexity normal bases,” Discrete Applied Mathematics, vol. 28, pp. 309–312, 1990. 220
P. K. S. Wah and M. Z. Wang, “Realization and application of the Massey-Omura lock,” presented at the IEEE Int. Zurich Seminar on Digital Communications, pp. 175–182, 1984. 213, 213, 218
C. C. Wang, T. K. Truong, H. M. Shao, L. J. Deutsch, J. K. Omura and I. S. Reed, “VLSI Architectures for Computing Multiplications and Inverses in GF(2 m),” IEEE Transactions on Computers, vol. 34, no. 8, pp. 709–716, Aug. 1985. 213, 217, 217, 217, 219, 219, 223, 223
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Reyhani-Masoleh, A., Hasan, M. (2000). On Efficient Normal Basis Multiplication. In: Roy, B., Okamoto, E. (eds) Progress in Cryptology —INDOCRYPT 2000. INDOCRYPT 2000. Lecture Notes in Computer Science, vol 1977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44495-5_19
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DOI: https://doi.org/10.1007/3-540-44495-5_19
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