Optimized simulated annealing for efficient generation of highly nonlinear S-boxes

Kuznetsov, Alexandr; Poluyanenko, Nikolay; Frontoni, Emanuele; Kandiy, Sergey; Pieshkova, Olha

doi:10.1007/s00500-023-09334-y

Cited by 3 publications

(1 citation statement)

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“…In [28] introduce an innovative cost function that revolutionizes the hill-climbing algorithm's efficiency in generating S-boxes. Lastly, our work [29], presents an optimized simulated annealing approach. By leveraging a multithreaded implementation and introducing refined exit criteria, their method exhibits a 30-40% improvement in generating highly nonlinear S-boxes, showcasing the potential for enhanced cryptographic security through computational efficiency.…”

Section: State Of the Artmentioning

confidence: 99%

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

Kuznetsov,

Poluyanenko,

Frontoni

et al. 2024

Cryptography

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In the realm of smart communication systems, where the ubiquity of 5G/6G networks and IoT applications demands robust data confidentiality, the cryptographic integrity of block and stream cipher mechanisms plays a pivotal role. This paper focuses on the enhancement of cryptographic strength in these systems through an innovative approach to generating substitution boxes (S-boxes), which are integral in achieving confusion and diffusion properties in substitution–permutation networks. These properties are critical in thwarting statistical, differential, linear, and other forms of cryptanalysis, and are equally vital in pseudorandom number generation and cryptographic hashing algorithms. The paper addresses the challenge of rapidly producing random S-boxes with desired cryptographic attributes, a task notably arduous given the complexity of existing generation algorithms. We delve into the hill climbing algorithm, exploring various cost functions and their impact on computational complexity for generating S-boxes with a target nonlinearity of 104. Our contribution lies in proposing a new cost function that markedly reduces the generation complexity, bringing down the iteration count to under 50,000 for achieving the desired S-box. This advancement is particularly significant in the context of smart communication environments, where the balance between security and performance is paramount.

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Section: State Of the Artmentioning

confidence: 99%

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

Kuznetsov,

Poluyanenko,

Frontoni

et al. 2024

Cryptography

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Hybrid Population-Based Hill Climbing Algorithm for Generating Highly Nonlinear S-boxes

Kuznetsov,

Poluyanenko,

Kuznetsova

et al. 2024

Computers

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This paper introduces the hybrid population-based hill-climbing (HPHC) algorithm, a novel approach for generating cryptographically strong S-boxes that combines the efficiency of hill climbing with the exploration capabilities of population-based methods. The algorithm achieves consistent generation of 8-bit S-boxes with a nonlinearity of 104, a critical threshold for cryptographic applications. Our approach demonstrates remarkable efficiency, requiring only 49,277 evaluations on average to generate such S-boxes, representing a 600-fold improvement over traditional simulated annealing methods and a 15-fold improvement over recent genetic algorithm variants. We present comprehensive experimental results from extensive parameter space exploration, revealing that minimal populations (often single-individual) combined with moderate mutation rates achieve optimal performance. This paper provides detailed analysis of algorithm behavior, parameter sensitivity, and performance characteristics, supported by rigorous statistical evaluation. We demonstrate that population size should approximate available thread count for optimal parallel execution despite smaller populations being theoretically more efficient. The HPHC algorithm maintains high reliability across diverse parameter settings while requiring minimal computational resources, making it particularly suitable for practical cryptographic applications.

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Enhancing Cryptographic Primitives through Dynamic Cost Function Optimization in Heuristic Search

Kuznetsov,

Poluyanenko,

Frontoni

et al. 2024

Electronics

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The efficiency of heuristic search algorithms is a critical factor in the realm of cryptographic primitive construction, particularly in the generation of highly nonlinear bijective permutations, known as substitution boxes (S-boxes). The vast search space of 256! (256 factorial) permutations for 8-bit sequences poses a significant challenge in isolating S-boxes with optimal nonlinearity, a crucial property for enhancing the resilience of symmetric ciphers against cryptanalytic attacks. Existing approaches to this problem suffer from high computational costs and limited success rates, necessitating the development of more efficient and effective methods. This study introduces a novel approach that addresses these limitations by dynamically adjusting the cost function parameters within the hill-climbing heuristic search algorithm. By incorporating principles from dynamic programming, our methodology leverages feedback from previous iterations to adaptively refine the search trajectory, leading to a significant reduction in the number of iterations required to converge on optimal solutions. Through extensive comparative analyses with state-of-the-art techniques, we demonstrate that our approach achieves a remarkable 100% success rate in locating 8-bit bijective S-boxes with maximal nonlinearity, while requiring only 50,000 iterations on average—a substantial improvement over existing methods. The proposed dynamic parameter adaptation mechanism not only enhances the computational efficiency of the search process, but also showcases the potential for interdisciplinary collaboration between the fields of heuristic optimization and cryptography. The practical implications of our findings are significant, as the ability to efficiently generate highly nonlinear S-boxes directly contributes to the development of more secure and robust symmetric encryption systems. Furthermore, the dynamic parameter adaptation concept introduced in this study opens up new avenues for future research in the broader context of heuristic optimization and its applications across various domains.

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Optimized simulated annealing for efficient generation of highly nonlinear S-boxes

Cited by 3 publications

References 36 publications

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

Hybrid Population-Based Hill Climbing Algorithm for Generating Highly Nonlinear S-boxes

Enhancing Cryptographic Primitives through Dynamic Cost Function Optimization in Heuristic Search

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