Manabu Hagiwara

Cryptographie key generation from PUF data using efficient fuzzy extractors

Physical unclonable functions (PUFs) and biometrics are inherently noisy. When used in practice as cryptographic key generators, they need to be combined with an extraction technique to derive reliable bit strings (i.e., cryptographic key). An approach based on an error correcting code was proposed by Dodis et al. and is known as a fuzzy extractor. However, this method appears to be difficult for non-specialists to implement. In our recent study, we reported the results of some example implementations using PUF data and presented a detailed implementation diagram. In this paper, we describe a more efficient implementation method by replacing the hash function output with the syndrome from the BCH code. The experimental results show that the Hamming distance between two keys vary according to the key size and information-theoretic security has been achieved.

Formalization of Shannon’s Theorems

The most fundamental results of information theory are Shannon’s theorems. These theorems express the bounds for (1) reliable data compression and (2) data transmission over a noisy channel. Their proofs are non-trivial but are rarely detailed, even in the introductory literature. This lack of formal foundations is all the more unfortunate that crucial results in computer security rely solely on information theory: this is the so-called “unconditional security”. In this article, we report on the formalization of a library for information theory in the SSReflect extension of the Coq proof-assistant. In particular, we produce the first formal proofs of the source coding theorem, that introduces the entropy as the bound for lossless compression, and of the channel coding theorem, that introduces the capacity as the bound for reliable communication over a noisy channel.

On ordered syndromes for multi insertion/deletion error-correcting codes

Classes of multi insertion/deletion error-correcting codes based on order theory and axiomatic algebra are proposed by an abstraction of Helbergs construction.

Performance Analysis for PUF Data Using Fuzzy Extractor

The extraction of a stable signal from noisy data is very useful in applications that aim to combine it with a cryptographic key. An approach based on an error correcting code was proposed by Dodis et al., which is known as a fuzzy extractor. Physical unclonable functions (PUFs) generate device-specific data streams, although PUFs are noisy functions. In this paper, we describe a method for preparing a PUF key during fuzzy extractor implementation. The experimental results showed that all possible combinations of input message length and the number of correctable errors were tested for a BCH code with codeword length N, which was the length of the PUF responses.

Multipermutation Ulam sphere analysis toward characterizing maximal code size

Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric. Multipermutation codes have also been proposed as a generalization of permutation codes that would improve code size. In this paper we analyze the Ulam metric in the context of multipermutations, noting similarities and differences with the Ulam metric in the context of permutations. We then consider sphere sizes for multipermutations under the Ulam metric and resulting bounds on code size.

Consolidation for compact constraints and Kendall tau LP decodable permutation codes

Invented in the 1960s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications, especially flash memory. In 2011 a polynomial time algorithm called linear programming (LP) decoding was introduced for a class of permutation codes where the feasible set of codewords was a subset of the vertex set of a code polytope. In this paper we investigate a new class of linear constraints for matrix polytopes with no fractional vertices through a new concept called “consolidation.” We then introduce a necessary and sufficient condition for which LP decoding methods, originally designed for the Euclidean metric, may be extended to provide an efficient decoding algorithm for permutation codes with the Kendall tau metric.

A Deep Neural Network Architecture Using Dimensionality Reduction with Sparse Matrices

We present a new deep neural network architecture, motivated by sparse random matrix theory that uses a low-complexity embedding through a sparse matrix instead of a conventional stacked autoencoder. We regard autoencoders as an information-preserving dimensionality reduction method, similar to random projections in compressed sensing. Thus, exploiting recent theory on sparse matrices for dimensionality reduction, we demonstrate experimentally that classification performance does not deteriorate if the autoencoder is replaced with a computationally-efficient sparse dimensionality reduction matrix.

Perfect codes for single balanced adjacent deletions

Two classes of perfect codes for single balanced adjacent deletions (BADs) are provided. These classes are inspired by Levenshteins work on binary perfect codes for single standard deletions. One of the classes is defined via inversion numbers and the other is defined via Levenshtein codes. The first half of this paper is devoted to the proof of perfectness and the second half is devoted to discussion on the other properties of the provided codes.

Formalization of Bing’s Shrinking Method in Geometric Topology

Bing’s shrinking method is a key technique for constructing homeomorphisms between topological manifolds in geometric topology. Applications of this method include the generalized Schoenflies theorem, the double suspension theorem for homology spheres, and the 4-dimensional Poincare conjecture. Homeomorphisms obtained in this method are sometimes counter-intuitive and may even be pathological. This makes Bing’s shrinking method a good target of formalization by proof assistants. We report our formalization of this method in Coq/Ssreflect.