On the Factorization of Lacunary Polynomials

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Filaseta0207302 The investigator and his collaborator Douglas Meade developand implement efficient algorithms for irreducibility testing andfactorization of polynomials with small Euclidean norm. Inaddition, they classify through similar algorithms all caseswhere reducibility occurs with Euclidean norm bounded by someprescribed amount. Issues relating to the complexity andparallel implementation of such algorithms are considered. Both factoring and, more generally, computationalmathematics have played a vital role in cryptography. Theimportance of algorithms in such applications continues toincrease as technology advances. This project deals withfactoring polynomials of high degree from both a theoretical andcomputational point of view. The work has application incryptography and in complexity theory, which deals with thequestion of how much work is needed to solve certain kinds ofproblems.