{"title":"质数共享最小有效位或最高有效位的多幂RSA模的分解","authors":"Omar Akchiche, O. Khadir","doi":"10.1515/gcc-2016-0002","DOIUrl":null,"url":null,"abstract":"Abstract We study the factorization of a balanced multi-power RSA moduli N = prq when the unknown primes p and q share t least or most significant bits. We show that if t ≥ 1/(1+r)log p, then it is possible to compute the prime decomposition of N in polynomial time in log N. This result can be used to mount attacks against several cryptographic protocols that are based on the moduli N.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"27 1","pages":"47 - 54"},"PeriodicalIF":0.1000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Factoring multi-power RSA moduli with primes sharing least or most significant bits\",\"authors\":\"Omar Akchiche, O. Khadir\",\"doi\":\"10.1515/gcc-2016-0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We study the factorization of a balanced multi-power RSA moduli N = prq when the unknown primes p and q share t least or most significant bits. We show that if t ≥ 1/(1+r)log p, then it is possible to compute the prime decomposition of N in polynomial time in log N. This result can be used to mount attacks against several cryptographic protocols that are based on the moduli N.\",\"PeriodicalId\":41862,\"journal\":{\"name\":\"Groups Complexity Cryptology\",\"volume\":\"27 1\",\"pages\":\"47 - 54\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Complexity Cryptology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/gcc-2016-0002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2016-0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Factoring multi-power RSA moduli with primes sharing least or most significant bits
Abstract We study the factorization of a balanced multi-power RSA moduli N = prq when the unknown primes p and q share t least or most significant bits. We show that if t ≥ 1/(1+r)log p, then it is possible to compute the prime decomposition of N in polynomial time in log N. This result can be used to mount attacks against several cryptographic protocols that are based on the moduli N.
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