Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
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
Low Complexity Multiplication in a Finite Field Using Ring Representation
IEEE Transactions on Computers
Parallel Multipliers Based on Special Irreducible Pentanomials
IEEE Transactions on Computers
Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials
IEEE Transactions on Computers
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
Bit-serial Reed - Solomon encoders
IEEE Transactions on Information Theory
Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Speedup of bit-parallel Karatsuba multiplier in GF(2 m) generated by trinomials
Information Processing Letters
| Hi-index | 0.00 |
In this paper we study the multiplication in fields F"2"^"n using the Shifted Polynomial Basis (SPB) representation of Fan and Dai [H. Fan, Y. Dai, Fast bit-parallel GF(2^n) multiplier for all trinomials, IEEE Transactions on Computers 54 (4) (2005) 485-490]. We give a simpler construction than in Fan and Dai (2005) of the matrix associated to the SPB used to perform the field multiplication. We present also a novel parallel architecture to multiply in SPB. This multiplier have a smaller time complexity (for good field it is equal to T"A+@?log"2(n)@?T"X) than all previously presented architecture. For practical field F"2"^"n, i.e., for n@?163, this roughly improves the delay by 10%. On the other hand the space complexity is increased by 25%: the space complexity is a little greater than the time gain.