Stream Ciphers in Modern Real-time IT Systems

Кuznetsov, Alexandr; Potii, Oleksandr Volodymyrovych; Poluyanenko, Nikolay; Gorbenko, Yurii Ivanovich; Kryvinska, Natalia

doi:10.1007/978-3-030-79770-6

Cited by 10 publications

(9 citation statements)

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“…The algorithm HC (Fig. 3) and the heuristic function WHS successfully coped with the task of generating such nonlinear substitutions [32,33]. These results are relevant, because most modern symmetric cryptographic algorithms use such substitutions.…”

Section: Discussionmentioning

confidence: 97%

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Optimizing Hill Climbing Algorithm Parameters for Generation of Cryptographically Strong S-Boxes

Кuznetsov

Romeo

Poluyanenko

et al. 2022

Preprint

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Nonlinear substitutions (S-boxes) are an important component of modern symmetric ciphers. They are designed to complicate the plaintext-ciphertext dependency. According to modern ideas, the S-box should be bijective, have high nonlinearity and algebraic immunity, low delta uniformity and linear redundancy. These criteria directly affect the cryptographic strength of ciphers, providing resistance to statistical, linear, algebraic, differential, and other cryptanalysis techniques. Many researchers have used various heuristic techniques to generate random S-boxes with high nonlinearity. However, the complexity of this task is still high. For example, the best-known algorithm to generate a random 8-bit bijective S-box with nonlinearity 104 requires high computational effort (i.e. more than 65 thousand intermediate estimates [search iterations]). In this article, we explore an iterative hill-climbing algorithm and optimize the heuristic search parameters. We show that the complexity of generating S-boxes can be significantly reduced. To search for a random bijective S-box with nonlinearity 104, only about 50 thousand intermediate search iterations are required. In addition, we generate Cryptographically Strong S-Boxes for which additional criteria are provided. We present estimates of the complexity of the search and estimates of the probabilities of generating substitutions with various cryptographic indicators. The extracted results demonstrate a significant improvement in our approach compared to the state of the art in terms of providing linear nonredundancy, nonlinearity (104), algebraic immunity (3) and delta uniformity (8).

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Section: Discussionmentioning

confidence: 97%

“…We need to perform on ). Such cryptographically strong S-boxes are currently integrated and used in modern symmetric ciphers [30][31][32][33].…”

Section: Related Workmentioning

confidence: 99%

Optimizing Hill Climbing Algorithm Parameters for Generation of Cryptographically Strong S-Boxes

Кuznetsov

Romeo

Poluyanenko

et al. 2022

Preprint

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“…По друге, S-блоки повинні забезпечувати необхідні криптографічні властивості, які значно ускладнюють реалізацію різних криптоаналітичних атак (диференційного, лінійного, статистичного та інш.) [3,6,7]. Отже задача генерації нелінійних підстановок є складною та надзвичайно важливою з точки зору подальшого удосконалення криптографічних алгоритмів із симетричним ключем.…”

Section: вступunclassified

Properties of the cost function in the iterative algorithm for generating nonlinear substitution

Kuznetsov¹,

Горбенко²,

Poluyanenko³

et al. 2022

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To ensure the security of information technology, cryptographic information protection tools are used, in particular block and stream encryption algorithms with a symmetric key. Reliability and cryptographic strength of cryptoalgorithms is provided by the properties of the applied primitives. For example, non-linear substitutions (S-boxes) are used as the main component of modern symmetric ciphers. Therefore, generation of substitutions is an important scientific task directly related to the security of information technology and improvement of modern symmetric ciphers. The paper investigates the properties of iterative algorithms for generating non-linear substitutions and special cost functions, which play a decisive role in the heuristic search for S-boxes with the required properties. We consider the cost function of the WCF (Cost Function of the content of the Walsh-Hadamard spectrum) and optimize its parameters. The obtained optimization results in combination with the Hill Climbing iterative search algorithm can reduce significantly the number of iterations. In particular, we show that for a substitution search with a non-linearity of 104, on average, we reduce the computational complexity of generation by more than 20%. In addition, it is possible to increase the success rate of the heuristic search. In particular, for the selected settings, in 100% of cases, a beaktive S-box with a non-linearity of 104 was found.

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“…Data encryption algorithms with symmetric keys are used in modern computer systems to ensure confidentiality, integrity, authenticity and other information security services [1][2][3]. The main condition for using such encryption algorithms is the availability of a secret key, which is identical for the sender and receiver of data.…”

Section: Introductionmentioning

confidence: 99%

“…According to modern concepts, nonlinear substitutions in cryptography should be random [2]. Nonrandom methods of substitution generation can cause vulnerabilities in cryptoalgorithms [6,7].…”

Section: Introductionmentioning

confidence: 99%

Optimization of a Simulated Annealing Algorithm for S-Boxes Generating

Kuznetsov

Więcław

Poluyanenko

et al. 2022

Sensors

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Cryptographic algorithms are used to ensure confidentiality, integrity and authenticity of data in information systems. One of the important areas of modern cryptography is that of symmetric key ciphers. They convert the input plaintext into ciphertext, representing it as a random sequence of characters. S-boxes are designed to complicate the input–output relationship of the cipher. In other words, S-boxes introduce nonlinearity into the encryption process, complicating the use of different methods of cryptanalysis (linear, differential, statistical, correlation, etc.). In addition, S-boxes must be random. This property means that nonlinear substitution cannot be represented as simple algebraic constructions. Random S-boxes are designed to protect against algebraic methods of cryptanalysis. Thus, generation of random S-boxes is an important area of research directly related to the design of modern cryptographically strong symmetric ciphers. This problem has been solved in many related works, including some using the simulated annealing (SA) algorithm. Some works managed to generate 8-bit bijective S-boxes with a nonlinearity index of 104. However, this required enormous computational resources. This paper presents the results of our optimization of SA via various parameters. We were able to significantly reduce the computational complexity of substitution generation with SA. In addition, we also significantly increased the probability of generating the target S-boxes with a nonlinearity score of 104.

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Stream Ciphers in Modern Real-time IT Systems

Cited by 10 publications

References 0 publications

Optimizing Hill Climbing Algorithm Parameters for Generation of Cryptographically Strong S-Boxes

Optimizing Hill Climbing Algorithm Parameters for Generation of Cryptographically Strong S-Boxes

Properties of the cost function in the iterative algorithm for generating nonlinear substitution

Optimization of a Simulated Annealing Algorithm for S-Boxes Generating

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