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How to Extract and Expand Randomness:A Summary and Explanation of Existing Results

机译:如何提取和扩展随机性:现有结果的概述和解释

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We examine the use of randomness extraction and expansion in key agreement (KA) protocols to generate uniformly random keys in the standard model. Although existing works provide the basic theorems necessary, they lack details or examples of appropriate cryptographic primitives and/or parameter sizes. This has lead to the large amount of min-entropy needed in the (non-uniform) shared secret being overlooked in proposals and efficiency comparisons of KA protocols. We therefore summarize existing work in the area and examine the security levels achieved with the use of various extractors and expanders for particular parameter sizes. The tables presented herein show that the shared secret needs a min-entropy of at least 292 bits (and even more with more realistic assumptions) to achieve an overall security level of 80 bits using the extractors and expanders we consider. The tables may be used to find the min-entropy required for various security levels and assumptions. We also find that when using the short exponent theorems of Gennaro et al., the short exponents may need to be much longer than they suggested.
机译:我们研究了在密钥协议(KA)协议中使用随机性提取和扩展来在标准模型中生成统一的随机密钥。尽管现有著作提供了必要的基本定理,但它们缺少适当的密码原语和/或参数大小的细节或示例。这导致在(非统一)共享秘密中所需的大量最小熵在KA协议的建议和效率比较中被忽略。因此,我们总结了该领域的现有工作,并研究了针对特定参数大小使用各种提取器和扩展器达到的安全级别。本文介绍的表格表明,共享密钥需要使用至少292位的最小熵(在更现实的假设下甚至还要更小),才能使用我们考虑的提取器和扩展器达到80位的总体安全级别。这些表可用于查找各种安全级别和假设所需的最小熵。我们还发现,在使用Gennaro等人的短指数定理时,短指数可能需要比他们建议的更长。

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