Cryptology ePrint Archive: Report 2009/136

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

Yvonne Cliff and Colin Boyd and Juan Gonzalez Nieto

Abstract: 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.

Category / Keywords: randomness extraction, randomness expansion, key agreement, key exchange protocols, pseudorandom function (PRF), universal hash function, leftover hash lemma (LHL)

Publication Info: An abridged version of this paper is to appear in ACNS 2009. This is the full version.

Date: received 23 Mar 2009, last revised 29 Mar 2009

Contact author: j gonzaleznieto at qut edu au

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Version: 20090330:011717 (All versions of this report)

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