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Advances in Mathematics of Communications

Open Access Articles

Ironwood meta key agreement and authentication protocol
Iris Anshel, Derek Atkins, Dorian Goldfeld and Paul E. Gunnells
2020 doi: 10.3934/amc.2020073 +[Abstract](225) +[HTML](168) +[PDF](438.53KB)
Abstract:

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.

Complete weight enumerators of a class of linear codes over finite fields
Shudi Yang, Xiangli Kong and Xueying Shi
2019 doi: 10.3934/amc.2020045 +[Abstract](676) +[HTML](344) +[PDF](337.74KB)
Abstract:

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).

Dual-Ouroboros: An improvement of the McNie scheme
Philippe Gaborit, Lucky Galvez, Adrien Hauteville, Jon-Lark Kim, Myeong Jae Kim and Young-Sik Kim
2020, 14(2): 301-306 doi: 10.3934/amc.2020021 +[Abstract](1014) +[HTML](472) +[PDF](299.97KB)
Abstract:

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).

Multi-point codes from the GGS curves
Chuangqiang Hu and Shudi Yang
2020, 14(2): 279-299 doi: 10.3934/amc.2020020 +[Abstract](851) +[HTML](466) +[PDF](430.21KB)
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 \begin{document}$ [216,190,\geqslant 18] $\end{document} over \begin{document}$ \mathbb{F}_{64} $\end{document} yields a new record.

Zero correlation zone sequence set with inter-group orthogonal and inter-subgroup complementary properties
Zhenyu Zhang, Lijia Ge, Fanxin Zeng and Guixin Xuan
2015, 9(1): 9-21 doi: 10.3934/amc.2015.9.9 +[Abstract](3135) +[PDF](424.1KB)
Abstract:
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.

2019  Impact Factor: 0.734

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