On the security of digital signature schemes based on error-correcting codes

We discuss the security of digital signature schemes based on error-correcting codes. Several attacks to the Xinmei scheme are surveyed, and some reasons given to explain why the Xinmei scheme failed, such as the linearity of the signature and the redundancy of public keys. Another weakness is found in the Alabbadi-Wicker scheme, which results in a universal forgery attack against it. This attack shows that the Alabbadi-Wicker scheme fails to implement the necessary property of a digital signature scheme: it is infeasible to find a false signature algorithm D from the public verification algorithm E such that E(D*(m)) = m for all messages m. Further analysis shows that this new weakness also applies to the Xinmei scheme

On Optimal Family of Codes for Archival DNA Storage

DNA based storage systems received attention by many researchers. This includes archival and re-writable random access DNA based storage systems. In this work, we have developed an efficient technique to encode the data into DNA sequence by using non-linear families of ternary codes. In particular, we proposes an algorithm to encode data into DNA with high information storage density and better error correction using a sub code of Golay code. Theoretically, 115 exabytes (EB) data can be stored in one gram of DNA by our method.Comment: Supplementary file and the software DNA Cloud 2.0 is available at http://www.guptalab.org/dnacloud This is the preliminary version of the paper that appeared in Proceedings of IWSDA 2015, pp. 143--14

Construction of Almost Disjunct Matrices for Group Testing

In a \emph{group testing} scheme, a set of tests is designed to identify a small number $t$ of defective items among a large set (of size $N$) of items. In the non-adaptive scenario the set of tests has to be designed in one-shot. In this setting, designing a testing scheme is equivalent to the construction of a \emph{disjunct matrix}, an $M \times N$ matrix where the union of supports of any $t$ columns does not contain the support of any other column. In principle, one wants to have such a matrix with minimum possible number $M$ of rows (tests). One of the main ways of constructing disjunct matrices relies on \emph{constant weight error-correcting codes} and their \emph{minimum distance}. In this paper, we consider a relaxed definition of a disjunct matrix known as \emph{almost disjunct matrix}. This concept is also studied under the name of \emph{weakly separated design} in the literature. The relaxed definition allows one to come up with group testing schemes where a close-to-one fraction of all possible sets of defective items are identifiable. Our main contribution is twofold. First, we go beyond the minimum distance analysis and connect the \emph{average distance} of a constant weight code to the parameters of an almost disjunct matrix constructed from it. Our second contribution is to explicitly construct almost disjunct matrices based on our average distance analysis, that have much smaller number of rows than any previous explicit construction of disjunct matrices. The parameters of our construction can be varied to cover a large range of relations for $t$ and $N$.Comment: 15 Page

Noise-Resilient Group Testing: Limitations and Constructions

We study combinatorial group testing schemes for learning $d$-sparse Boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of $\tilde{\Omega}(d^2 \log n)$ that is known for exact reconstruction of $d$-sparse vectors of length $n$ via non-adaptive measurements, by a multiplicative factor $\tilde{\Omega}(d)$. Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with $m=O(d \log n)$ measurements, that allow efficient reconstruction of $d$-sparse vectors up to $O(d)$ false positives even in the presence of $\delta m$ false positives and $O(m/d)$ false negatives within the measurement outcomes, for any constant $\delta < 1$. We show that, information theoretically, none of these parameters can be substantially improved without dramatically affecting the others. Furthermore, we obtain several explicit constructions, in particular one matching the randomized trade-off but using $m = O(d^{1+o(1)} \log n)$ measurements. We also obtain explicit constructions that allow fast reconstruction in time \poly(m), which would be sublinear in $n$ for sufficiently sparse vectors. The main tool used in our construction is the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the same title) in proceedings of the 17th International Symposium on Fundamentals of Computation Theory (FCT 2009