Progress on the Discrete Logarithm Problem

A team of French mathematicians and computer scientists have developed a new algorithm that makes substantial progress on certain types of discrete logarithms. The general discrete log problem is given a and b from a finite field find n also from the finite field such that a = bn. It turns out that this problem has about the same difficulty as factoring and, in fact, the two problems are related.

The discrete logarithm problem is important because its difficulty is what makes the Diffie-Hellman key exchange protocol and elliptic curve cryptography secure. Additionally, progress with the discrete logarithm problem can often be carried over to the factorization problem.

The French team's algorithm works only for low characteristic finite fields, which means it does not affect Diffie-Hellman or elliptic curve cryptography but does effect certain other less-used cryptosystems. The bottom line is that there's no reason for panic: all our important asymmetric cryptosystems are still secure. Still, as Bruce Schneier says, attacks only get better.

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