Fastest parallel molecular algorithms for the elliptic curve discrete logarithm problem over GF(2n)

摘要: Cryptography based on Elliptic Curves (ECC) has emerged as an effective alternative to the existing public-key cryptosystems (RSA and DSA). Its success was due both fact that no fast algorithms were known break it exceptional security levels could be obtained by using short keys. The Curve Discrete Logarithm (ECDL) problem is cornerstone of much present-day ECCs. It classifed a computationally intractable and, consequently, reliable unbreakable cryptosystem. In recent work, Li et al. built molecular computer designed solve over GF(2n). two DNA-inspired al gorithms: parallel adder multiplier, working in O(n) O(n2) respectively, where n input size. this paper, we first present faster biological implementations, O(log(n)) O(n • log(n))respectively (worst case). Then, propose our model reference solution ECDL finally highlight computational power such natureinspired paradigm.