VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
IEEE Transactions on Computers - Special issue on computer arithmetic
Efficient Multiplier Architectures for Galois Fields GF(24n)
IEEE Transactions on Computers
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
New Low-Complexity Bit-Parallel Finite Field Multipliers Using Weakly Dual Bases
IEEE Transactions on Computers
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Architecture For A Low Complexity Rate-Adaptive Reed-Solomon Encoder
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
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 Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over GF(2n)
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Low Complexity Multiplication in a Finite Field Using Ring Representation
IEEE Transactions on Computers
A Generalized Method for Constructing Subquadratic Complexity GF(2^k) Multipliers
IEEE Transactions on Computers
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Quadrinomial Modular Arithmetic using Modified Polynomial Basis
ITCC '05 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume I - Volume 01
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SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
IEEE Transactions on Computers
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
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WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
High performance GHASH function for long messages
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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
Scalable Gaussian Normal Basis Multipliers over GF(2m) Using Hankel Matrix-Vector Representation
Journal of Signal Processing Systems
GF(2m) finite-field multipliers with reduced activity variations
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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Based on Toeplitz matrix-vector products and coordinate transformation techniques, we present a new scheme for subquadratic space complexity parallel multiplication in GF(2^{n}) using the shifted polynomial basis. Both the space complexity and the asymptotic gate delay of the proposed multiplier are better than those of the best existing subquadratic space complexity parallel multipliers. For example, with n being a power of 2, the space complexity is about 8 percent better, while the asymptotic gate delay is about 33 percent better, respectively. Another advantage of the proposed matrix-vector product approach is that it can also be used to design subquadratic space complexity polynomial, dual, weakly dual, and triangular basis parallel multipliers. To the best of our knowledge, this is the first time that subquadratic space complexity parallel multipliers are proposed for dual, weakly dual, and triangular bases. A recursive design algorithm is also proposed for efficient construction of the proposed subquadratic space complexity multipliers. This design algorithm can be modified for the construction of most of the subquadratic space complexity multipliers previously reported in the literature.