Abstract
The CGL hash function is a provably secure hash function using walks on isogeny graphs of supersingular elliptic curves. A dominant cost of its computation comes from iterative computations of power roots over quadratic extension fields. In this paper, we reduce the necessary number of power root computations by almost half, by applying and also extending an existing method of efficient isogeny sequence computation on Legendre curves (Hashimoto and Nuida, CASC 2021). We also point out some relationship between 2-isogenies for Legendre curves and those for Edwards curves, which is of independent interests, and develop a method of efficient computation for 2e-th roots in quadratic extension fields.
Original language | English |
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Pages (from-to) | 1131-1140 |
Number of pages | 10 |
Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
Volume | E106.A |
Issue number | 9 |
DOIs | |
Publication status | Published - Sept 1 2023 |
All Science Journal Classification (ASJC) codes
- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics