Differences among summation polynomials over various forms of elliptic curves

Chen Mou Cheng, Kenta Kodera, Atsuko Miyaji

研究成果: 期刊稿件文章同行評審

1 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)1061-1071
頁數11
期刊IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
E102A
發行號9
DOIs
出版狀態已出版 - 2019
對外發佈

文獻附註

Publisher Copyright:
Copyright © 2019 The Institute of Electronics, Information and Communication Engineers.

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