Abstract
In this article, we present a new sequential multiplier for extended binary finite fields. Like its existing counterparts, the proposed multiplier has a linear complexity in flip-flop or temporary storage requirements, but a sub-linear complexity in gate counts. For the underlying polynomial multiplication, the proposed field multiplier relies on the Horner scheme.
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Daemen J., Rijmen V.: The Design of Rijndael: AES—The Advanced Encryption Standard. Springer, Verlag (2002)
Fan H., Hasan M.A.: A new approach to sub-quadratic space complexity parallel multipliers for extended binary fields. IEEE Trans. Comput. 56(2), 224–233 (2007)
Fan, H., Sun, J., Gu, M., Lam, K.-Y.: Overlap-free karatsuba-ofman polynomial multiplication algorithms. Cryptology ePrint Archive, Report 2007/393 (2007)
Guajardo G., Guneysu T., Paar C., Kumar S., Pelzl J.: Efficient hardware implementation of finite fields with applications to cryptography. Acta Applicandae Mathematicae 93(1–3), 75–118 (2006)
Hasan M.A., Wang M., Bhargava V.K.: A modified Massey-Omura parallel multiplier for a class of finite fields. IEEE Trans. Comput. 42(10), 1278–1280 (1993)
Koblitz N.: Elliptic curve cryptosystems. Math. Comput. 48, 203–209 (1987)
Leone, M.: A new low complexity parallel multiplier for a class of finite fields. In Proceedings of CHES’01, London, UK, pp. 160–170. Springer, Berlin (2001)
Mastrovito, E.: VLSI designs for multiplication over finite fields F (2m). In: 6th International Conference on Applied Algebra, Algebraic Algorithm and Error-Correcting Codes (AAECC-6), pp. 297–309 (1988)
Miller, V.: Use of elliptic curves in cryptography. In: Advances in Cryptology, proceeding’s of CRYPTO’85. LNCS, vol. 218, pp. 417–426. Springer, Berlin (1986)
Paar C.: A new architecture for a parallel finite field multiplier with low complexity based on composite fields. IEEE Trans. Comput. 45(7), 856–861 (1996)
Reyhani-Masoleh, A.: A new bit-serial architecture for field multiplication using polynomial bases. In: CHES 2008, pp. 300–314 (2008)
Song L., Parhi K.K.: Low-energy digit-serial/parallel finite field multipliers. J. VLSI Signal Process. Syst. 19(2), 149–166 (1998)
Sunar B., Koc C.: Mastrovito multiplier for all trinomials. IEEE Trans. Comput. 48(5), 522–527 (1999)
Wang M., Blake I.F.: Bit serial multiplication in finite fields. SIAM J. Discret. Math. 3(1), 140–148 (1990)
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Hasan, M.A., Negre, C. Sequential multiplier with sub-linear gate complexity. J Cryptogr Eng 2, 91–97 (2012). https://doi.org/10.1007/s13389-012-0035-1
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DOI: https://doi.org/10.1007/s13389-012-0035-1