Initial minors – a conjecture to solve the elliptic curve discrete logarithm problem
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The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. We try to establish that initial minors are a viable way to solve this problem. We have developed a code using C++ and NTL to solve the elliptic curve discrete logarithm problem, which can be downloaded from www.bitbucket.org. This paper presents necessary algorithms for the code. The code is written to verify the conjecture of initial minors using Schur complements along with solving the elliptic curve discrete logarithm problem. We were able to solve the problem for groups of order 2^50.
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