D. Augot - Connections between decoding Reed-Solomon codes and solving discrete logarithms over extension fields

Joint work wih Francois Morain. A connection between the discrete logarithm problem over Fq^h and the problem of decoding Reed-Solomon codes over Fq has been proposed and studied by Cheng, Wang at FOCS 2004, essentially in a theoretical manner to study the hardness of decoding a ReedSolomon codes when a large number of errors occurs. We propose to study this reduction in a reverse direction from a practical point of view : how do decoding algorithms help in solving the discrete logarithm problem over finite fields. The first step is to consider a unique decoding algorithm, like Gao's algorithm, and to adapt it to the discrete logarithm problem. We have implemented this approach in Magma and NTL and have made numerical computations. Although the method seems less efficient than the original Adleman index-calculus method, there are some original directions that we will discuss.