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Impact of Differentials in SIMON32 Algorithm for Lightweight Security of Internet of Things

Jonathan Cook, Sabih ur Rehman, M. Arif Khan

Abstract

SIMON and SPECK were among the first efficient encryption algorithms introduced for resource-constrained applications. SIMON is suitable for Internet of Things (IoT) devices and has rapidly attracted the attention of the research community to understand its structure and analyse its security. To analyse the security of an encryption algorithm, researchers often employ cryptanalysis techniques. However, cryptanalysis is a resource and time-intensive task. To improve cryptanalysis efficiency, state-of-the-art research has proposed implementing heuristic search and sampling methods. Despite recent advances, the cryptanalysis of the SIMON cypher remains inefficient. Contributing factors are the large size of the difference distribution tables utilised in cryptanalysis and the scarcity of differentials with a high transition probability. To address these limitations, we introduce an analysis of differential properties of the SIMON32 cypher, revealing differential characteristics that pave the way for future efficiency enhancements. Our analysis has further increased the number of targeted rounds by identifying high probability differentials within a partial difference distribution table of the SIMON cypher, exceeding existing state-of-the-art benchmarks. The code designed for this work is available at https://github.com/johncook1979/simon32-analysis.

Impact of Differentials in SIMON32 Algorithm for Lightweight Security of Internet of Things

Abstract

SIMON and SPECK were among the first efficient encryption algorithms introduced for resource-constrained applications. SIMON is suitable for Internet of Things (IoT) devices and has rapidly attracted the attention of the research community to understand its structure and analyse its security. To analyse the security of an encryption algorithm, researchers often employ cryptanalysis techniques. However, cryptanalysis is a resource and time-intensive task. To improve cryptanalysis efficiency, state-of-the-art research has proposed implementing heuristic search and sampling methods. Despite recent advances, the cryptanalysis of the SIMON cypher remains inefficient. Contributing factors are the large size of the difference distribution tables utilised in cryptanalysis and the scarcity of differentials with a high transition probability. To address these limitations, we introduce an analysis of differential properties of the SIMON32 cypher, revealing differential characteristics that pave the way for future efficiency enhancements. Our analysis has further increased the number of targeted rounds by identifying high probability differentials within a partial difference distribution table of the SIMON cypher, exceeding existing state-of-the-art benchmarks. The code designed for this work is available at https://github.com/johncook1979/simon32-analysis.
Paper Structure (9 sections, 1 theorem, 7 equations, 5 figures, 2 tables, 5 algorithms)

This paper contains 9 sections, 1 theorem, 7 equations, 5 figures, 2 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Create pDDT
  4. Sorting differentials
  5. Compare hamming weight distribution
  6. Extract promising differentials
  7. Generate differential trails
  8. Results and Analysis
  9. Conclusion

Key Result

Proposition 1

The DP of the XOR operation combined with addition modulo $2n$ decreases as the word size of the differences $a$, $b$, $c$ increases, such that:

Figures (5)

  • Figure 1: Our methodology
  • Figure 2: Frequency distribution of significant differentials
  • Figure 3: Frequency distribution of non-significant differentials
  • Figure 4: Boxplot of differential Hamming Weights
  • Figure 5: Heat map of mean best hamming weight grouped by input differentials

Theorems & Definitions (1)

  • Proposition 1