The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups

Rahimipour, Ali Reza; Ashrafi, Ali Reza

doi:10.1007/s10013-021-00489-5

Cited by 2 publications

(5 citation statements)

References 23 publications

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“…. In such case, the brute force attack complexity is equivalent to 3 q . Our first step is a key generation stage.…”

Section: ( ) ( 1) a P Q Qmentioning

confidence: 99%

“…has an estimation of complexity. For a practical attack, the message m is also unknown and has uncertainty to choose from 3 q . This renders a brute-force attack on a key unfeasible.…”

Section: Conclusion and Security Checkmentioning

confidence: 99%

“…This renders a brute-force attack on a key unfeasible. If we consider an attack model with known plaintext, the complexity of a brute-force attack on the ciphertext remains unchanged and is equivalent to 3 q . Brute force attack on the cyphertext 2 y .…”

Section: Conclusion and Security Checkmentioning

confidence: 99%

“…Our research corpus comprises over a dozen papers [1][2][3][4][5][6][7][8][9][10]. One approach to establishing quantum-resistant cryptosystems, predicated on the word problem, hinges on the utilization of permutation groups.…”

Section: Introductionmentioning

confidence: 99%

“…In [3], a comprehensive framework for the construction of Strongly Aperiodic Logarithmic Signatures (SALS) for elementary abelian pgroups is established. The introduction of SALS significantly broadens the spectrum of manual logarithmic signatures employed within the MST3 cryptosystem.…”

Section: Introductionmentioning

confidence: 99%

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Method of Security Improvement for MST3 Cryptosystem Based on Automorphism Group of Ree Function Field

Kotukh,

Khalimov,

Korobchinskiy

2023

TACS

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This article is a part of a research endeavor focused on creating a quantum-resistant cryptosystem for secure encryption and decryption. Our approach employs a challenging word problem while emphasizing cost-effective implementation. Previous research has involved the development of encryption schemes based on high-order groups, offering potential security enhancements. The choice of the non-abelian group is a critical factor in shaping the encryption algorithms, feasibility of implementation, and system parameters. Our central objective is to design a cryptosystem that effectively thwarts quantum cryptanalysis. To achieve this, we employ a logarithmic signature along with a random cover across an entire finite non-abelian group. Our unique contribution lies in optimizing finite group selection, parameters, and circuit solutions for the logarithmic signature to meet specific security and implementation criteria. Within this paper, we introduce an encryption scheme utilizing automorphisms of the Ree functional field and propose a method for enhancing resistance to cryptanalysis through the binding of session keys.

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“…. In such case, the brute force attack complexity is equivalent to 3 q . Our first step is a key generation stage.…”

Section: ( ) ( 1) a P Q Qmentioning

confidence: 99%

“…has an estimation of complexity. For a practical attack, the message m is also unknown and has uncertainty to choose from 3 q . This renders a brute-force attack on a key unfeasible.…”

Section: Conclusion and Security Checkmentioning

confidence: 99%

Section: Conclusion and Security Checkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Method of Security Improvement for MST3 Cryptosystem Based on Automorphism Group of Ree Function Field

Kotukh,

Khalimov,

Korobchinskiy

2023

TACS

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Applications of Finite Non-Abelian Simple Groups to Cryptography in the Quantum Era

Vasco,

Kahrobaei,

McKemmie

2024

La Matematica

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The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modeling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian simple groups to cryptography and discuss different scenarios in which this theory is clearly central, providing the relevant definitions to make the material accessible to both cryptographers and group theorists, in the hope of stimulating further interaction between these two (non-disjoint) communities. In particular, we look at constructions based on various group-theoretic factorization problems, review group theoretical hash functions, and discuss fully homomorphic encryption using simple groups. The Hidden Subgroup Problem is also briefly discussed in this context.

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The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups

Cited by 2 publications

References 23 publications

Method of Security Improvement for MST3 Cryptosystem Based on Automorphism Group of Ree Function Field

Method of Security Improvement for MST3 Cryptosystem Based on Automorphism Group of Ree Function Field

Applications of Finite Non-Abelian Simple Groups to Cryptography in the Quantum Era

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