Information Sets of Multiplicity Codes

We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party. We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions. We also give a complexity estimate of the associated encoding algorithm.Comment: International Symposium on Information Theory, Jun 2015, Hong-Kong, China. IEE

On self-dual affine-invariant codes

AbstractAn extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Reed-Muller code [2m, 2m−1, 2(m+1)2] is affine-invariant and self-dual, and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2m for m = 7 and m = 9. For each odd m, m ⩾ 9, we exhibit a self-dual affine-invariant code of length 2m over GF(2) which is not the self-dual Reed-Muller code. In the first part of the paper, we present the class of self-dual affine-invariant codes of length 2m over GF(2r), and the tools we apply later to the binary codes

Minimizing the effect of sinusoidal trends in detrended fluctuation analysis

The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been claimed to be a superior technique, recent reports have indicated its susceptibility to trends in the data. In this report, a smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log-log plots obtained by DFA and MF-DFA techniques

Interpolation de signaux par conservation de la régularité Höldérienne

é - On considère le problème de l'interpolation d'un signal dans Rd connu à une certaine résolution. On suppose que le signal appartient à une classe de signaux caractérisée par des contraintes sur la régularité locale, qui peuvent être traduites par un certain comportement inter-échelles des coefficients d'ondelette. Ces contraintes permettent de prédire les coefficients de l'échelle n + 1 à partir de ceux des échelles précédentes. Nous donnons quelques propriétés de cette technique d'interpolation, concernant en particulier la régularité Hôldérienne du signal raffiné et son comportement asymptotique. Les résultats théoriques et numériques montrent que notre méthode permet d'obtenir des signaux ou des images interpolés de bonne qualité. En particulier, l'aspect visuel de régularité ou d'irrégularité est respecté après interpolation

Bounds on the minimum distance of the duals of BCH codes

International audienceWe consider primitive cyclic codes of length p^m-1 over Fp. The codes of interest here are duals of BCH codes. For these codes, a lower bound on their minimum distance can be found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We shall fill this gap by giving, in the first part of the correspondence, a lower bound for an infinite class of duals of BCH codes. Since this family is a filtration of the duals of BCH codes, the bound obtained for it induces a bound for all duals. In the second part we present a lower bound obtained by implementing an algorithmic method due to Massey and Schaub (1988)-the rank-bounding algorithm. The numerical results are surprisingly higher than all previously known bound

A Composable Look at Updatable Encryption

Updatable Encryption (UE), as originally defined by Boneh et al. in 2013, addresses the problem of key rotation on outsourced data while maintaining the communication complexity as low as possible. The security definitions for UE schemes have been constantly updated since then. However, the security notion that is best suited for a particular application remains unclear. To solve this problem in the ciphertext-independent setting, we use the Constructive Cryptography (CC) framework defined by Maurer et al. in 2011. We define and construct a resource that we call Updatable Server-Memory Resource USMR, and study the confidentiality guarantees it achieves when equipped with a UE protocol, that we also model in this framework. With this methodology, we are able to construct resources tailored for each security notion. In particular, we prove that IND-UE-RCCA is the right security notion for many practical UE schemes. As a consequence, we notably rectify a claim made by Boyd et al. , namely that their IND-UE security notion is better than the IND-ENC+UPD notions, in that it hides the age of ciphertexts. We show that this is only true when ciphertexts can leak at most one time per epoch. We stress that UE security is thought of in the context of adaptive adversaries, and UE schemes should thus bring post-compromise confidentiality guarantees to the client. To handle such adversaries, we use an extension of CC due to Jost et al. and give a clear, simple and composable description of the post-compromise security guarantees of UE schemes. We also model semi-honest adversaries in CC. Our adaption of the CC framework to UE is generic enough to model other interactive protocols in the outsourced storage setting

More on the Covering Radius of BCH Codes

Résumé disponible dans le fichier PD

Bounds on the minimum distance of the duals of BCH codes

International audienceWe consider duals of BCH codes of length p^m-1 over GF(p). A lower bound on their minimum distance is found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We partially fill this gap by giving a lower bound for an infinite class of duals of BCH codes. We also present a lower bound obtained with an algorithm due to Massey and Schaub (1988). In the case of binary codes of length 127 and 255, the results are surprisingly higher than all previously known bound

Polynomial equivalence problems and applications to multivariate cryptosystems

At Eurocrypt'96, J.Patarin proposed a signature and authentication scheme whose security relies on the difficulty of the Isomorphism of Polynomials problem . In this paper, we study a variant of this problem, namely the Isomorphism of Polynomials with one secret problem and we propose new algorithms to solve it, which improve on all the previously known algorithms. As a consequence, we prove that, when the number of polynomials (u) is close to the number of variables (n), the instances considered in and can be broken. We point out that the case n-u small is the most relevant one for cryptographic applications. Besides, we show that a large class of instances that have been presumed difficult in and can be solved in deterministic polynomial time. We also give numerical results to illustrate our methods

Scale invariant correlations and the distribution of prime numbers

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.Comment: 13 pages, 8 figures, version to appear in J. Phys.