Efficient Multiplier Architectures for Galois Fields GF(24n)
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
IEEE Transactions on Computers
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Parallel Multipliers Based on Special Irreducible Pentanomials
IEEE Transactions on Computers
Self-Reciprocal Irreducible Polynomials Over Finite Fields
Designs, Codes and Cryptography
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
Low-Complexity Bit-Parallel Systolic Montgomery Multipliers for Special Classes of GF(2^m)
IEEE Transactions on Computers
Efficient Bit-Parallel Multiplier for Irreducible Pentanomials Using a Shifted Polynomial Basis
IEEE Transactions on Computers
Bit-Parallel Polynomial Basis Multiplier for New Classes of Finite Fields
IEEE Transactions on Computers
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Explicit formulas for efficient multiplication in F36m
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Redundant trinomials for finite fields of characteristic 2
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
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Hardware implementation of multiplication in finite field GF(2^m) based on sparse polynomials is found to be advantageous in terms of space-complexity as well as the time-complexity. In this paper, we present a new permutation method to construct the irreducible like-trinomials of the form (x+1)^m+(x+1)^n+1 for the implementation of efficient bit-parallel multipliers. For implementing the multiplications based on such polynomials, we have defined a like-polynomial basis (LPB) as an alternative to the original polynomial basis of GF(2^m). We have shown further that the modular arithmetic for the binary field based on like-trinomials is equivalent to the arithmetic for the field based on trinomials. In order to design multipliers for composite fields, we have found another permutation polynomial to convert irreducible polynomials into like-trinomials of the forms (x^2+x+1)^m+(x^2+x+1)^n+1, (x^2+x)^m+(x^2+x)^n+1 and (x^4+x+1)^m+(x^4+x+1)^n+1. The proposed bit-parallel multiplier over GF(2^4^m) is found to offer a saving of about 33% multiplications and 42.8% additions over the corresponding existing architectures.