{"title":"O(n)深度电路模求幂算法","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1995-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":"{\"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\":null,\"pages\":null},\"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}","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
摘要
提出了一种O(n)深度多项式大小的组合电路算法,用于n位模求幂,即对任意整数x, y, m进行“x/sup y/ mod m”的计算。表示为n位二进制整数,在2/sup n-1//spl les/m>
O(n)-depth circuit algorithm for modular exponentiation
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>