Cryptology ePrint Archive: Report 2018/701

How to Correct More Errors in a Secure Sketch

Yen-Lung Lai

Abstract: Secure sketch produces public information of its input $w$ without revealing it, yet, allows the exact recovery of $w$ given another value $w'$ that is close to $w$. Therefore, it can be used to reliably reproduce any error-prone biometric data stored in a database, without jeopardizing the user privacy. In addition to this, secure sketch enables fuzzy extractor, by using a randomness extractor to convert the noisy reading $w'$ of its original value $w$ into the same uniform key $R$. Standard secure sketch should work on all type of available input sources. However, some sources have lower entropy compared to the error itself, formally called ``more error than entropy", a standard secure sketch cannot show its security promise perfectly to these kinds of sources. Besides, when same input is reused for multiple sketches generation, the complex error process of the input further results to security uncertainty, and offer no security guarantee. Fuller et al., (Asiacrypt 2016) defined the fuzzy min-entropy is necessary to show security for different kind of sources over different distributions. This paper focuses on secure sketch. We propose a new technique to generate re-usable secure sketch. We show security to low entropy sources and enable error correction up to Shannon bound. Our security defined information theoretically with min-entropy under distribution uncertain setting. In particular, our new technique offers security guarantee for all family of input distributions, as long as the sources possessing ``meaningful amount" of min-entropy that is equivalent to the min-entropy of some random distributions over a larger metric space, parametrized by a chosen error correction code.

Category / Keywords: Secure Sketch, Error Correction, Fuzzy Extractor, Information Theory

Date: received 24 Jul 2018, last revised 28 Jan 2019

Contact author: yenlung lai at monash edu

Available format(s): PDF | BibTeX Citation

Note: revised correctness and efficiency of decoding algo.

Version: 20190128:181412 (All versions of this report)

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