TY - JOUR
T1 - Efficient Isogeny Computations on Twisted Edwards Curves
AU - Kim, Suhri
AU - Yoon, Kisoon
AU - Kwon, Jihoon
AU - Hong, Seokhie
AU - Park, Young Ho
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. NRF-2017R1A2B4011599).
Publisher Copyright:
© 2018 Suhri Kim et al.
PY - 2018
Y1 - 2018
N2 - The isogeny-based cryptosystem is the most recent category in the field of postquantum cryptography. However, it is widely studied due to short key sizes and compatibility with the current elliptic curve primitives. The main building blocks when implementing the isogeny-based cryptosystem are isogeny computations and point operations. From isogeny construction perspective, since the cryptosystem moves along the isogeny graph, isogeny formula cannot be optimized for specific coefficients of elliptic curves. Therefore, Montgomery curves are used in the literature, due to the efficient point operation on an arbitrary elliptic curve. In this paper, we propose formulas for computing 3 and 4 isogenies on twisted Edwards curves. Additionally, we further optimize our isogeny formulas on Edwards curves and compare the computational cost of Montgomery curves. We also present the implementation results of our isogeny computations and demonstrate that isogenies on Edwards curves are as efficient as those on Montgomery curves.
AB - The isogeny-based cryptosystem is the most recent category in the field of postquantum cryptography. However, it is widely studied due to short key sizes and compatibility with the current elliptic curve primitives. The main building blocks when implementing the isogeny-based cryptosystem are isogeny computations and point operations. From isogeny construction perspective, since the cryptosystem moves along the isogeny graph, isogeny formula cannot be optimized for specific coefficients of elliptic curves. Therefore, Montgomery curves are used in the literature, due to the efficient point operation on an arbitrary elliptic curve. In this paper, we propose formulas for computing 3 and 4 isogenies on twisted Edwards curves. Additionally, we further optimize our isogeny formulas on Edwards curves and compare the computational cost of Montgomery curves. We also present the implementation results of our isogeny computations and demonstrate that isogenies on Edwards curves are as efficient as those on Montgomery curves.
UR - http://www.scopus.com/inward/record.url?scp=85051005854&partnerID=8YFLogxK
U2 - 10.1155/2018/5747642
DO - 10.1155/2018/5747642
M3 - Article
AN - SCOPUS:85051005854
SN - 1939-0122
VL - 2018
JO - Security and Communication Networks
JF - Security and Communication Networks
M1 - 5747642
ER -