Group key management based on semigroup actions

López-Ramos, J. A.; Rosenthal, Joachim; Schipani, Davide; Schnyder, Reto

doi:10.1142/s0219498817501481

Cited by 16 publications

(11 citation statements)

References 15 publications

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“…It is an active area of cryptology, where the cryptographic primitives and systems are based on algebraic structures like groups, semigroups and noncommutative rings (see [26]- [33]). This direction of security research has very rapid development (see [34], [35] and further references in these publications).…”

Section: On Cryptosystems Based On New Multivariate Platforms Of Nmentioning

confidence: 99%

Expanding graphs of the Extremal Graph Theory and expanded platforms of Post Quantum Cryptography

Ustimenko

Romańczuk-Polubiec

Wróblewska

2019

Annals of Computer Science and Information Systems

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Explicit constructions in Extremal Graph Theory give appropriate lower bounds for Turan type problems. In the case of prohibited cycles, the explicit constructions can be used for various problems of Information Security. We observe recent applications of algebraic constructions of regular graphs of large girth and graphs with large cycle indicator to Coding Theory and Cryptography. In particular, we present a new multivariate platforms of postquantum Non-commutative Cryptography defined in graph theoretical terms. Index Terms-graphs of large girth, graphs of large cycle indicator, graph based stream ciphers, multivariate cryptography, non-commutative cryptography I. SOME DEFINITIONS OF EXTREMAL GRAPH THEORY T HE missing definitions of graph-theoretical concepts in the case of simple graphs which appears in this paper can be found in [1]. All graphs we consider are simple ones, i. e. undirected without loops and multiple edges. When it is convenient, we shall identify Γ with the corresponding antireflexive binary relation on V (Γ), i.e. E(Γ) is a subset of V (Γ)×V (Γ). The girth of a graph Γ, denoted by g = g(Γ), is the length of the shortest cycle in Γ. The diameter d = d(Γ) of the graph Γ is the maximal length of the shortest pass between its two vertices. Let g x = g x (Γ) be the length of the minimal cycle through the vertex x from the set V (Γ) of vertices in graph Γ. We refer to Cind(Γ) = max {g x , x ∈ V (Γ)} as cycle indicator of the graph Γ. The family Γ i of connected k-regular graphs of constant degree is a family of small world graphs, if d(Γ i) ≤ c log k (v i), for some constant c, c > 0. Recall that family of regular graphs Γ i of degree k and increasing order v i is a family of graphs of large girth, if g(Γ i) ≥ c log k (v i), for some independent constant c, c > 0. We refer to the family of regular simple graphs Γ i of degree k and order v i as a family of graphs of large cycle indicator, if Cind(Γ i) ≥ c log k (v i) for some independent constant c, c > 0. Notice that for vertex-transitive graph its girth and cycle indicator coincide. Defined above families plays an important role in Extremal Graph Theory, Theory of LDPC codes and Cryptography (see [2] and further references).

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Section: On Cryptosystems Based On New Multivariate Platforms Of Nmentioning

confidence: 99%

Expanding graphs of the Extremal Graph Theory and expanded platforms of Post Quantum Cryptography

Ustimenko

Romańczuk-Polubiec

Wróblewska

2019

Annals of Computer Science and Information Systems

View full text Add to dashboard Cite

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Section: On Cryptosystems Based On New Multivariate Platforms Of Nmentioning

confidence: 99%

Position Papers of the 2019 Federated Conference on Computer Science and Information Systems

2019

Annals of Computer Science and Information Systems

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Position papers comprise two categories of contributions-challenge papers and emerging research papers. Challenge papers propose and describe research challenges in theory or practice of computer science and information systems. Papers in this category are based on deep understanding of existing research or industrial problems. Based on such understanding and experience, they define new exciting research directions and show why these directions are crucial to the society at large. Emerging research papers present preliminary research results from work-in-progress based on sound scientific approach but presenting work not completely validated as yet. They describe precisely the research problem and its rationale. They also define the intended future work including the expected benefits from solution to the tackled problem. Subsequently, they may be more conceptual than experimental. FedCSIS 2019 was Chaired by prof. Bogdan Franczyk, while prof. Rainer Unland acted as the Chair of the Organizing Committee. This year, FedCSIS was organized by the Polish Information Processing Society (Mazovia Chapter

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“…The protocol below gives n users the possibility to share an initial common key built using their private keys. A proof of its correctness and security against passive attacks can be found in [2,4], assuming the Diffie-Hellman problem is hard for the given group action.…”

Section: An Initial Key Agreement Protocolmentioning

confidence: 99%

“…We will consider in particular one of the proposed initial key agreements referred to (in [4]) as IKA.2. The authors generalize these schemes in [2], considering a general action on a semigroup, and this is how IKA.2 is presented below.…”

Section: Introductionmentioning

confidence: 99%