# American Institute of Mathematical Sciences

ISSN:
1930-5346

eISSN:
1930-5338

All Issues

## Advances in Mathematics of Communications

Open Access Articles

2020, 14(3): i-i doi: 10.3934/amc.2020101 +[Abstract](588) +[HTML](180) +[PDF](91.27KB)
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2020 doi: 10.3934/amc.2020073 +[Abstract](771) +[HTML](416) +[PDF](438.53KB)
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Number theoretic public-key solutions, currently used in many applications worldwide, will be subject to various quantum attacks, making them less attractive for longer-term use. Certain group theoretic constructs are now showing promise in providing quantum-resistant cryptographic primitives, and may provide suitable alternatives for those looking to address known quantum attacks. In this paper, we introduce a new protocol called a Meta Key Agreement and Authentication Protocol (MKAAP) that has some characteristics of a public-key solution and some of a shared-key solution. Specifically, it has the deployment benefits of a public-key system, allowing two entities that have never met before to authenticate without requiring real-time access to a third-party, but does require secure provisioning of key material from a trusted key distribution system (similar to a symmetric system) prior to deployment. We then describe a specific MKAAP instance, the Ironwood MKAAP, discuss its security, and show how it resists certain quantum attacks such as Shor's algorithm or Grover's quantum search algorithm. We also show Ironwood implemented on several "internet of things" (IoT devices), measure its performance, and show how it performs significantly better than ECC using fewer device resources.

2021, 15(2): 207-218 doi: 10.3934/amc.2020053 +[Abstract](1537) +[HTML](590) +[PDF](373.36KB)
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We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly \begin{document}$45 \%$\end{document} compared to the classic {McE}liece cryptosystem proposed by Bernstein et al.

2021, 15(1): 99-112 doi: 10.3934/amc.2020045 +[Abstract](1222) +[HTML](606) +[PDF](408.68KB)
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We investigate a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. These codes have at most three weights and some of them are almost optimal so that they are suitable for applications in secret sharing schemes. This is a supplement of the results raised by Wang et al. (2017) and Kong et al. (2019).

2020, 14(2): 301-306 doi: 10.3934/amc.2020021 +[Abstract](1562) +[HTML](634) +[PDF](299.97KB)
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McNie [8] is a code-based public key encryption scheme submitted to the NIST Post-Quantum Cryptography standardization [10] as a candidate. In this paper, we present Dual-Ouroboros, an improvement of McNie, which can be seen as a dual version of the Ouroboros-R protocol [1], another candidate to the NIST competition. This new improved protocol permits, first, to avoid an attack proposed by Gaborit [7] and second permits to benefit from a reduction security to a standard problem (as the original Ouroboros protocol).

2020, 14(2): 279-299 doi: 10.3934/amc.2020020 +[Abstract](1255) +[HTML](650) +[PDF](430.21KB)
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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 \begin{document}$[216,190,\geqslant 18]$\end{document} over \begin{document}$\mathbb{F}_{64}$\end{document} yields a new record.

2020, 14(1): i-i doi: 10.3934/amc.2020012 +[Abstract](1800) +[HTML](479) +[PDF](212.1KB)
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2019, 13(4): ⅰ-ⅱ doi: 10.3934/amc.2019033 +[Abstract](1510) +[HTML](402) +[PDF](96.27KB)
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2017, 11(2): i-i doi: 10.3934/amc.201702i +[Abstract](2629) +[HTML](130) +[PDF](29.6KB)
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2016, 10(3): i-ii doi: 10.3934/amc.201603i +[Abstract](1006) +[PDF](133.8KB)
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The present issue of the Advances in Mathematics of Communications is dedicated to the conference

2016, 10(1): i-i doi: 10.3934/amc.2016.10.1i +[Abstract](2249) +[PDF](98.6KB)
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The $4^{th}$International Castle Meeting on Coding Theory and its Applications (4ICMCTA) took place in the Palmela Castle, Portugal, on September 15--18, 2014. It was organized under the auspices of the Research & Development Center for Mathematics and Applications (CIDMA) from the University of Aveiro. Following in the spirit of the previous installments held at La Mota Castle, Spain, in 1999 and 2008, and at Cardona Castle, Spain, in 2011, the meeting has been a good opportunity for communicating new results, exchanging ideas, strengthening international cooperation, and introducing young researchers into the Coding Theory community.

