{"title":"Probabilistic algorithms in finite fields","authors":"M. Ben-Or","doi":"10.1109/SFCS.1981.37","DOIUrl":null,"url":null,"abstract":"We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theory, algebraic symbol manipulation, and number theory. These algorithms have a very transparent, easy to program structure. For finite fields of large characteristic p, so that exhaustive search through ${\\text{Z}}_p $, is not feasible, our algorithms are of lower order in the degrees of the polynomial and fields in question, than previously published algorithms.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1980-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"213","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1981.37","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 213
Abstract
We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theory, algebraic symbol manipulation, and number theory. These algorithms have a very transparent, easy to program structure. For finite fields of large characteristic p, so that exhaustive search through ${\text{Z}}_p $, is not feasible, our algorithms are of lower order in the degrees of the polynomial and fields in question, than previously published algorithms.