4 ms·
Interesting, but no more. The commonly used curve P-256 has the prime order 115792089210356248762697446949407573529996955224135760342422259061068512044369. Fr
by brohee 10y ago
Interesting, but no more.
The commonly used curve P-256 has the prime order 115792089210356248762697446949407573529996955224135760342422259061068512044369.
From the paper "The largest group of elliptic group of prime order that we tested is 129159847, in which a discrete logarithm problem was solved.".
- PaulAJ 10y agoThanks. I was just about to ask.
- dvdkhlng 10y agoThe paper closes with > However, we felt that computing the determinant for all possible sub matrices is a bottleneck for this algorithm and ways should be found to make this more efficient. That last step is obviously of exponential complexity in the parameters r and t. I wonder whether the algorithm's total run-time becomes more acceptable when that last step is replaced by a polynomial-complexity computation. To me it looks like an O(log(n)*n³) algorithm should be feasible, by replacing the submatrix-determinants with operations on determinants on large matrices that are generated in a way that ensures det=0 when any of the sub-matrices has det=0. Unfortunately I don't really understand enough about the remainder of the paper to actually see how the useful the algorithm would be with that "bottleneck" removed.
- dvdkhlng 10y agoToo late to edit my comment, but for correctness' sake: the algorithm as described is exponential in k (and thus n), not r and t.