Subexponential time relations in the class group of large degree number fields
Jean‐François Biasse · Advances in Mathematics of Communications · 2014
Hafner and McCurley described a subexponential time algorithmto compute the ideal class group of a quadratic field, whichwas generalized to families of fixed degree number fields by Buchman.The main ingredient of this method is a subexponential time algorithmto derive relations between primes of norm bounded by a subexponentialvalue. Besides ideal class group computation, this was successfully usedto evaluate isogenies, compute endomorphism rings, solve the discretelogarithm problem in the class group and find a generator of a principalideal. In this paper, we present a generalization of the relation searchto classes of number fields with degree growing to infinity.