Des. Codes Cryptogr. https://doi.org/10.1007/s10623-018-0492-3 A variant of the Galbraith–Ruprai algorithm for discrete logarithms with improved complexity 1,2 1 Yuqing Zhu · Jincheng Zhuang · 1,2 1 1 Hairong Yi · Chang Lv · Dongdai Lin Received: 11 February 2018 / Revised: 24 April 2018 / Accepted: 7 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The discrete logarithm problem (DLP) in a group is a fundamental assumption that underpins the security of many systems. Hence evaluating its hardness is important. For efﬁcient implementation of cryptographic algorithms, sometimes groups with additional structures are preferred. However, these structures may be used to obtain faster attacks. By using equivalence classes, Galbraith and Ruprai proposed a faster algorithm to solve the DLPinanintervalofsize N , with expected running time of 1.361 N group operations. Liu generalized their algorithm to the 2-dimensional case, which required 1.450 N group operations. Further, for an elliptic curve with an efﬁciently computable endomorphism, Liu reduced the complexity to 1.026 N . In this paper, we propose a variant of the Galbraith– Ruprai algorithm. This variant has average-case asymptotic complexity close to 1.253 N for sufﬁciently large N . For certain practical parameters, the complexity
Designs, Codes and Cryptography – Springer Journals
Published: Jun 1, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera