Selected RNS Bases for Modular Multiplication

Author

Bajard, J.C. ; Kaihara, M. ; Plantard, T.

Author_Institution

LIRMM, Univ. Montpellier 2, Montpellier, France

fYear

2009

fDate

8-10 June 2009

Firstpage

25

Lastpage

32

Abstract

The selection of the elements of the bases in an RNS modular multiplication method is crucial and has a great impact in the overall performance.This work proposes specific sets of optimal RNS moduli with elements of Hamming weight three whose inverses used in the MRS reconstruction have very small Hamming weight. This property is exploited in RNS bases conversions, to completely remove and replace the products by few additions/subtractions and shifts, reducing the time complexity of modular multiplication.These bases are specially crafted to computation with operands of sizes 256 or more and are suitable for cryptographic applications such as the ECC protocols.

Keywords

cryptography; residue number systems; Hamming weight; RNS; cryptographic applications; modular multiplication; residue number system; Application software; Australia; Costs; Cryptographic protocols; Digital arithmetic; Digital signal processing; Elliptic curve cryptography; Hamming weight; Public key cryptography; Signal processing algorithms; cryptography application; modular arithmetic; residue number systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic, 2009. ARITH 2009. 19th IEEE Symposium on

Conference_Location

Portland, OR

ISSN

1063-6889

Print_ISBN

978-0-7695-3670-5

Type

conf

DOI

10.1109/ARITH.2009.20

Filename

5223368