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International audience; Located in the Southwest Pacific Ocean, the New Caledonian archipelago hosts a diversified and original ichthyofauna. Marine ecosystems host 2,339 species of fish, including ~1,450 for coral reefs alone and a total of 94 endemics, especially in deep environments. the proximity of the centre of biodiversity (the "coral triangle"), as well as a great variety of coastal habitats and their relatively good "state of health" are probably major reasons for this high species richness. Freshwaters (excluding estuaries and brackish water) have 94 species, including 12 introduced and 8 endemics. Most of these species are diadromous, essentially amphidromous, and illustrate biological traits adapted to local rivers. new Caledonian ichthyofauna is subject to various disturbances of varying intensity and/or frequency. some disturbances are natural and affect habitats rather than the fish species, such as cyclones, which can affect both coastal ecosystems (coral reefs, seagrass beds, mangroves) and freshwater ecosystems. anthropogenic pressures on ichthyofauna are of several natures. Fishing is widely practiced, both in rivers and in coastal environments and in the EEZ, but does not currently seem to pose a serious threat to targeted populations. New Caledonian aquaculture is largely focused on shrimp farming, but fish farming (currently marginal) could develop in the near future. Mining activities related to the extraction of nickel ore (and cobalt to a lesser extent) are however a much more serious problem. the potential impacts of these mining activities differ from those of cyclones, in particular by their regular (if not permanent) and non-punctual nature on the one hand, and by the fact that they considerably increase the risk of contamination of freshwater and coastal environments by metallic trace elements on the other hand. these metallic elements as well as various organic contaminants (pesticides and PCBs) are indeed found in coral reef fish. Other more specific threats concern freshwater fish, such as hydraulic developments or the proliferation of certain introduced and invasive species. For all new Caledonian aquatic ecosystems, the major issue of climate change cannot be ignored, but its impacts still remain poorly documented. About 15,000 km² of coral reef and lagoon areas have been listed as UNESCO World heritage since 2008 and are therefore protected and regulated, with regard to the activities authorized within these areas. in addition, there are more informal protections in other coastal areas where the Melanesian tribes have a customary management. Finally, various regulations exist at local authority level (environmental codes) to protect certain sensitive species.; Situé dans le sud-ouest de l’océan Pacifique, l’archipel néo-calédonien héberge une ichtyofaune diversifiée et originale. Les milieux marins rassemblent 2339 espèces de poissons, dont ~1450 pour les seuls récifs coralliens et un total de 94 endémiques, surtout en milieux profonds. La proximité du centre de biodiversité (le “triangle de corail”), ainsi que la très grande variété des habitats côtiers et leur relatif bon “état de santé” sont probablement des raisons majeures pour expliquer cette richesse spécifique élevée. Les eaux douces (hors estuaires et eaux saumâtres) comptent 94 espèces, dont 12 introduites et 8 endémiques. La plupart de ces espèces sont diadromes et surtout amphidromes et illustrent un mode de vie adapté aux rivières locales. L’ichtyofaune néo-calédonienne est soumise à différentes perturbations d’intensité et/ou de fréquence variables. Certaines perturbations sont naturelles et vont affecter les habitats plus que les espèces de poissons elles-mêmes, comme par exemple les cyclones qui peuvent affecter à la fois les écosystèmes côtiers (récifs coralliens, herbiers de phanérogames, mangroves) et d’eaux douces. Les pressions anthropiques sur l’ichtyofaune sont de plusieurs natures. La pêche est largement pratiquée, tant en rivière qu’en milieux côtiers et dans la ZEE, mais ne semble pas actuellement constituer une grave menace pour les populations ciblées. L’aquaculture néo-calédonienne est très largement focalisée sur la crevetticulture, mais la pisciculture (actuellement marginale) pourrait se développer dans les années à venir. Les activités minières en lien avec l’extraction du nickel (et accessoirement du cobalt) sont une problématique nettement plus sérieuse. Les impacts potentiels de ces activités minières diffèrent de ceux des cyclones notamment par leur côté régulier (sinon permanent) et non ponctuel d’une part, et par le fait qu’ils accroissent considérablement le risque de contamination des milieux dulçaquicoles et côtiers par des éléments traces métalliques d’autre part. Ces éléments métalliques ainsi que divers contaminants organiques (pesticides et PCBs) sont en effet retrouvés dans les poissons coralliens. D’autres menaces plus spécifiques concernent les poissons d’eau douce, comme les aménagements hydrauliques ou encore la prolifération de certaines espèces introduites et invasives. Pour tous les écosystèmes aquatiques néo-calédoniens, l’enjeu majeur du changement climatique ne peut être ignoré, mais ses impacts restent encore peu documentés. Environ 15 000 km² de zones récifo-lagonaires sont inscrites au Patrimoine Mondial de l’UNESCO depuis 2008 et sont, de ce fait, protégées et règlementées. À ceci s’ajoute des protections plus informelles dans d’autres secteurs côtiers où les tribus mélanésiennes assurent une gestion coutumière. Enfin, diverses règlementations existent au niveau des collectivités locales (codes de l’environnement) pour protéger certaines espèces sensibles.

