论文信息 - Mastrovito Multiplier for General Irreducible Polynomials

Mastrovito Multiplier for General Irreducible Polynomials

We present a new formulation of the Mastrovito multiplication matrix and an architecture for the multiplication operation in the field GF(2m) generated by an arbitrary irreducible polynomial. We study in detail several specific types of irreducible polynomials, e.g., trinomials, all-one-polynomials, and equally-spaced-polynomials, and obtain the time and space complexity of these designs. Particular examples, illustrating the properties of the proposed architecture, are also given. The complexity results established in this paper match the best complexity results known to date. The most important new result is the space complexity of the Mastrovito multiplier for an equally-spaced-polynomial, which is found as (m2 - Δ) XOR gates and m2 AND gates, where Δ is the spacing factor.

Çetin Kaya Koç | Alper Halbutogullari | Ç. Koç | A. Halbutogullari

[1] Toshiya Itoh,et al. Structure of Parallel Multipliers for a Class of Fields GF(2^m) , 1989, Inf. Comput..

[2] Berk Sunar,et al. Mastrovito Multiplier for All Trinomials , 1999, IEEE Trans. Computers.

[3] Christof Paar,et al. chitecture for a Parallel Finite lier with Low Complexity Based on Composite Fields Fi , 1996 .

[4] B. Sunar,et al. Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[5] Çetin Kaya Koç,et al. Mastrovito Multiplier for General Irreducible Polynomials , 2000, IEEE Trans. Computers.

[6] Jacques Calmet,et al. Algebraic Algorithms and Error-Correcting Codes , 1985, Lecture Notes in Computer Science.

[7] Alfred Menezes,et al. Elliptic curve public key cryptosystems , 1993, The Kluwer international series in engineering and computer science.

[8] A. Menezes,et al. Applications of Finite Fields , 1992 .

[9] Edoardo D. Mastrovito,et al. VLSI Designs for Multiplication over Finite Fields GF (2m) , 1988, AAECC.

[10] Harald Niederreiter,et al. Introduction to finite fields and their applications: Preface , 1994 .

[11] Gene H. Golub,et al. Matrix computations , 1983 .

[12] Vijay K. Bhargava,et al. Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF(2^m) , 1992, IEEE Trans. Computers.