A New Look at the Key Equation
Patrick M. Fitzpatrick · 2005
We describe a new algorithm based on Grobner bases of modules for solving for the pair (a, b) the multivariable polynomial congruence as = b mod I where I is an ideal in k[x/sub 1/, ... ,x/sub n/] and s is given. The restriction to one variable gives a new approach to decoding BCH and (classical) Goppa codes.