International audience; Three specimens of Hippichthys albomaculosus Jenkins and Mailautoka, 2010, only known from Fiji, were recently collected from the North Province of New Caledonia. Morphomeristic values confirm the identity of specimens. This study constitutes the first record of this species in New Caledonia and outside of its type locality.; Trois spécimens d'Hippichthys albomaculosus Jenkins & Mailautoka, 2010, connu uniquement des Fidji, ont été récemment collectés dans la province Nord de la Nouvelle-Calédonie. Les valeurs morpho-méristiques confirment l'identité des spécimens. Cette étude constitue le premier signalement de cette espèce en Nouvelle-Calédonie et hors de sa localité type.

Motivation Global freshwater fish biodiversity and the responses of fishes to global changes have been explored intensively using taxonomic data, whereas functional aspects remain understudied owing to the lack of knowledge for most species. To fill this gap, we compiled morphological traits related to locomotion and feeding for the world freshwater fish fauna based on pictures and scientific drawings available from the literature. Main types of variables contained The database includes 10 morphological traits measured on 8,342 freshwater fish species, covering 48.69% of the world freshwater fish fauna. Spatial location and grain Global. Major taxa and level of measurement The database considers ray-finned fishes (class Actinopterygii). Measurements were made at the species level. Software format .csv. Main conclusion The FISHMORPH database provides the most comprehensive database on fish morphological traits to date. It represents an essential source of information for ecologists and environmental managers seeking to consider morphological patterns of fish faunas throughout the globe, and for those interested in current and future impacts of human activities on the morphological structure of fish assemblages. Given the high threat status of freshwater environments and the biodiversity they host, we believe this database will be of great interest for future studies on freshwater ecology research and conservation.

MDS matrices are of great importance in the design of block ciphers and hash functions. MDS matrices are not sparse and have a large description and thus induce costly implementation in software/hardware. To overcome this problem, in particular for applications in light-weight cryptography, it was proposed by Guo et al. to use recursive MDS matrices. A recursive MDS matrix is an MDS matrix which can be expressed as a power of some companion matrix. Following the work of Guo et al., some ad-hoc search techniques are proposed to find recursive MDS matrices which are suitable for hardware/software implementation. In another direction, coding theoretic techniques are used to directly construct recursive MDS matrices: Berger technique uses Gabidulin codes and Augot et al. technique uses shortened BCH codes. In this paper, we first characterize the polynomials that yield recursive MDS matrices in a more general setting. Based on this we provide three methods for obtaining such polynomials. Moreover, the recursive MDS matrices obtained using shortened BCH codes can also be obtained with our first method. In fact we get a larger set of polynomials than the method which uses shortened BCH codes. Our other methods appear similar to the method which uses Gabidulin codes. We get a new infinite class of recursive MDS matrices from one of the proposed methods. Although we propose three methods for the direct construction of recursive MDS matrices, our characterization results pave the way for new direct constructions.

