Finite field for scientists and engineers
Finite field for scientists and engineers
IEEE Transactions on Computers - Special issue on computer arithmetic
Designs, Codes and Cryptography
Finite field inversion over the dual basis
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
Fast Algorithms for Digital Signal Processing
Fast Algorithms for Digital Signal Processing
Shift Register Sequences
GF(2m) Multiplication and Division Over the Dual Basis
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
A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields
IEEE Transactions on Computers
Comments on "Five, Six, and Seven-Term Karatsuba-Like Formulae"
IEEE Transactions on Computers
IEEE Transactions on Computers
A Novel Architecture for Galois Fields GF(2^m) Multipliers Based on Mastrovito Scheme
IEEE Transactions on Computers
On multiplication in finite fields
Journal of Complexity
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Speedup of bit-parallel Karatsuba multiplier in GF(2 m) generated by trinomials
Information Processing Letters
Improved three-way split formulas for binary polynomial multiplication
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
GF(2m) finite-field multipliers with reduced activity variations
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
WEWoRC'11 Proceedings of the 4th Western European conference on Research in Cryptology
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We introduce a generalized method for constructing subquadratic complexity multipliers for even characteristic field extensions. The construction is obtained by recursively extending short convolution algorithms and nesting them. To obtain the short convolution algorithms, the Winograd short convolution algorithm is reintroduced and analyzed in the context of polynomial multiplication. We present a recursive construction technique that extends any d point multiplier into an n=d^k point multiplier with area that is subquadratic and delay that is logarithmic in the bit-length n. We present a thorough analysis that establishes the exact space and time complexities of these multipliers. Using the recursive construction method, we obtain six new constructions, among which one turns out to be identical to the Karatsuba multiplier. All six algorithms have subquadratic space complexities and two of the algorithms have significantly better time complexities than the Karatsuba algorithm.