Categorical interpretations of some key agreement protocols

Inassaridze, Nick; Kandelaki, Tamaz; Ladra, M.

doi:10.1007/s10958-013-1588-y

Cited by 6 publications

(8 citation statements)

References 6 publications

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“…In [28], the categorical interpretation of MPF, taken from [22], is presented in the context of the construction of several key agreement protocols. We slightly reformulate the notions used in this interpretation by the following statement, which is more appropriate for our study.…”

Section: Lemmamentioning

confidence: 99%

Enhanced Matrix Power Function for Cryptographic Primitive Construction

Sakalauskas

2018

Symmetry

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Abstract:A new enhanced matrix power function (MPF) is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ) problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left-right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1) the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2) the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ) problem which can be reckoned as hard; (3) the estimation of the effectiveness of direct MPF value computation; and (4) the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF), since the effective (polynomial-time) inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP) is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources.

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Section: Lemmamentioning

confidence: 99%

Enhanced Matrix Power Function for Cryptographic Primitive Construction

Sakalauskas

2018

Symmetry

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“…Hence, w 1 = w 2 and ϕ α, β is one-to-one. Now, we prove the identity given in (17). Let w 1 , w 2 represent the words as in (17)…”

Section: Mpf Isomorphismmentioning

confidence: 86%

“…Let S nf be a subset of words in S nf with fixed boundary elements. □ Theorem 2: Mapping ϕ α, β : S nf → Z × Z 2p is an isomorphism defined by (17), where Z 2p = {0, 1, 2, …, 2p − 1} is a semi-ring of integers modulo 2p.…”

Section: Mpf Isomorphismmentioning

confidence: 99%

Security analysis of KAP based on enhanced MPF

Sakalauskas

Mihalkovich

Uselis

2020

IET Information Security

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“…To be concise, we will use the notation MPF R S for the definition of MPF with base matrix defined over the platform semigroup S in M S and with power matrices defined over the exponent semiring R in M R . The categorical interpretation of MPF is presented in [15], in the context of the construction of several key agreement protocols. We slightly reformulate the notions used in the authors' interpretation by the following proposition, which is more appropriate for our study.…”

Section: Definitionmentioning

confidence: 99%

“…If we have any word w ∈ S and exponentiate it by i, then after the reduction of exponents corresponding to the generators a and b the uniform distribution of resulting exponents will be obtained. After that the generators are grouped according to the normal form defined in (15) and this grouping simply corresponds to computing expressions of the type a i a j = a i+j . Hence the grouping procedure will not change the uniform distribution.…”

Section: Proof Ofmentioning

confidence: 99%

Sigma Identification Protocol Construction Based on MPF

2021

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A new sigma identification protocol (SIP) based on matrix power function (MPF) defined over the modified medial platform semigroup and power near-semiring is proposed. It is proved that MPF SIP is resistant against direct and eavesdropping attacks. Our security proof relies on the assumption that MPF defined in the paper is a candidate for one-way function (OWF). Therefore, the corresponding MPF problem is reckoned to be a difficult one. This conjecture is based on the results demonstrated in our previous studies, where a certain kind of MPF problem was proven to be NP-complete.

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Categorical interpretations of some key agreement protocols

Abstract: Abstract. We give interpretations of some known key agreement protocols in the framework of category theory and in this way we give a method of constructing of many new key agreement protocols.

Cited by 6 publications

References 6 publications

Enhanced Matrix Power Function for Cryptographic Primitive Construction

Enhanced Matrix Power Function for Cryptographic Primitive Construction

Security analysis of KAP based on enhanced MPF

Sigma Identification Protocol Construction Based on MPF

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