MDS matrices allow to build optimal linear diffusion layers in the design of block ciphers and hash functions. There has been a lot of study in designing efficient MDS matrices suitable for software and/or hardware implementations. In particular recursive MDS matrices are considered for resource constrained environments. Such matrices can be expressed as a power of simple companion matrices, i.e., an MDS matrix $$M = C_g^k$$M=Cgk for some companion matrix corresponding to a monic polynomial $$g(X) \in \mathbb {F}_q[X]$$g(X)źFq[X] of degree k. In this paper, we first show that for a monic polynomial g(X) of degree $$k\ge 2$$kź2, the matrix $$M = C_g^k$$M=Cgk is MDS if and only if g(X) has no nonzero multiple of degree $$\le 2k-1$$≤2k-1 and weight $$\le k$$≤k. This characterization answers the issues raised by Augot et al. in FSE-2014 paper to some extent. We then revisit the algorithm given by Augot et al. to find all recursive MDS matrices that can be obtained from a class of BCH codes (which are also MDS) and propose an improved algorithm. We identify exactly what candidates in this class of BCH codes yield recursive MDS matrices. So the computation can be confined to only those potential candidate polynomials, and thus greatly reducing the complexity. As a consequence we are able to provide formulae for the number of such recursive MDS matrices, whereas in FSE-2014 paper, the same numbers are provided by exhaustively searching for some small parameter choices. We also present a few ideas making the search faster for finding efficient recursive MDS matrices in this class. Using our approach, it is possible to exhaustively search this class for larger parameter choices which was not possible earlier. We also present our search results for the case $$k=8$$k=8 and $$q=2^{16}$$q=216.

International audience; This paper studies the security level expected by the canon-ical form of the Self-Synchronizing Stream Cipher (SSSC). A SSSC can be viewed as the combination of a shift register together with a filtering function. The maximum security of such a cipher is reached when the filtering function is random. However, in practice, Pseudo Random Functions (PRF) are used as filtering functions. In this case, we show that the security against chosen ciphertext attacks (IND-CCA security) cannot be reached for the canonical form of the SSSC, but it is however secure against chosen plaintext attacks (IND-CPA secure). Then, a weaker property than pseudo-randomness is introduced in order to characterize the security of the canonical SSSC from its filtering function. A connection with the left-or-right indistinguishability (LOR-IND) is made. This property provides a necessary and sufficient condition to characterize the indistinguishablity of SSSC.

International audience; LS-designs are a family of bitslice ciphers aiming at efficient masked implementations against side-channel analysis. This paper discusses their security against invariant subspace attacks, and describes an alternative family of eXtended LS-designs (XLS-designs), that enables additional options to prevent such attacks. LS-and XLS-designs provide a large family of ciphers from which efficient implementations can be obtained, possibly enhanced with countermeasures against physical attacks. We argue that they are interesting primitives in order to discuss the general question of " how simple can block ciphers be? " .

In a frequency hopping multiple access (FHMA) system a set of users communicates simultaneously using frequency hopping sequences defined on the same set of frequency channels. A frequency hopping sequence is comprised of frequency channels used to switch channels as communication progresses. Much of the research on the performance of FHMA systems is based on either pairwise mutual interference or adver-sarial interference but not both. In this paper, we evaluate the performance of an FHMA system with respect to both group-wise mutual interference and adversarial interference (jamming), bearing in mind that more than two users may be transmitting simultaneously in the presence of an adversary. Our main contributions are as follows. We point out a correspondence between a cover-free code and a frequency hopping scheme. Cover-free codes give a well defined structure on the transmission capacity of a frequency hopping multiple access system. Further, we specify a jammer model for an FHMA. Considering the resources and knowledge of a jammer, we look at the possible mitigation strategies to be employed by a frequency hopping scheme against the jammer, and determine necessary and desirable additional properties of cover-free codes such that they may be used in the presence of adversarial interference.

International audience; Polynomials of type x^{q^3 +q^2 +q+2} +bx over the field F_{q^4} , where q = 2^m , m ≥ 2, are considered. All cases when these polynomials are permutation polynomials are classified.

An s-subset of codewords of a binary code X is said to be (s,l)-bad in X if the code X contains a subset of other l codewords such that the conjunction of the l codewords is covered by the disjunctive sum of the s codewords. Otherwise, the s-subset of codewords of X is called (s,l)-good in X. A binary code X is said to be a cover-free (CF) (s,l)-code if the code X does not contain (s,l)-bad subsets. In this paper, we introduce a natural probabilistic generalization of CF (s,l)-codes, namely: a binary code X is said to be an almost CF (s,l)-code if the relative number of its (s,l)-good s-subsets is close to 1. We develop a random coding method based on the ensemble of binary constant weight codes to obtain lower bounds on the capacity of such codes. Our main result shows that the capacity for almost CF (s,l)-codes is essentially greater than the rate for ordinary CF (s,l)-codes.

