A new method for solving the elliptic curve discrete logarithm problem

The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue that initial minors are a viable way to solve this problem....

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Bibliographic Details
Published inGroups, complexity, cryptology Vol. 12, Issue 2
Main Authors Abdullah, Ansari, Mahalanobis, Ayan, Mallick, Vivek M.
Format Journal Article
LanguageEnglish
Published Episciences 01.01.2020
Subjects
computer science - cryptography and security
mathematics - algebraic geometry
mathematics - number theory
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Summary:The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue that initial minors are a viable way to solve this problem. This paper will present necessary algorithms for this attack. We have written a code to verify the conjecture of initial minors using Schur complements. We were able to solve the problem for groups of order up to $2^{50}$.
ISSN:1869-6104
1869-6104
DOI:10.46298/jgcc.2020.12.2.6649