Generating safe primes
Generating safe primes
复制标题
生成安全素数
DOI：
10.1515/jmc-2013-5011
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
I. Shparlinski
中科院分区：
文献类型：
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作者：
J. Gathen;I. Shparlinski
抽象的。安全素数和安全RSA模数被用于几种密码方案中。最常见的概念是素数p，也就是素数。后者则是索菲·日尔曼的素数。在适当的启发式算法下，它们大量存在，并且可以高效地生成。但到目前为止，解析数论的现代方法甚至不允许证明它们的数量是无穷多的。因此，对于这个安全素数的概念，文献中没有一个算法可以无条件地被证明是终止的，更不用说是有效的了。本文考虑了安全素数和模数的不同概念。它们可以在多项式时间内生成，没有任何未经证实的假设，并且对于我们所知道的密码应用程序来说已经足够好了。
Abstract. Safe primes and safe RSA moduli are used in several cryptographic schemes. The most common notion is that of a prime p, where is also prime. The latter is then a Sophie Germain prime. Under appropriate heuristics, they exist in abundance and can be generated efficiently. But the modern methods of analytic number theory have – so far – not even allowed to prove that there are infinitely many of them. Thus for this notion of safe primes, there is no algorithm in the literature that is unconditionally proven to terminate, let alone to be efficient. This paper considers a different notion of safe primes and moduli. They can be generated in polynomial time, without any unproven assumptions, and are good enough for the cryptographic applications that we are aware of.