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$GF(2^n)$ Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials
implementation implementation
2016/1/26
We present explicit formulae and complexities of bit-parallel GF(2n) squarers for a new class of irreducible pentanomials xn+xn−1+xk+x+1, where n is odd and 1 squarer is bas...
A Chinese Remainder Theorem Approach to Bit-Parallel GF(2^n) Polynomial Basis Multipliers for Irreducible Trinomials
implementation Irreducible Trinomials
2016/1/5
We show that the step “modulo the degree-n field generating irreducible polynomial” in the classical definition of the GF(2^n) multiplication operation can be avoided. This leads to an alternative rep...
Low Space Complexity CRT-based Bit-Parallel GF(2^n) Polynomial Basis Multipliers for Irreducible Trinomials
Finite field multiplication polynomial basis
2015/12/30
By selecting the largest possible value of k∈(n/2,2n/3], we further reduce the AND and XOR gate complexities of the CRT-based hybrid parallel GF(2^n) polynomial basis multipliers for the irreduc...
Toeplitz matrix-vector product based GF(2^n) shifted polynomial basis multipliers for all irreducible pentanomials
subquadratic space complexity multiplier shifted polynomial basis
2014/3/11
Besides Karatsuba algorithm, optimal Toeplitz matrix-vector product (TMVP) formulae is another approach to design GF(2^n) subquadratic multipliers. However, when GF(2^n) elements are represented using...