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

  • Yvonne Cliff
  • Colin Boyd
  • Juan Gonzalez Nieto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5536)


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.


randomness extraction randomness expansion key agreement key exchange protocols pseudorandom function (PRF) universal hash function leftover hash lemma (LHL) 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yvonne Cliff
    • 1
  • Colin Boyd
    • 1
  • Juan Gonzalez Nieto
    • 1
  1. 1.Information Security InstituteQueensland University of TechnologyBrisbaneAustralia

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