Abstract
We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 b + c+ x b + c+ x b+ x c+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F 2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.
Original language | English |
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Pages (from-to) | 359–373 |
Number of pages | 15 |
Journal | Journal of Cryptographic Engineering |
Volume | 9 |
Issue number | 4 |
Early online date | 9 Nov 2018 |
DOIs | |
Publication status | Published - 1 Nov 2019 |
Keywords
- Finite fields
- Irreducible pentanomials
- Modular reduction
- Polynomial multiplication