On the Factorization of Lacunary Polynomials

Filaseta0207302 研究者和他的合作者道格拉斯米德开发和实现了有效的算法，不可约测试和因式分解的多项式与小欧几里德范数。 此外，他们通过类似的算法进行分类，所有的情况下，其中约简发生与欧几里德范数有界的一些规定的数额。 这些算法的复杂性和并行实现有关的问题被认为是。 因式分解和更普遍的计算数学在密码学中扮演了至关重要的角色。 算法在这些应用中的重要性随着技术的进步而不断增加。 这个项目从理论和计算的角度处理高次多项式的因子分解。 这项工作在密码学和复杂性理论中都有应用，复杂性理论涉及解决某些问题需要多少工作。

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.