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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 1arer is bas...
New bit-parallel Montgomery multiplier for trinomials using squaring operation
Montgomery multiplication squaring bit-parallel
2016/1/23
In this paper, a new bit-parallel Montgomery multiplier for GF(2m) is presented, where the field is generated with an irreducible trinomial. We first present a slightly generalized version of a newly...
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...
Low Complexity Bit-Parallel Square Root Computation over GF(2m) for all Trinomials
Finite field arithmetic binary extension fields cryptography
2008/11/13
In this contribution we introduce a low-complexity bit-parallel algorithm
for computing square roots over binary extension fields. Our proposed
method can be applied for any type of irreducible poly...
