On the Factorization of Lacunary Polynomials

关于无缺多项式的因式分解

• 批准号: 0207302
• 负责人: Michael Filaseta
• 金额: $ 15.12万
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-15 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0207302&HistoricalAwards=false
• 关键词: Factorization; Lacunary; Polynomials

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.

Filaseta0207302和他的合作者Douglas Meade开发并实现了小欧氏范数多项式的不可约性检验和因式分解的高效算法。此外，它们还通过类似的算法对欧几里得范数有界于某一规定量的可约性进行分类。考虑了与这些算法的复杂性和并行实现有关的问题。因式分解，更广泛地说，计算数学在密码学中都发挥了至关重要的作用。随着技术的进步，算法在这类应用中的重要性不断增加。这个项目从理论和计算的角度处理高次分解多项式。这项工作在密码学和复杂性理论中都有应用，它涉及到需要多少工作才能解决某些类型的问题。