Although calculating the exact time/memory complexity of algorithms based on the Grobner basis is not easy, the new approach is interesting:
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of Boolean equations. Under a first fall degree assumption the regularity degree of the system is at most $4$. Extensive experimental data which supports the assumption is provided. An heuristic analysis suggests a new asymptotical complexity bound $2^{c\sqrt{n\ln n}}, c\approx 1.69$ for computing discrete logarithms on an elliptic curve over a field of size $2^n$. For several binary elliptic curves recommended by FIPS the new method performs better than Pollard's. <http://eprint.iacr.org/2015/310.pdf> or <http://arxiv.org/pdf/1504.01175v1> -- Regards, ASK _______________________________________________ cryptography mailing list cryptography@randombit.net http://lists.randombit.net/mailman/listinfo/cryptography