TY - JOUR

T1 - Low complexity bit-parallel multiplier for F2n defined by repeated polynomials

AU - Chang, Nam Su

AU - Kang, Eun Sook

AU - Hong, Seokhie

N1 - Funding Information:
This research was supported by Next-Generation Information Computing Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. NRF-2014M3C4A7030649 ).
Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2018/5/31

Y1 - 2018/5/31

N2 - 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.

AB - 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.

KW - Finite field

KW - Irreducible polynomial

KW - Multiplication

KW - Polynomial basis

UR - http://www.scopus.com/inward/record.url?scp=84995624257&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2016.07.014

DO - 10.1016/j.dam.2016.07.014

M3 - Article

AN - SCOPUS:84995624257

VL - 241

SP - 2

EP - 12

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -