文章基本信息

标题：The Security of all RSA and Discrete Log Bits
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作者：Johan Hastad, Mats Näslund
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1999
卷号：1999
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We study the security of individual bits in an RSA encrypted message EN(x). We show that given EN(x), predicting any single bit in x with only a non-negligible advantage over the trivial guessing strategy, is (through a polynomial time reduction) as hard as breaking RSA\@. Moreover, we prove that blocks of O(loglogN) bits of x are computationally indistinguishable from random bits. The results carry over to the Rabin encryption scheme. Considering the discrete exponentiation function gx modulo p, with probability 1−o(1) over random choices of the prime p, the analog results are demonstrated. Finally, we prove that the bits of ax+b modulo p give hard core predicates for any one-way function f.
关键词：bitsecurity, Discrete logarithm, hard-core predicate, RSA-function