{"title":"一个对素数取模的多项式乘法的并行实现","authors":"M. Law, M. Monagan","doi":"10.1145/2790282.2790291","DOIUrl":null,"url":null,"abstract":"We present a parallel implementation in Cilk C of a modular algorithm for multiplying two polynomials in Zq[x] for integer q > 1, for multi-core computers. Our algorithm uses Chinese remaindering. It multiplies modulo primes p1, p2, ... in parallel and uses a parallel FFT for each prime. Our software multiplies two polynomials of degree 109 modulo a 32 bit integer q in 83 seconds on a 20 core computer.","PeriodicalId":384227,"journal":{"name":"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A parallel implementation for polynomial multiplication modulo a prime\",\"authors\":\"M. Law, M. Monagan\",\"doi\":\"10.1145/2790282.2790291\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a parallel implementation in Cilk C of a modular algorithm for multiplying two polynomials in Zq[x] for integer q > 1, for multi-core computers. Our algorithm uses Chinese remaindering. It multiplies modulo primes p1, p2, ... in parallel and uses a parallel FFT for each prime. Our software multiplies two polynomials of degree 109 modulo a 32 bit integer q in 83 seconds on a 20 core computer.\",\"PeriodicalId\":384227,\"journal\":{\"name\":\"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation\",\"volume\":\"51 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2015 International Workshop on Parallel Symbolic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2790282.2790291\",\"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 2015 International Workshop on Parallel Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2790282.2790291","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A parallel implementation for polynomial multiplication modulo a prime
We present a parallel implementation in Cilk C of a modular algorithm for multiplying two polynomials in Zq[x] for integer q > 1, for multi-core computers. Our algorithm uses Chinese remaindering. It multiplies modulo primes p1, p2, ... in parallel and uses a parallel FFT for each prime. Our software multiplies two polynomials of degree 109 modulo a 32 bit integer q in 83 seconds on a 20 core computer.
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