Sharp lower bounds on the extractable randomness from non-uniform sources

被引:8
|
作者
Skoric, Boris [1 ]
Obi, Chibuzo [1 ]
Verbitskiy, Evgeny [2 ]
Schoenmakers, Berry [1 ]
机构
[1] Eindhoven Univ Technol, NL-5600 MB Eindhoven, Netherlands
[2] Leiden Univ, NL-2300 RA Leiden, Netherlands
关键词
Leftover Hash Lemma; Universal hash function; Randomness extraction;
D O I
10.1016/j.ic.2011.06.001
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Extraction of uniform randomness from (noisy) non-uniform sources is an important primitive in many security applications, e.g. (pseudo-)random number generators, privacy-preserving biometrics, and key storage based on Physical Unclonable Functions. Generic extraction methods exist, using universal hash functions. There is a trade-off between the length of the extracted bit string and the uniformity of the string. In the literature there are proven lower bounds on this length as a function of the desired uniformity. The best known bound involves a quantity known as smooth min-entropy. Unfortunately, there exist at least three definitions of smooth entropy. In this paper we compare three of these definitions, and we derive improved lower bounds on the extractable randomness. We also investigate the use of almost universal hash functions, which are slightly worse at extracting randomness than universal hash functions, but are preferable in practice because they require far less resources in devices. We show that using them has negligible effect on the extractable randomness. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:1184 / 1196
页数:13
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