2015, 9(1): 9-21 doi: 10.3934/amc.2015.9.9 +[Abstract](3721) +[PDF](424.1KB)
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In this paper, a novel method for constructing complementary sequence set with zero correlation zone (ZCZ) is presented by interleaving and combining three orthogonal matrices. The constructed set can be divided into multiple sequence groups and each sequence group can be further divided into multiple sequence subgroups. In addition to ZCZ properties of sequences from the same sequence subgroup, sequences from different sequence groups are orthogonal to each other while sequences from different sequence subgroups within the same sequence group possess ideal cross-correlation properties, that is, the proposed ZCZ sequence set has inter-group orthogonal (IGO) and inter-subgroup complementary (ISC) properties. Compared with previous methods, the new construction can provide flexible choice for ZCZ width and set size, and the resultant sequences which are called IGO-ISC sequences in this paper can achieve the theoretical bound on the set size for the ZCZ width and sequence length.
2014, 8(4): i-ii doi: 10.3934/amc.2014.8.4i +[Abstract](2144) +[PDF](106.0KB)
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Every second year, the GEOCRYPT conference brings together researchers from arithmetic geometry and cryptography. After Guadeloupe in 2009 and Corsica in 2011, French Polynesia was the host of its 2013 edition which took place in Punaauia, on the island of Tahiti, October 7-11.
The main topic of GEOCRYPT has always been the application of pure mathematical techniques to the safety and efficiency of modern communication systems, with particular interest in the fields of arithmetic and algebraic geometry over finite fields, algorithms for finite fields, error correcting codes, cryptology, boolean functions, discrete dynamical systems, and their interactions. The 2013 edition had the honour to feature six invited and eleven contributed talks from renowned international experts presenting strong results recently obtained on topics ranging from pure mathematics to cryptographic algorithms. The GEOCRYPT 2013 Program Committee carefully evaluated the submitted abstracts and selected the best contributions for presentation at the conference.

2013, 7(1): i-i doi: 10.3934/amc.2013.7.1i +[Abstract](2225) +[PDF](97.8KB)
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Six years have passed since the founding of Advances in Mathematics of Communications, a journal devoted to all mathematical aspects of information and communications technology. As expressed in the editorial of the inaugural volume, communications technology is omnipresent in contemporary life. However, its ubiquity sometimes obscures the fact that the foundations of communications technology are genuinely mathematical, as are its methods, both analytical and constructive.

2011, 5(2): i-ii doi: 10.3934/amc.2011.5.2i +[Abstract](2230) +[PDF](127.0KB)
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The present issue of the Advances in Mathematics of Communications has been dedicated to the conference

ALCOMA'10

(Algebraic Combinatorics and Applications, Designs and Codes)

which took place April 11-18, 2010 in the picturesque village of Thurnau near Bay\-reuth, Germany.
The purpose of this meeting was to bring together mathematicians from around the world to exchange recent results in all areas of Discrete Mathematics and Mathematics of Communications based on algebraic methods. Special emphasis was placed on the constructive theory of finite structures, in particular on combinatorial designs and codes. The conference was the third of its kind, after the inaugural meeting ALCOMA'99 in Gößweinstein, which was later followed by ALCOMA'05 at the same venue.

2010, 4(2): i-ii doi: 10.3934/amc.2010.4.2i +[Abstract](2037) +[PDF](42.7KB)
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The Conference on Hyperellptic Curves, Discrete Logarithms, Encryption, etc. took place March 16-20, 2009 in Frutillar, Chile. This event derives its acronym CHiLE 2009 from its Spanish title

Curvas Hiperelĺpticas, Logaritmos discretos, Encriptación, etc.

The goal of this conference was to bring together researchers working on cryptographic aspects of algebraic geometry from all over the world, and especially from South America. It was hoped that this would help promote the development and expansion of this field of research in South America.

2007, 1(1): i-ii doi: 10.3934/amc.2007.1.1i +[Abstract](2533) +[PDF](53.2KB)
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Almost 60 years have passed since Claude E.~Shannon's celebrated two-part article A Mathematical Theory of Communication appeared in July and October of 1948. With that paper, Shannon founded a discipline, whose wide reach could hardly have been foreseen at the time.
To commemorate the occasion of the 50th anniversary of the birth of Information Theory as a discipline, the IEEE Transactions on Information Theory published a special issue that included the following statement in its preface:
With communication engineering at the epicenter of the bombshell, the sensational aftermath of Shannon's paper soon reached Mathematics, Physics, Statistics, Computing, and Cryptology. Even Economics, Biology, Linguistics and other fields in the natural and social sciences felt the ripples of Shannon's new theory.

2019  Impact Factor: 0.734