Abstract
The security of elliptic curve cryptography is closely related to the computational complexity of the elliptic curve discrete logarithm problem (ECDLP). Today, the best practical attacks against ECDLP are exponential-time generic discrete logarithm algorithms such as Pollard’s rho method. A recent line of inquiry in index calculus for ECDLP started by Semaev, Gaudry, and Diem has shown that, under certain heuristic assumptions, such algorithms could lead to subexponential attacks to ECDLP. In this study, we investigate the computational complexity of ECDLP for elliptic curves in various forms—including Hessian, Montgomery, (twisted) Edwards, and Weierstrass representations—using index calculus. Using index calculus, we aim to determine whether there is any significant difference in the computational complexity of ECDLP for elliptic curves in various forms. We provide empirical evidence and insight showing an affirmative answer in this paper.
Original language | English |
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Pages (from-to) | 1061-1071 |
Number of pages | 11 |
Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
Volume | E102A |
Issue number | 9 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:Copyright © 2019 The Institute of Electronics, Information and Communication Engineers.
Keywords
- ECDLP
- Index calculus
- Point decomposition problem
- Security evaluation
- Summation polynomial