On Hardware and Software Implementation of Arithmetic in Finite Fields of Characteristic 7 for Calculation of Pairings

Author

Gashkov, S.B. ; Bolotov, Anatoli A. ; Burtzev, A.A. ; Frolov, A.B. ; Yu, Z.S.

Author_Institution

Lomonosov Moscow State Univ., Moscow, ID, USA

fYear

2009

fDate

June 30 2009-July 2 2009

Firstpage

261

Lastpage

270

Abstract

We study scheme (hardware) and program (software) methods of multiplication of polynomials over fields of characteristic 7 in order to apply them to cryptographic protocols on elliptic curves based on parings. We consider hardware and software implementations of arithmetic in GF(7), GF(7²), GF(7ⁿ), GF(7⁷ⁿ), and GF(7¹⁴ⁿ) and estimate the complexity of corresponding schemes and programs.

Keywords

arithmetic; computational complexity; cryptographic protocols; mathematics computing; public key cryptography; arithmetic; characteristic 7; cryptographic protocols; elliptic curves; hardware implementation; polynomials; software implementation; Cryptographic protocols; Digital arithmetic; Elliptic curve cryptography; Elliptic curves; Galois fields; Hardware; Large scale integration; Physics; Polynomials; Power engineering computing; Duursma-Lee-Kwon algorithm; Tate pairing; exponentiation; finite field of odd characteristic; hyperelliptic curve of genus three; multiplication;

fLanguage

English

Publisher

ieee

Conference_Titel

Dependability of Computer Systems, 2009. DepCos-RELCOMEX '09. Fourth International Conference on

Conference_Location

Brunow

Print_ISBN

978-0-7695-3674-3

Type

conf

DOI

10.1109/DepCoS-RELCOMEX.2009.37

Filename

5260995