{"title":"有限域上求不可约多项式的新算法","authors":"V. Shoup","doi":"10.1109/SFCS.1988.21944","DOIUrl":null,"url":null,"abstract":"An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of factoring polynomials over the prime field of K.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"223","resultStr":"{\"title\":\"New algorithms for finding irreducible polynomials over finite fields\",\"authors\":\"V. Shoup\",\"doi\":\"10.1109/SFCS.1988.21944\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of factoring polynomials over the prime field of K.<<ETX>>\",\"PeriodicalId\":113255,\"journal\":{\"name\":\"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"223\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1988.21944\",\"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 1988] 29th Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1988.21944","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New algorithms for finding irreducible polynomials over finite fields
An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of factoring polynomials over the prime field of K.<>
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