A dimension extractor is an algorithm designed to increase the effective dimension – i.e., the computational information density – of an infinite sequence. A constructive dimension extractor is exhibited by showing that every sequence of positive constructive dimension is Turing equivalent to a sequence of constructive strong dimension arbitrarily close to 1. Similar results are shown for compu...

This chapter presents a general approach for handling secret biometric data in cryptographic applications. The generality manifests itself in two ways: we attempt to minimize the assumptions we make about the data, and to present techniques that are broadly applicable wherever biometric inputs are used. Because biometric data comes from a variety of sources that are mostly outside of anyone’s c...

Randomness extractors are efficient algorithms which convert weak random sources into nearly perfect ones. While such purification of randomness was the original motivation for constructing extractors, these constructions turn out to have strong pseudorandom properties which found applications in diverse areas of computer science and combinatorics. We will highlight some of the applications, as...

The MAGIC telescope uses a 300 MHz FADC system to sample the shaped PMT signals produced by the captured Cherenkov photons of air showers. Different algorithms to reconstruct the signal from the read-out samples (extractors) have been developed and are described and compared. Criteria based on the obtained charge and time resolution/bias are defined and used to judge the different extractors, by

Zimand [24] presented simple constructions of locally computable strong extractors whose analysis relies on the direct product theorem for one-way functions and on the Blum-Micali-Yao generator. For N -bit sources of entropy γN , his extractor has seed O(logN) and extracts N random bits. We show that his construction can be analyzed based solely on the direct product theorem for general functio...

An extractor is a function that receives some randomness and either “improves” it or produces “new” randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov extractors and modify it to resourcebounded version of Kolmogorov complexity. Following Zimand we prove the existence of such objects with certain parameters. The uti...

Fuzzy extractors derive strong keys from noisy sources. Their security is defined informationtheoretically, which limits the length of the derived key, sometimes making it too short to be useful. We ask whether it is possible to obtain longer keys by considering computational security, and show the following. • Negative Result: Noise tolerance in fuzzy extractors is usually achieved using an in...

We study the suitability of common pseudorandomness modes associated with cryptographic hash functions and block ciphers (CBCMAC, Cascade and HMAC) for the task of “randomness extraction”, namely, the derivation of keying material from semi-secret and/or semirandom sources. Important applications for such extractors include the derivation of strong cryptographic keys from non-uniform sources of...