Introduction to finite fields and their applications
Introduction to finite fields and their applications
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
IEEE Transactions on Computers - Special issue on computer arithmetic
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
IEEE Transactions on Computers
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
VLSI performance evaluation and analysis of systolic and semisystolic finite field multipliers
ACSAC'05 Proceedings of the 10th Asia-Pacific conference on Advances in Computer Systems Architecture
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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.