A review of the tropical approach in cryptography

Ahmed, K.; Pal, Saibal K.; Mohan, Radha

doi:10.1080/01611194.2021.1994486

Cited by 8 publications

(3 citation statements)

References 33 publications

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“…Jiang et al [21] cracked the scheme through tropical linear equations. Ahmed et al [22] summarizes and analyzes the previous tropical cryptography schemes. Other cryptographic schemes based on tropical algebra can be found in the references [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Cryptography Based on the Tropical Jones Matrix

Huang,

Kong,

2024

Symmetry

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In recent years, the tropical polynomial factorization problem, the tropical matrix decomposition problem, and the tropical multivariate quadratic equation solving problem have been proved to be NP-hard. Some asymmetric cryptographic systems based on tropical semirings have been proposed, but most of them are insecure and have been successfully attacked. In this paper, a new key exchange protocol and a new encryption protocol are proposed based on the difficulty of finding the multiple exponentiation problem of the tropical Jones matrices. The analysis results indicate that our protocol can resist various existing attacks. The complexity of attacking an MEP by adversaries is raised due to the larger number of combinations in the tropical Jones matrices compared to regular matrix polynomials. Furthermore, the index semiring is the non-negative integer cyclic matrix semiring, leading to a higher efficiency in key generation.

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Section: Introductionmentioning

confidence: 99%

Asymmetric Cryptography Based on the Tropical Jones Matrix

Huang,

Kong,

2024

Symmetry

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“…They modify the Stickel's protocol using polynomial over tropical matrix algebra. Then some studies in tropical cryptography are followed such that (Grigoriev & Ponomarenko, 2005), (Grigoriev & Shpilrain, 2018), (Grigoriev & Shpilrain, 2019), (Muanalifah & Sergeev, 2020), (Ahmed et al, 2023a), (Ahmed et al, 2023b), (Durcheva et al, 2014). For analysis security the tropical cryptography, there are also some studies such that (Kotov & Ushakov, 2018), (Muanalifah & Sergeev, 2022), (Isaac & Kahrobaei, 2021), (Rudy & Monico, 2020), (Huang et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

The tropical version of El Gamal Encryption

Muanalifah,

Isnawati,

Artes Jr.

et al. 2023

J. Nat. Scien. & Math. Res.

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“…A series of protocols based on different idempotent semirings was proposed by references [10]- [13]. A review of the cryptanalysis of most schemes known from the literature can be seen in [14]. Reference [15] showed attacks on the protocols presented in [8] based on patterns of higher powers of tropical matrices.…”

Section: Introductionmentioning

confidence: 99%

TrES: Tropical Encryption Scheme Based on Double Key Exchange

Durcheva

2022

COMPUTE

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Shor’s quantum algorithm establishes a polynomial time attack on the discrete logarithm problem in any group. Recent announcements of progress in building quantum computers highlight the need for new concepts to create cryptosystems that are resistant to quantum attacks. In this paper, we present а new message encryption scheme. To enhance the security of the scheme, we suggest double key-exchange protocol (KEP). The first stage of the key exchange uses a matrix power function (MPF) in a tropical semiring. These functions are based on the action of a matrix semiring acting on some matrix set. MPFs can be considered as one-way functions because they are based on some generalized satisfiability problems that are potentially NP-complete. The obtained shared secret key at the first stage of the key exchange serves as an input for the second stage. The security of the second phase relies on the difficulty of the semiring action problem. In our protocol, we suggest using left or right action of the tropical semiring (which can be both min-plus and max-plus) on the group of commutative matrices (circulant matrices, in our case). The fact that the key-exchange protocol works in two phases contributes to its security, since an attacker needs to solve two difficult problems in order to break it. The main advantages of the presented protocol are: the increased efficiency and improved security.

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A review of the tropical approach in cryptography

Cited by 8 publications

References 33 publications

Asymmetric Cryptography Based on the Tropical Jones Matrix

Asymmetric Cryptography Based on the Tropical Jones Matrix

The tropical version of El Gamal Encryption

TrES: Tropical Encryption Scheme Based on Double Key Exchange

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