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**2018/554**

**Title:**

A new class of irreducible pentanomials for polynomial based multipliers in binary fields

**Authors:**
Gustavo Banegas, Ricardo Custodio, Daniel Panario

**Abstract:**

We introduce a new class of irreducible pentanomials over {\mathbb F}_{2^m} of the form f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1. Let m=2b+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 \mathbb{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.

**ePrint:**
https://eprint.iacr.org/2018/554

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