Improved encryption scheme based on the automorphism group of the Ree function field

Khalimov, Gennady; Kotukh, Yevgen; Khalimova, Svitlana

doi:10.1109/iemtronics52119.2021.9422514

Cited by 8 publications

(7 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…B 1(4) 00000 0,0,0,0 00000 0,0,0,0 00000 0,0,0,0 00000 0,0,0,0 10000 α 0 ,0,0,0 10000 0,α 0 ,0,0 10000 0,0,α 0 ,0 10000 0,0,0,α 0 01000 α 1 ,0,0,0 01000 0,α 1 ,0,0 B 2(3) 01000 0,0,0,α 1 11000 α 14 ,0,0,0 11000 0,α 14 ,0,0 00000 0,0,0,0 11000 0,0,0,α 14 B 2(1) B 2(2) 11000 0,0,α 14 ,0 B 2(4) 01000 α 1 ,0,0,0 11000 0,α 14 ,0,0 10100 0,0,α 28 ,0 00000 0,0,0,0 10100 α 28 ,0,0,0 11100 0,α 22 ,0,0 01100 0,0,α 15 ,0 00100 0,0,0,α 2 11010 α 26 ,0,0,0 10010 0,α 5 ,0,0 Б 3 (3) Б 3 (4) 00110 α 16 ,0,0,0 00110 0,α 16 ,0,0 01000 0,0,α 1 ,0 01000 0,0,0,α 1 10001 α 25 ,0,0,0 B 3(2) 10010 0,0,α 5 ,0 00110 0,0,0,α 16 11101 α 21 ,0,0,0 10000 0,α 0 ,0,0 01101 0,0,α 27 ,0 00001 0,0,0,α 4 10011 α 18 ,0,0,0 10011 0,α 18 ,0,0 10111 0,0,α 9 ,0 11011 0,0,0,α 19 11111 α 20 ,0,0,0 Побудуємо випадкові накриття k  для того самого типу, що й () k  :…”

Section: практичні обчисленняunclassified

“…A 1(4) α 6 , α 11 , α 17 , α 27 α 17 , α 5 , α 26 , α 28 α 0 , α 2 , α 14 , α 20 α 20 , α 14 , α 30 , α 13 α 11 , α 5 , α 7 , α 5 α 20 , α 14 , α 19 , α 24 α 17 , α 27 , α 16 , α 10 α 4 , α 2 , α 13 , α 17 α 21 ,α 18 ,0,α 16 α 30 , α 21 , α 6 , α 3 A 2(3) α 19 , α 13 , α 26 , α 22 α 5 , α 29 , α 12 , α 16 α 6 , α 9 , α 13 , α 22 α 28 ,α 29 ,0,α 25 α 6 , α 28…”

Section: практичні обчисленняunclassified

See 1 more Smart Citation

Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

Kotukh,

Khalimov,

Korobchinskyi

2023

View full text Add to dashboard Cite

This article presents a new implementation of encryption based on MST, focused on generalized Suzuki 2-groups. The well-known MST cryptosystem, based on Suzuki groups, is constructed using a logarithmic signature at the center of the group, leading to a large array of logarithmic signatures. The proposed encryption is based on multi-parameter noncommutative groups, with a focus on the generalized multi-parameter Suzuki 2-group. This approach responds to the progress in the development of quantum computers, which may pose a threat to the security of many open cryptosystems, especially those based on factorization problems and discrete logarithms, such as RSA or ECC. The use of noncommutative groups to create quantum-resistant cryptosystems has been a known approach for the last two decades. The unsolvable word problem, proposed by Wagner and Magyarik, is used in the field of permutation groups and is key to the development of cryptosystems. Logarithmic signatures, introduced by Magliveras, represent a unique type of factorization suitable for finite groups. The latest version of such an implementation, known as MST3, is based on the Suzuki group. In 2008, Magliveras introduced the LS transitivity limit for the MST3 cryptosystem, and later Swaba proposed an improved version of the cryptosystem, eMST3. In 2018, T. van Trung suggested applying the MST3 approach using strong aperiodic logarithmic signatures for abelian p-groups. Kong and his colleagues conducted a deep analysis of MST3 and noted that due to the absence of publications on the quantum vulnerability of this algorithm, it can be considered a potential candidate for use in the post-quantum era. The main distinction of the new system is the use of homomorphic encryption to construct logarithmic signature coverings for all group parameters, which improves the secrecy of the cryptosystem, particularly against brute-force attacks.

show abstract

Section: практичні обчисленняunclassified

Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

Kotukh,

Khalimov,

Korobchinskyi

2023

View full text Add to dashboard Cite

show abstract

“…A 3(2) α 97 , α 107 , α 71 α 110 , α 100 , α 44 α 35 , α 28 , α 15 α 106 , α 78 , α 81 α 43 , α 16 , α 90 α 99 , α 93 , α 87 α 107 , α 82 , α 55 α 67 ,α 2 ,α 87 α 105 , α 19…”

Section: практична реалізаціяunclassified

“…) 28 , α 81 , α 39 α 7 ,α 93 ,α 65 α 92 , α 16 , α 80 α 103 , α 42 , α 93 α 87 , α 27 , α 14 α 101 , α 79 , α 29 α 28 , α 52 , α 39 α 7 ,α 115 ,α 17 α 92 , α 53 , α 102 α 103 , α 42 , α 99 α 87 , α 27 , α 120 α 101 , α 79 , α 51 α 28 , α 32 , α 49 α 7 ,α 56 ,α 42 α 92 , α 51 , α 117 α 103 , α 42 , α 80 α 87 , α 27 , α 16 α 101 , α 79 , α 55 α 28 , α 42 , α 92 α 7 ,α 66 ,α 105 α 92 , α 57 , α 114 α 103 , α 42 , α 22…”

Section: практична реалізаціяunclassified

Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

Kotukh,

Khalimov,

Korobchinskyi

2023

View full text Add to dashboard Cite

This article presents a new encryption method based on the group of automorphisms of Suzuki's functional field, which enhances the security level of the existing MST3 cryptosystem. This approach is a response to the progress in developing powerful quantum computers, which can threaten the security of many public-key encryption systems, particularly those based on factorization and discrete logarithm problems, such as RSA or ECC. Using non-commutative groups to create quantum-resistant cryptosystems has been a known approach over the last two decades. The unsolvable word problem, proposed by Wagner and Magyarik, applied in the realm of permutation groups, is key to the development of cryptosystems. Logarithmic signatures, introduced by Magliveras, represent a unique type of factorization suitable for finite groups. The latest version of such implementation, known as MST3, is based on the Suzuki group. In 2008, Magliveras presented the LS limit of transitivity for the MST3 cryptosystem. Later, Svaba proposed an improved version of the cryptosystem eMST3 with enhanced protective features, including secret homomorphic covering. In 2018, T. van Trung suggested the application of the MST3 approach using strong aperiodic logarithmic signatures for Abelian p-groups. Kong and his colleagues conducted an in-depth analysis of MST3 and noted that due to the lack of publications on the quantum vulnerability of this algorithm, it can be considered as a potential candidate for use in the post-quantum era. One of the key ideas is to increase encryption efficiency by optimizing computational resources, particularly through reducing the size of the key space. This method is applied to the calculations of logarithmic signatures within the group. It was implemented over finite fields of small sizes.

show abstract

“…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%

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

Kotukh,

Khalimov,

Korobchinskiy

2023

TACS

View full text Add to dashboard Cite

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.

show abstract

Improved encryption scheme based on the automorphism group of the Ree function field

Cited by 8 publications

References 9 publications

Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

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

Contact Info

Product

Resources

About