Coding Solutions for the Secure Biometric Storage Problem

The paper studies the problem of securely storing biometric passwords, such as fingerprints and irises. With the help of coding theory Juels and Wattenberg derived in 1999 a scheme where similar input strings will be accepted as the same biometric. In the same time nothing could be learned from the stored data. They called their scheme a "fuzzy commitment scheme". In this paper we will revisit the solution of Juels and Wattenberg and we will provide answers to two important questions: What type of error-correcting codes should be used and what happens if biometric templates are not uniformly distributed, i.e. the biometric data come with redundancy. Answering the first question will lead us to the search for low-rate large-minimum distance error-correcting codes which come with efficient decoding algorithms up to the designed distance. In order to answer the second question we relate the rate required with a quantity connected to the "entropy" of the string, trying to estimate a sort of "capacity", if we want to see a flavor of the converse of Shannon's noisy coding theorem. Finally we deal with side-problems arising in a practical implementation and we propose a possible solution to the main one that seems to have so far prevented real life applications of the fuzzy scheme, as far as we know.Comment: the final version appeared in Proceedings Information Theory Workshop (ITW) 2010, IEEE copyrigh

Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information Theory; parts of the results were presented at the 2013 IEEE Information Theory Worksho