Abstract
Wu recently proposed three types of irreducible polynomials for low-complexity bit-parallel multipliers over F2n . In this paper, we consider new classes of irreducible polynomials for low-complexity bit-parallel multipliers over F2n , namely, repeated polynomial (RP). The complexity of the proposed multipliers is lower than those based on irreducible pentanomials. A repeated polynomial can be classified by the complexity of bit-parallel multiplier based on RPs, namely, C1, C2 and C3. If we consider finite fields that have neither a ESP nor a trinomial as an irreducible polynomial when n≤1000, then, in Wu's result, only 11 finite fields exist for three types of irreducible polynomials when n≤1000. However, in our result, there are 181, 232(52.4%), and 443(100%) finite fields of class C1, C2 and C3, respectively.
Original language | English |
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Pages (from-to) | 2-12 |
Number of pages | 11 |
Journal | Discrete Applied Mathematics |
Volume | 241 |
DOIs | |
Publication status | Published - 2018 May 31 |
Bibliographical note
Publisher Copyright:© 2016 Elsevier B.V.
Keywords
- Finite field
- Irreducible polynomial
- Multiplication
- Polynomial basis
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics