Acknowledgement
This work was supported by Korea Institute for Advancement of Technology(KIAT) grant funded by the Korea Government(MOTIE) (P0017011, HRD Program for Industrial Innovation) The authors are thankful to IDEC for EDA tool support.
Proceedings of the Korean Institute of Information and Commucation Sciences Conference (한국정보통신학회:학술대회논문집)
- 2022.05a
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- Pages.246-248
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- 2022
An Efficient Hardware Implementation of 257-bit Point Scalar Multiplication for Binary Edwards Curves Cryptography
이진 에드워즈 곡선 공개키 암호를 위한 257-비트 점 스칼라 곱셈의 효율적인 하드웨어 구현
- Kim, Min-Ju (Kumoh National Institute of Technology) ;
- Jeong, Young-su (Kumoh National Institute of Technology) ;
- Shin, Kyung-Wook (Kumoh National Institute of Technology)
- Published : 2022.05.26
Abstract
Binary Edwards curves (BEdC), a new form of elliptic curves proposed by Bernstein, satisfy the complete addition law without exceptions. This paper describes an efficient hardware implementation of point scalar multiplication on BEdC using projective coordinates. Modified Montgomery ladder algorithm was adopted for point scalar multiplication, and binary field arithmetic operations were implemented using 257-bit binary adder, 257-bit binary squarer, and 32-bit binary multiplier. The hardware operation of the BEdC crypto-core was verified using Zynq UltraScale+ MPSoC device. It takes 521,535 clock cycles to compute point scalar multiplication.
Bernstein이 제안한 새로운 타원곡선 형태인 이진 에드워즈 곡선 (binary Edwards curves; BEdC)는 예외점이 없어 완전한 덧셈 법칙이 만족한다. 본 논문에서는 투영 좌표계를 적용한 BEdC 상의 점 스칼라 곱셈의 효율적인 하드웨어 구현에 대해 기술한다. 점 스칼라 곱셈을 위해 modified Montgomery ladder 알고리듬을 적용하였으며, 257-비트 이진 덧셈기와 이진 제곱기, 32-비트 이진 곱셈기를 사용하여 하위 이진체 연산을 구현했다. Zynq UltraScale+ MPSoC 디바이스에 구현하여 설계된 BEdC 크립토 코어를 검증하였으며, 점 스칼라 곱셈 연산에 521,535 클록 사이클이 소요된다.
Keywords
- Binary Edwards curves;
- projective coordinates;
- point scalar multiplication;
- modified Montgomery ladder