SIDH 기반 암호 구현에 대한 홀수 차수 아이소제니 적용
On the Use of Odd-Degree Isogenies for Implementing SIDH-Based Cryptography
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초록
본 논문에서는 3차, 5차 아이소제니만 이용해 SIDH를 구현할 경우 몽고메리, 에드워드, 허프 곡선 중 어느 곡선에서 더 효율적인지 분석한다. 본 논문에서는 각 타원곡선의 형태에 대해 SIDH 암호를 구성하는 단위연산에 대한 연산량을 비교한 뒤, 홀수 차수만 활용해 SIDH를 구현하기 위해 소수와 파라미터를 설정하는 방법에 관해 설명한다. 본 논문의 결과 몽고메리와 허프 곡선에서 연산량은 유사하며, 에드워드 곡선보다 0.8% 효율적임을 알 수 있다. SIDH 기반 암호에 대한 다양한 파라미터 사용 가능성으로 인해 5차 아이소제니 구현은 필수적이므로, 본 논문은 이러한 SIDH 기반 암호에 대해 어느 타원곡선을 선택해야 하는지에 대해 가이드라인을 제공할 수 있다.
Abstract
In this paper, when SIDH is instantiated using only 3- and 5-isogeny, we demonstrate which curve is more efficientamong the Montgomery, Edwards, and Huff curves. To this end, we present the computational cost of the building blocksof SIDH on Montgomery, Edwards, and Huff curves. We also present the prime we used and parameter settings forimplementation. The result of our work shows that the performance of SIDH on Montgomery and Huff curves is almost thesame and they are 0.8% faster than Edwards curves. With the possibility of using isogeny of degree other than 3 and 4,the performance of 5-isogeny became even more essential. In this regard, this paper can provide guidelines on the selectionof the form of elliptic curves for implementation.
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