Modifying the tropical version of Stickel's key exchange protocol

Muanalifah, Any; Sergeev, Sergĕı

doi:10.21136/am.2020.0325-19

Cited by 18 publications

(11 citation statements)

References 5 publications

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“…(4) Generalized KU attack. In order to remedy Grigoreiv-Shpilrain's protocols, Muanalifah and Sergeev suggested some modifications that use two types of matrices that are Jones matrices and Linde-de la Puente matrices [22]. But the authors also pointed out that their modifications cannot resist the generalized KU attack which can also decompose the public matrix into the product of two Jones matrices (Linde-de la Puente matrices) expressed as the linear form of the tropical basic elementary matrix.…”

Section: Possible Attacksmentioning

confidence: 99%

“…However, some attacks on the improved protocols are recently suggested by Rudy and Monico [19], Isaac and Kahrobei [20], and Muanalifah and Sergeev [21]. In order to remedy Grigoreiv-Shpilrain's protocols, Muanalifah and Sergeev suggested some modifications that use two classes of commuting matrices in tropical algebra [22]. But the authors also pointed out that their modifications cannot resist the generalized KU attack since the user's secret matrix can still be expressed in the linear form of the power of the basic elementary matrix.…”

Section: Introductionmentioning

confidence: 99%

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Tropical Cryptography Based on Multiple Exponentiation Problem of Matrices

Huang

2022

Security and Communication Networks

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Because there is no multiplication of numbers in tropical algebra and the problem of solving the systems of polynomial equations in tropical algebra is NP-hard, in recent years some public key cryptography based on tropical semiring has been proposed. But most of them have some defects. This paper proposes new public key cryptosystems based on tropical matrices. The security of the cryptosystem relies on the difficulty of the problem of finding multiple exponentiations of tropical matrices given the product of the matrices powers when the subsemiring is hidden. This problem is a generalization of the discrete logarithm problem. But the problem generally cannot be reduced to discrete logarithm problem or hidden subgroup problem in polynomial time. Since the generating matrix of the used commutative subsemirings is hidden and the public key matrices are the product of more than two unknown matrices, the cryptosystems can resist KU attack and other known attacks. The cryptosystems based on multiple exponentiation problem can be considered as a potential postquantum cryptosystem.

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Section: Possible Attacksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tropical Cryptography Based on Multiple Exponentiation Problem of Matrices

Huang

2022

Security and Communication Networks

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“…However, the authors do not explicitly state the security of this scheme. Stickel's key exchange protocol in tropical algebra was updated by the authors [8] utilizing commuting matrices, and they also proposed additional protocols.…”

Section: Introductionmentioning

confidence: 99%

A Secure Key Exchange Protocol and a Public Key Cryptosystem for Healthcare Systems

2024

Contemp. Math.

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Diffie-Hellman (DH) is the reason for the existence of a solution to the key distribution problem, where two parties can mutually set up a shared secret key over an insecure channel without any previous communication. In this study, a novel key exchange protocol based on the difficulty of the Discrete Logarithm Problem with Factor Problem (DLPFP) utilizing matrices in non-commutative semigroup over semiring is proposed. The security and complexity analyses of the protocol are discussed. Also, an ElGamal cryptosystem based on a group of invertible matrices and DLPFP over a semiring to encrypt the Sensitive Health Information (SHI) in healthcare systems is suggested.

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“…Diverse matrix forms were incorporated, ranging from singular [2,3] and non-singular matrices [4] to matrices over bit strings [5]; Tribonacci matrices [6]; Hadamar matrices [7]; non-negative [8] and lattice matrices [9]. Tropical matrices are also of interest ( [10][11][12][13][14][15]). Yet, despite these developments, vulnerabilities have persisted, as evidenced by different documented attacks (see, for example, [16][17][18][19]).…”

Section: Introductionmentioning

confidence: 99%

Secure Key Exchange in Tropical Cryptography: Leveraging Efficiency with Advanced Block Matrix Protocols

Durcheva,

Danilchenko

2024

Preprint

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In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging tropical semirings’ computational prowess and block matrices’ structural resilience. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde-de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, and using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. We also provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication.

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Modifying the tropical version of Stickel's key exchange protocol

Cited by 18 publications

References 5 publications

Tropical Cryptography Based on Multiple Exponentiation Problem of Matrices

Tropical Cryptography Based on Multiple Exponentiation Problem of Matrices

A Secure Key Exchange Protocol and a Public Key Cryptosystem for Healthcare Systems

Secure Key Exchange in Tropical Cryptography: Leveraging Efficiency with Advanced Block Matrix Protocols

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