International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 12 October 2015

Koh-ichi Nagao
ePrint Report ePrint Report
Here, we propose new algorithm for solving ECDLP named \"Bit Coincidence Mining Algorithm!\", from which ECDLP is reduced to solving some quadratic equations system.

In this algorithm, ECDLP of an elliptic curve $E$ defined over $\\bF_q$ ($q$ is prime or power of primes) reduces to solving quadratic equations system of $d-1$ variables and $d+C_0-1$ equations where $C_0$ is small natural number and $d \\sim C_0 \\, \\log_2 q$.

This equations system is too large and it can not be solved by computer.

However, we can show theoritically the cost for solving this equations system by xL algorithm is subexponential under the reasonable assumption of xL algorithm.

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