Improved Three-Way Split Formulas for Binary Polynomial Multiplication
In this paper we deal with 3-way split formulas for binary field multiplication with five recursive multiplications of smaller sizes. We first recall the formula proposed by Bernstein at CRYPTO 2009 and derive the complexity of a parallel multiplier based on this formula. We then propose a new set of 3-way split formulas with five recursive multiplications based on field extension. We evaluate their complexities and provide a comparison.
KeywordsCritical Path Polynomial Multiplication Elliptic Curve Cryptography Inductive Relation Arithmetic Complexity
- 2.Cenk, M., Koç, Ç., Özbudak, F.: Polynomial Multiplication over Finite Fields Using Field Extensions and Interpolation. In: 19th IEEE Symposium on Computer Arithmetic, ARITH 2009, pp. 84–91 (2009)Google Scholar
- 5.Fan, H., Sun, J., Gu, M., Lam, K.-Y.: Overlap-free Karatsuba-Ofman Polynomial Multiplication Algorithm (May 2007)Google Scholar
- 6.Karatsuba, A.A.: The Complexity of Computations. In: Proceedings of the Steklov Institute of Mathematics, vol. 211, pp. 169–183 (1995)Google Scholar
- 9.Miller, V.: Use of Elliptic Curves in Cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)Google Scholar