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

Abstract

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.

Enhancing Cryptographic Primitives through Dynamic Cost Function Optimization in Heuristic Search

“…The use of a small change in the parameter R (up to three units) allowed us to reduce the average statistical value l|i=48| by another two (to l|i=48| = 20) compared to the best result obtained in the first series of tests. 5,6] X ≥ 32 l|i| = 0 R ∈ [6,7,8] X ≥ 36 l|i| = 0 R ∈ [8,9,10] X ≥ 28 l|i| = 0 R ∈ [10,11,12] X ≥ 24 l|i| = 0 R ∈ [12,13,14] X ≥ 20 l|i| = 0 i = 48 R X l|i| Despite the fact that the total number of iterations increases with an increasing R (Figures 17-22d), the best result is shown by cycles with a smaller value of R. For all cycles, the value l |i=52| = 0 is achieved (Figures 17-22a).…”

“…Values of parameters R and X at which the minimum value l |i| is achieved. 5,6] X ≥ 32 l|i| = 0 R ∈ [6,7,8] X ≥ 36 l|i| = 0 R ∈ [8,9,10] X ≥ 28 l|i| = 0 R ∈ [10,11,12] X ≥ 24 l|i| = 0 R ∈ [12,13,14] X ≥ 20 l|i| = 0 [4,5,6] X ≥ 36 l|i| = 20 R ∈ [6,7,8] X ≥ 36 l|i| = 21 R ∈ [8,9,10] X ≥ 36 l|i| = 22 R ∈ [10,11,12] X ≥ 36 l|i| = 25 R ∈ [12,13,14] X ≥ 36 l|i| = 28…”

“…12 ≥ X ≥ 28 l|i| = 150 R ∈ [4,5,6] X ≤ 20 l|i| = 160 R ∈ [6,7,8] X ≤ 20 l|i| = 160 R ∈ [8,9,10] X ≤ 4 l|i| = 160 R ∈ [10,11,12] X ≤ 4 l|i| = 180 R ∈ [12,13,14] X ≤ 4 l|i| = 200…”

“…However, more recent studies have demonstrated a clear trend of improvement. The works of [7,19,20] showcased significant reductions in the number of iterations needed, as well as higher success rates. This progress can be attributed to advancements in heuristic techniques, such as the development of more efficient cost functions and the fine-tuning of algorithm parameters.…”