Cryptanalysis of a 2-party key establishment based on a semigroup action problem

Steinwandt, Rainer; Corona, Adriana Suárez

doi:10.3934/amc.2011.5.87

Cited by 9 publications

(4 citation statements)

References 2 publications

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“…The upper bound for the size of this set is 2 100 and the least value is 2 25 . The cryptanalysis of this example has been done in [20] and the choice of the above parameters is considered insufficient for practical use. According to the cryptanalysis discussed in [20], if the above parameters are used, then a complete session key can be recovered easily.…”

Section: Security Of Sap and Cryptographic Protocols Against Brute Fomentioning

confidence: 99%

“…The cryptanalysis of this example has been done in [20] and the choice of the above parameters is considered insufficient for practical use. According to the cryptanalysis discussed in [20], if the above parameters are used, then a complete session key can be recovered easily. Therefore, the parameters choices prescribed in [11] is not suggested for practical use and further research is required to achieve a good bound with better choice of parameters.…”

Section: Security Of Sap and Cryptographic Protocols Against Brute Fomentioning

confidence: 99%

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Survey on SAP and its application in public-key cryptography

Goel

Gupta

Dass

2020

Journal of Mathematical Cryptology

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AbstractThe concept of the semigroup action problem (SAP) was first introduced by Monico in 2002. Monico explained in his paper that the discrete logarithm problem (DLP) can be generalized to SAP. After defining the action problem in a semigroup, the concept was extended using different mathematical structures. In this paper, we discuss the concept of SAP and present a detailed survey of the work which has been done using it in public-key cryptography.

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Section: Security Of Sap and Cryptographic Protocols Against Brute Fomentioning

confidence: 99%

Section: Security Of Sap and Cryptographic Protocols Against Brute Fomentioning

confidence: 99%

Survey on SAP and its application in public-key cryptography

Goel

Gupta

Dass

2020

Journal of Mathematical Cryptology

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“…d) In [8,Example 5.13] the authors illustrate the use of a semiring of order 6 to construct an example of a practical SAP. This was later cryptanalyzed in [16] due not to a general attack, but rather to the structure of this ring. However, we can use the semiring of order 20 given in [8,Example 5.8] to analogously define another SAP and its cryptanalysis is still an open question.…”

Section: Examplesmentioning

confidence: 99%

Group key management based on semigroup actions

et al. 2016

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In this work we provide a suite of protocols for group key management based on general semigroup actions. Construction of the key is made in a distributed and collaborative way. Examples are provided that may in some cases enhance the security level and communication overheads of previous existing protocols. Security against passive attacks is considered and depends on the hardness of the semigroup action problem in any particular scenario.

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“…In 2007, Maze, Monico, and Rosenthal proposed one of the first cryptosystems based on semigroups and semirings [9], using some ideas from [10], as well as from their previous article [11]. However, then it was broken by Steinwandt et al [12]. Atani published a cryptosystem using semimodules over factor semirings [13].…”

Section: Introductionmentioning

confidence: 99%

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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Cryptanalysis of a 2-party key establishment based on a semigroup action problem

Cited by 9 publications

References 2 publications

Survey on SAP and its application in public-key cryptography

Survey on SAP and its application in public-key cryptography

Group key management based on semigroup actions

Tropical Cryptography Based on Multiple Exponentiation Problem of Matrices

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