Two hardware implementations of the group operations necessary for implementing an elliptic curve cryptosystem over a characteristic two finite field

Author

Potgieter, MJ ; Van Dyk, BJ

Author_Institution

Pretoria Univ., South Africa

Volume

1

fYear

2002

fDate

2-4 Oct. 2002

Firstpage

187

Abstract

Two FPGA (field-programmable gate array) implementations of the elliptic curve scalar multiplication operation are presented. The main design objective influencing all implementation decisions was complete scalability. Scalability refers to being able to change both the field size and the elliptic curve parameters without reprogramming the hardware. Measures were taken during the design process to ensure near-optimal performance for the set of algorithms used despite the scalable nature of the hardware. A new field multiplication algorithm is used in one of the implementations, improving performance by approximately 50%.

Keywords

Galois fields; application specific integrated circuits; cryptography; field programmable gate arrays; finite state machines; hardware description languages; multiplying circuits; ASIC; FPGA implementations; VHDL; classical field multiplier; combined field multiplier; elliptic curve cryptosystem; encryption; field multiplication algorithm; field-programmable gate array; finite fields; finite-state machines; group operations; hardware implementations; near-optimal performance; scalability; scalar multiplication operation; Application specific integrated circuits; Elliptic curve cryptography; Elliptic curves; Field programmable gate arrays; Galois fields; Hardware; Public key; Public key cryptography; Scalability; Security;

fLanguage

English

Publisher

ieee

Conference_Titel

Africon Conference in Africa, 2002. IEEE AFRICON. 6th

Print_ISBN

0-7803-7570-X

Type

conf

DOI

10.1109/AFRCON.2002.1146831

Filename

1146831