A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field

Using the Weyl commutation relations over a finite field we introduce a family of error-correcting quantum stabilizer codes based on a class of symmetric matrices over the finite field satisfying certain natural conditions. When the field is GF(2) the existence of a rich class of such symmetric matrices is demonstrated by a simple probabilistic argument depending on the Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these symmetric matrices are assumed to be circulant it is possible to obtain concrete examples by a computer program. The quantum codes thus obtained admit elegant encoding circuits.Comment: 16 pages, 2 figure

Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance

Classic McEliece Implementation with Low Memory Footprint

The Classic McEliece cryptosystem is one of the most trusted quantum-resistant cryptographic schemes. Deploying it in practical applications, however, is challenging due to the size of its public key. In this work, we bridge this gap. We present an implementation of Classic McEliece on an ARM Cortex-M4 processor, optimized to overcome memory constraints. To this end, we present an algorithm to retrieve the public key ad-hoc. This reduces memory and storage requirements and enables the generation of larger key pairs on the device. To further improve the implementation, we perform the public key operation by streaming the key to avoid storing it as a whole. This additionally reduces the risk of denial of service attacks. Finally, we use these results to implement and run TLS on the embedded device

Faster Algorithms for Solving LPN

The LPN problem, lying at the core of many cryptographic constructions for lightweight and post-quantum cryptography, receives quite a lot attention recently. The best published algorithm for solving it at Asiacrypt 2014 improved the classical BKW algorithm by using covering codes, which claimed to marginally compromise the $80$-bit security of HB variants, LPN-C and Lapin. In this paper, we develop faster algorithms for solving LPN based on an optimal precise embedding of cascaded concrete perfect codes, in a similar framework but with many optimizations. Our algorithm outperforms the previous methods for the proposed parameter choices and distinctly break the 80-bit security bound of the instances suggested in cryptographic schemes like HB$^+$, HB$^\#$, LPN-C and Lapin

Targeting vascular endothelial growth factor receptor 2 and protein kinase d1 related pathways by a multiple kinase inhibitor in angiogenesis and inflammation related processes in vitro.

Emerging evidence suggests that the vascular endothelial growth factor receptor 2 (VEGFR2) and protein kinase D1 (PKD1) signaling axis plays a critical role in normal and pathological angiogenesis and inflammation related processes. Despite all efforts, the currently available therapeutic interventions are limited. Prior studies have also proved that a multiple target inhibitor can be more efficient compared to a single target one. Therefore, development of novel inflammatory pathway-specific inhibitors would be of great value. To test this possibility, we screened our molecular library using recombinant kinase assays and identified the previously described compound VCC251801 with strong inhibitory effect on both VEGFR2 and PKD1. We further analyzed the effect of VCC251801 in the endothelium-derived EA.hy926 cell line and in different inflammatory cell types. In EA.hy926 cells, VCC251801 potently inhibited the intracellular activation and signaling of VEGFR2 and PKD1 which inhibition eventually resulted in diminished cell proliferation. In this model, our compound was also an efficient inhibitor of in vitro angiogenesis by interfering with endothelial cell migration and tube formation processes. Our results from functional assays in inflammatory cellular models such as neutrophils and mast cells suggested an anti-inflammatory effect of VCC251801. The neutrophil study showed that VCC251801 specifically blocked the immobilized immune-complex and the adhesion dependent TNF-alpha -fibrinogen stimulated neutrophil activation. Furthermore, similar results were found in mast cell degranulation assay where VCC251801 caused significant reduction of mast cell response. In summary, we described a novel function of a multiple kinase inhibitor which strongly inhibits the VEGFR2-PKD1 signaling and might be a novel inhibitor of pathological inflammatory pathways

Blackbox secret sharing revisited: A coding-theoretic approach with application to expansionless near-threshold schemes

A blackbox secret sharing (BBSS) scheme works in exactly the same way for all finite Abelian groups G; it can be instantiated for any such group G and only black-box access to its group operations and to random group elements is required. A secret is a single group element and each of the n players’ shares is a vector of such elements. Share-computation and secret-reconstruction is by integer linear combinations. These do not depend on G, and neither do the privacy and reconstruction parameters t, r. This classical, fundamental primitive was introduced by Desmedt and Frankel (CRYPTO 1989) in their context of “threshold cryptography.” The expansion factor is the total number of group elements in a full sharing divided by n. For threshold BBSS with t-privacy (Formula presented)-reconstruction and arbitrary n, constructions with minimal expansion (Formula presented) exist (CRYPTO 2002, 2005). These results are firmly rooted in number theory; each makes (different) judicious choices of orders in number fields admitting a vector of elements of very large length (in the number field degree) whose corresponding Vandermonde-determinant is sufficiently controlled so as to enable BBSS by a suitable adaptation of Shamir’s scheme. Alternative approaches generally lead to very large expansion. The state of the art of BBSS has not changed for the last 17 years. Our contributions are two-fold. (1) We introduce a novel, nontrivial, effective construction of BBSS based on coding theory instead of number theory. For threshold-BBSS we also achieve minimal expansion factor O(log n).(2) Our method is more versatile. Namely, we show, for the first time, BBSS that is near-threshold, i.e., r-t is an arbitrarily small constant fraction of n, and that has expansion factor O(1), i.e., individual share-vectors of constant length (“asymptotically expansionless”). Threshold can be concentrated essentially freely across full range. We also show expansion is minimal for near-threshold and that such BBSS cannot be attained by previous methods. Our general construction is based on a well-known mathematical principle, the local-global principle. More precisely, we first construct BBSS over local rings through either Reed-Solomon or algebraic geometry codes. We then “glue” these schemes together in a dedicated manner to obtain a global secret sharing scheme, i.e., defined over the integers, which, as we finally prove using novel insights, has the desired BBSS properties. Though our main purpose here is advancing BBSS for its own sake, we also briefly address possible protocol applications