ISSN:

1930-5346

eISSN:

1930-5338

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## Advances in Mathematics of Communications

May 2020 , Volume 14 , Issue 2

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**Abstract:**

Proxy signature is a cryptographic primitive that allows an entity to delegate singing rights to another entity. Noticing the ad-hoc nature of security analysis prevalent in the existing literature, Boldyreva, Palacio and Warinschi proposed a formal security model for proxy signature. We revisit their proposed security definition in the context of the most natural construction of proxy signature – delegation-by-certificate. Our analysis indicates certain limitations of their definition that arise due to malleability of proxy signature as well as signature ownership in the context of standard signature. We propose a stronger definition of proxy signature to address these issues. However, we observe that the natural reductionist security argument of the delegation-by certificate proxy signature construction under this definition seems to require a rather unnatural security property for a standard signature.

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**Abstract:**

Although currently several traceable (or linkable) ring signature schemes have been proposed, most of them are constructed on pairings. In this paper, we present an efficient traceable ring signature (TRS) scheme without pairings, which is based on the modified EDL signature (first proposed by D.Chaum et al. in Crypto 92). Compared with other ring signature schemes, the proposed scheme does not employ pairing computation and has some computational advantages, whose security can be reduced to the computational Diffie-Hellman (CDH) and decisional Diffie-Hellman (DDH) assumptions in the random oracle model. Also, the proposed scheme is similar to certificateless signature scheme, where user and key generating center make interaction to generate ring key. We give a formal security model for ring signature and prove that the proposed scheme has the properties of traceability and anonymity.

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**Abstract:**

We use group algebra methods to study cyclic codes over finite chain rings and under some restrictive hypotheses, described in section 2, for codes of length

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**Abstract:**

Based on the relation between resilient functions and large sets of orthogonal arrays, two classes of

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**Abstract:**

A Locally Recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. We study Locally Recoverable Algebraic Geometry codes arising from certain curves defined by equations with separated variables. The recovery of erasures is obtained by means of Lagrangian interpolation in general, and simply by one addition in some particular cases.

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**Abstract:**

This paper is concerned with the construction of algebraic-geometric (AG) codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated with some rational places, which enables us to study multi-point AG codes. Along this line, we characterize explicitly the Weierstrass semigroups and pure gaps by an exhaustive computation for the basis of Riemann-Roch spaces from GGS curves. In addition, we determine the floor of a certain type of divisor and investigate the properties of AG codes. Multi-point codes with excellent parameters are found, among which, a presented code with parameters

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**Abstract:**

McNie [

*+*[Abstract](1312)

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**Abstract:**

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. Recently, a series of paper has been published for analysis of expansion complexity and for testing sequences in terms of this new measure of randomness. In this paper, we continue this analysis. First we study the expansion complexity in terms of the Gröbner basis of the underlying polynomial ideal. Next, we prove bounds on the expansion complexity for random sequences. Finally, we study the expansion complexity of sequences defined by differential equations, including the inversive generator.

*+*[Abstract](1398)

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**Abstract:**

We study

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**Abstract:**

A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to have multiple repair groups. In this paper we consider robust locally repairable coding schemes which guarantee that there exist multiple distinct (not necessarily disjoint) alternative local repair groups for any single failure such that the failed node can still be repaired locally even if some of the repair groups are not available. We use linear programming techniques to establish upper bounds on the size of these codes. We also provide two examples of robust locally repairable codes that are optimal regarding our linear programming bound. Furthermore, we address the update efficiency problem of the distributed data storage networks. Any modification on the stored data will result in updating the content of the storage nodes. Therefore, it is essential to minimise the number of nodes which need to be updated by any change in the stored data. We characterise the update-efficient storage code properties and establish the necessary conditions of existence update-efficient locally repairable storage codes.

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**Abstract:**

Let

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**Abstract:**

In this paper, we introduce additive Toeplitz codes over

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