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

Waveform Design for Secure SISO Transmissions and Multicasting

Wireless physical-layer security is an emerging field of research aiming at preventing eavesdropping in an open wireless medium. In this paper, we propose a novel waveform design approach to minimize the likelihood that a message transmitted between trusted single-antenna nodes is intercepted by an eavesdropper. In particular, with knowledge first of the eavesdropper's channel state information (CSI), we find the optimum waveform and transmit energy that minimize the signal-to-interference-plus-noise ratio (SINR) at the output of the eavesdropper's maximum-SINR linear filter, while at the same time provide the intended receiver with a required pre-specified SINR at the output of its own max-SINR filter. Next, if prior knowledge of the eavesdropper's CSI is unavailable, we design a waveform that maximizes the amount of energy available for generating disturbance to eavesdroppers, termed artificial noise (AN), while the SINR of the intended receiver is maintained at the pre-specified level. The extensions of the secure waveform design problem to multiple intended receivers are also investigated and semidefinite relaxation (SDR) -an approximation technique based on convex optimization- is utilized to solve the arising NP-hard design problems. Extensive simulation studies confirm our analytical performance predictions and illustrate the benefits of the designed waveforms on securing single-input single-output (SISO) transmissions and multicasting

Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning

The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a connection between machine learning and error-correcting coding. This proposed approach has implications for the development of new embedding methods based on trapping sets. Statistical physics and number geometry applied for optimize error-correcting codes, leading to these embedding and sparse factorization methods. The paper establishes a direct connection between DNN architecture and error-correcting coding by demonstrating how state-of-the-art architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range arena can be equivalent to of block and convolutional LDPC codes (Cage-graph, Repeat Accumulate). QC codes correspond to certain types of chemical elements, with the carbon element being represented by the mixed automorphism Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix are elaborated upon in detail. The Quantum Approximate Optimization Algorithm (QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous to the back-propagation loss function landscape in training DNNs. This similarity creates a comparable problem with TS pseudo-codeword, resembling the belief propagation method. Additionally, the layer depth in QAOA correlates to the number of decoding belief propagation iterations in the Wiberg decoding tree. Overall, this work has the potential to advance multiple fields, from Information Theory, DNN architecture design (sparse and structured prior graph topology), efficient hardware design for Quantum and Classical DPU/TPU (graph, quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text overlap with arXiv:2109.08184 by other author

On fuzzy syndrome hashing with LDPC coding

The last decades have seen a growing interest in hash functions that allow some sort of tolerance, e.g. for the purpose of biometric authentication. Among these, the syndrome fuzzy hashing construction allows to securely store biometric data and to perform user authentication without the need of sharing any secret key. This paper analyzes this model, showing that it offers a suitable protection against information leakage and several advantages with respect to similar solutions, such as the fuzzy commitment scheme. Furthermore, the design and characterization of LDPC codes to be used for this purpose is addressed.Comment: in Proceedings 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies (ISABEL), ACM 2011. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistributio