A New Double Point Multiplication Algorithm and Its Application to Binary Elliptic Curves with Endomorphisms

Author

Azarderakhsh, Reza ; Karabina, Koray

Author_Institution

Dept. of Comput. Eng., Rochester Inst. of Technol., Rochester, NY, USA

Volume

63

Issue

10

fYear

2014

fDate

Oct. 2014

Firstpage

2614

Lastpage

2619

Abstract

We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Based on operation counts, we expect to gain accelerations of 30% and 18% for computing single point multiplication with and without availability of parallel multipliers, respectively, and these results are verified in our implementations.

Keywords

public key cryptography; binary elliptic curves; computable endomorphisms; differential addition chains; double point multiplication algorithm; hardware implementation; parallel multipliers; side channel analysis attacks; single point multiplication; Algorithm design and analysis; Elliptic curve cryptography; Elliptic curves; Resistance; Elliptic curve cryptosystems; differential addition chains; double point multiplication; endomorphism;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/TC.2013.112

Filename

6514031