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes., The Danish Council for Independent Research (DFF-4002-00367), the Spanish MINECO/FEDER (MTM2015-65764-C3-2-P), Japan Society for the Promotion of Science (23246071 and 26289116), the Villum Foundation through their VELUX Visiting Professor Programme 2013-2014, and the "Program for Promoting the Enhancement of Research Universities'' at Tokyo Institute of Technology.

Let k be the finite field of characteristic p and order q = p e , and suppose that gcd(d, q − 1) = 1. Then the map x → x d is a permutation of k, known as a power permutation. If Tr is the absolute trace from k to the prime field F p , then x → Tr(x d) is a p-ary function that is of interest in differential cryptanalysis. The Walsh transform compares our p-ary function with all the F p-linear functionals, which have the form x → Tr(ax) with a ∈ F p. Thus the Walsh transform is used to determine the nonlinearity of our p-ary function. If we let ψ k (x) = e 2πiTr(x)/p be the canonical additive character of k, then the spectrum of the Walsh transform is given by the values of a Weil sum with ψ k applied to a binomial argument, W k,d (a) = x∈k ψ k (x d − ax), where k and d are fixed, and we let a run through k. In fact, since W k,d (0) = 0 trivially, our interest is in the distribution of values as a runs through k ×. The values of W k,d give not only the Walsh transform of a power permutation , but also to the cross-correlation spectrum of a pair of maximal linear recursive sequences of length q − 1 and relative decimation d, as well as the weight distribution of the dual of the cyclic code of length q −1 whose zeroes are two primitive elements α and α d of the field k. If d is a power of p modulo q − 1, then the canonical additive character ψ k has the same value when applied to the binomial x d − ax as it does when applied to the monomial (1 − a)x, and we obtain W k,d (1) = q and W k,d (a) = 0 for all a = 1. Thus the Weil sum can only take two distinct values, and we say that d is degenerate over k. In 1976, Helleseth proved that if d is nondegenerate over k, then W k,d assumes at least three values. We are interested in the case whenWk,d takes exactly three values for a ∈ k ×, in which case we say that Wk,d is three-valued.We shall examine all the known infinite families of fields k and exponents d that produce three-valued Weil sums. Then we shall indicate patterns, both conjectured and proved, that have been observed in the three-valued spectra. We review recent progress on these conjectures, and conclude with some open problems.

In this article we study the application of multiple righthand sides (MRHS) equations in algebraic attacks against ciphers with low multiplicative complexity. Each AND gate in the circuit description is converted to a corresponding MRHS equation. The resulting system is transformed into a syndrome decoding problem. The complexity of the decoding problem then depends on the number of AND gates, and on the relative number of known output bits with respect to the number of unknown key bits. This allows us to apply results from coding theory, and explicitly connect the complexity of algebraic cryptanalysis to the multiplicative complexity of the cipher.

In this paper, we revisit some existing techniques in Salsa20 cryptanalysis, and provide some new ideas as well. As a new result, we explain how a valid initial state can be obtained from a Salsa20 state after one round. This helps in studying the non-randomness of Salsa20 after 5 rounds. In particular, it can be seen that the 5-round bias reported by Fischer et al. (Indocrypt 2006) is a special case of our analysis. Towards improving the existing results, we revisit the idea of Probabilistic Neutral Bit (PNB) and how a proper choice of certain parameters reduce the complexity of the existing attacks. For cryptanalysis against 8-round Salsa20, we could achieve the key search complexity of 2 247.2 compared to the earlier results of 2 251 (FSE 2008) and 2 250 (ICISC 2012).

In this work, we extend research in the area of reconstruction of private RSA keys using few random bits made available through partial key exposure attacks such as the Cold Boot Attack. Our work discusses an approach to reconstruct private components of RSA from the most significant bit (MSB) side given only 26% of the secret bits. Our approach shows significant improvement over previous works on reconstruction from the MSB side. Our results closely match those of the Heninger and Shacham that gives reconstruction from the LSB side.

The lower bound of the covering radius of binary irreducible Goppa codes is obtained.

