{"title":"O(n)-depth circuit algorithm for modular exponentiation","authors":"T. Hamano, N. Takagi, S. Yajima, F. Preparata","doi":"10.1109/ARITH.1995.465360","DOIUrl":null,"url":null,"abstract":"An O(n)-depth polynomial-size combinational circuit algorithm is proposed for n-bit modular exponentiation, i.e., for the computation of \"x/sup y/ mod m\" for arbitrary integers x, y and m. Represented as n-bit binary integers, within bounds 2/sup n-1//spl les/m<2/sup n/ and 0/spl les/x,y<m. The algorithm is a generalization of the square-and-multiply method. An obvious implementation of the square-and-multiply method yields a circuit of depth O(nlogn) and size O(n/sup 3/). In the proposed algorithm, the terms x/sup 2/ mod m's for all i's /spl epsiv.<<ETX>>","PeriodicalId":332829,"journal":{"name":"Proceedings of the 12th Symposium on Computer Arithmetic","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 12th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1995.465360","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 18
Abstract
An O(n)-depth polynomial-size combinational circuit algorithm is proposed for n-bit modular exponentiation, i.e., for the computation of "x/sup y/ mod m" for arbitrary integers x, y and m. Represented as n-bit binary integers, within bounds 2/sup n-1//spl les/m<2/sup n/ and 0/spl les/x,y>