Bit Coincidence Mining Algorithm (Draft)
نویسنده
چکیده
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 Fq (q is prime or power of primes) reduces to solving quadratic equations system of d − 1 variables and d+C0−1 equations where C0 is small natural number and d ∼ C0 log2 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.
منابع مشابه
Bit Coincidence Mining Algorithm II (Draft)
In [14], Petit et al. shows that under the algebraic geometrical assumption named ”First Fall degree Assumption”, the complexity of ECDLP over binary extension field F2n is in O(exp(n)) where limn→∞ o(1) = 0 and there are many generalizations and improvements for the complexity of ECDLP under this assumption [10], [11], [5], [16]. In [13], the author proposes the bit coincidence mining algorith...
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تاریخ انتشار 2015