In this paper, we consider symmetric disjunctive list-decoding (SLD) codes, which are a class of binary codes based on a symmetric disjunctive sum (SDS) of binary symbols. By definition, the SDS takes values from the ternary alphabet {0, 1, * }, where the symbol * denotes " erasure ". Namely: SDS is equal to 0 (1) if all its binary symbols are equal to 0 (1), otherwise SDS is equal to *. The main purpose of this work is to obtain bounds on the rate of these codes.

RC4 is one of the most popular stream cipher with wide industrial applications, it has received serious attention in cryptology literature in the last two decades. In 1995, Roos pointed out that the elements SN [y] of the permutation SN after the Key Scheduling Algorithm for the first few values of y are biased to certain combinations of secret key bytes. These correlations were theoretically studied by Paul and Maitra (SAC 2007). The formula for the correlation probabilities provided by them gives a wrong impression that the probabilities decrease as the value of y becomes larger, which is not true. In this paper, we point out some gaps in their analysis and present a detailed analysis of Roos Bias. We provide a more accurate formula for the correlation probabilities.

Field inversion in F2m dominates the cost of modern software implementations of certain elliptic curve cryptographic operations, such as point encoding/hashing into elliptic curves. [7, 6, 2] Itoh–Tsujii inversion using a polynomial basis and precomputed table-based multi-squaring has been demonstrated to be highly effective for software implementations [19, 14, 2], but the performance and memory use depend critically on the choice of addition chain and multi-squaring tables, which in prior work have been determined only by suboptimal ad-hoc methods and manual selection. We thoroughly investigated the performance/memory tradeoff for table-based linear transforms used for efficient multi-squaring. Based upon the results of that investigation, we devised a comprehensive cost model for Itoh–Tsujii inversion and a corresponding optimization procedure that is empirically fast and provably finds globally-optimal solutions. We tested this method on 8 binary fields commonly used for elliptic curve cryptography; our method found lower-cost solutions than the ad-hoc methods used previously, and for the first time enables a principled exploration of the time/memory tradeoff of inversion implementations.

International audience; This manuscript deals with extending a normal basis to a new basis which permits both computationally inexpensive exponentia-tion and multiplication. These new bases are motivated by Artin-Schreier theory, and are particularly useful when creating bases in Artin-Schreier extensions of finite fields.

In this work, we completely characterize (i) permutation bi-nomials of the form f (x) = x^{( 2^n −1)/( 2^k −1) +1} + ax ∈ F2^n [x], k odd and n = 2^r k(r ≥ 1), a ∈ F *_{2^{2k}} , and (ii) permutation trinomials of the form x^{ 2^r +1} +x^{ 2^r−1} +1 +αx ∈ F _{2^k} [x], k odd. First result, which was our primary motivation, is a consequence of the second result. Second result may be of independent interest.

International audience; We prove a better than previously known lower bound on the rate of codes for multiple access adder channel with noise and discuss its application to well-known coin weighing problem with not exact measurements.

In this paper we investigate univariate algebraic attacks on filter generators over extension fields F_q = F_{2^n} with focus on the Welch-Gong (WG) family of stream ciphers. Our main contribution is to break WG-5,WG-7,WG-8 and WG-16 by combining results on the so-called spectral immunity (minimum distance of certain cyclic codes) with properties of the WG type stream cipher construction.The spectral immunity is the univariate analog of algebraic immunity and instead of measuring degree of multiples of a multivariate polynomial, it measures the minimum number of nonzero coecients of a multiple of a univariate polynomial. Based on the structure of the general WG-construction, we deduce better bounds for the spectral immunity and the univariate analog of algebraic attacks.

No abstract provided by the authors.

We study an RSA variant with moduli of the form N = p r q l with r > l ≥ 2. This variant was mentioned by Boneh et al. (Crypto 1999). Later Kim et al. (Indocrypt 2000) showed that this variant is much faster than standard RSA moduli in the decryption process. In this paper, for the first time, we give some cryptanalysis results on this RSA variant. Our analysis show that in some cases, this cryptosystem can be totally broken.

This work is related to new multicomponent network codes for a channel with random linear transformations and packet errors. New code construction is a generalization of Gabidulin-Pilipchuk codes, and similarly uses rank codes with restrictions as subcodes. Usage of a greedy algorithm, when selecting the code components, allows us to increase code cardinality compared with the previously known constructions. We provide the conditions under which the described multicomponent code can correct both erasures and packet errors in the channel. Finally, we present an efficient algorithm of decoding both types of errors and give some examples.

Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound holds only in the linear case. In this paper we identify code parameters (q, d, k) for which the Griesmer bound holds also in the (systematic) nonlinear case. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit counterexamples. On the other hand, we are also able to provide some versions of the Griesmer bound holding for all systematic codes.

Gyarmati, Mauduit and Sarkozy introduced the cross-correlation measure $$\Phi _k(\mathcal {F})$$ to measure the randomness of families of binary sequences $$\mathcal {F}\subset \{-1,1\}^N$$ . In this paper we study the order of magnitude of the cross-correlation measure $$\Phi _k(\mathcal {F})$$ for typical families. We prove that, for most families $$\mathcal {F}\subset \{-1,1\}^N$$ of size $$2\le |\mathcal {F}

In this paper we experiment with cube testers on reduced round Trivium that can act as a distinguisher. Using heuristics, we obtain several distinguishers for Trivium running more than 800 rounds (maximum 829) with cube sizes not exceeding 27. In the process, we also exploit state biases that has not been explored before. Further, we apply our techniques to analyse Trivia-SC, a stream cipher proposed by modifying the parameters of Trivium and used as a building block for TriviA-ck (an AEAD scheme, which is submitted to the ongoing CAE-SAR competition). We obtain distinguishers till 900 rounds of Trivia-SC with a cube size of 21 only and our results refute certain claims made by the designers. These are the best results reported so far, though our work does not affect the security claims for the ciphers with full initialization rounds, namely 1152.

Multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions which have multiple poles/zeros on their defining curves. The one-point codes which are viewed as its subclass can be decoded efficiently up to the Feng-Rao bound by using the BMS algorithm with majority logic [1]. Recently we published [2] a fast method for decoding primal multipoint codes from curves based on the vectorial BMS algorithm [3]. Although the simulation shows that the method can correct most error patterns of weight up to 1/2 d_G, it is guaranteed theoretically that every error of weight only up to 1/2 (d_G − g) can be corrected, where g is the genus of the defining curve. In this paper we present a fast method for decoding dual multipoint codes from algebraic curves up to the Kirfel-Pellikaan bound, based on the vectorial BMS algorithm with majority logic.

International audience; Among statistical attacks, we often make a distinction between attacks in the linear context, for which the knowledge of plaintexts and corresponding ciphertexts is enough to perform the attack, and attacks in the differential context, for which the plaintexts are chosen. Such attacks are usually referred as known-or chosen-plaintext attacks. It is commonly believed that attacks in the known-plaintext model are more practical than attacks in the chosen-plaintext model. Nevertheless , it is usual in the literature, to only compare the data, time and memory complexity of these attacks without considering the model. In this paper, we reconsider some known-plaintext attacks, by considering them in the distinct-known-plaintext model. We explain and develop the statistical model for the multiple zero-correlation linear cryptanalysis, multidimensional linear cryptanalysis, as well as for the key-difference-invariant-bias related-key attack introduced at ASIACRYPT 2013. Based on these models validated by experiments, we improve attacks on some ciphers.

International audience; In this paper, we propose a new encoding scheme for space-time coding. This encoding relies on the generalisation [2] of Gabidulin codes to innite elds. This enables to make use of the properties of Gabidulin codes, namely, we can use algebraic decoding algorithms.

We obtain a bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound in the case of classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer's BCH bound. We compare our bounds' performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results.

In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1]. (C) 2016 Elsevier Inc. All rights reserved.

International audience; The advent of a heuristic quasi-polynomial complexity algorithm in 2013 for solving the discrete logarithm problem over small characteristic finite fields has had the consequence that this problem can no longer be considered as being sufficiently hard for cryptographic needs. We will describe the idea of the algorithm, its more recent modifications, and consider directions for extensions to other contexts.

We discover some important properties of cover-free (CF) codes, separating system (SS) codes and completely separating system (CSS) codes connected with the concept of constant weight CF codes. New upper and lower bounds on the rate of CF and SS codes based on the known results for CF and CSS codes are obtained. Tables of numerical values for the improved upper and lower bounds are presented.