Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cryptanalysis of the SIMON Cypher Using Neo4j

Jonathan Cook, Sabih ur Rehman, M. Arif Khan

TL;DR

The novel use of knowledge graphs are introduced to identify intricate relationships between differentials in the SIMON LEA, allowing for the identification of optimal paths throughout the differentials, and increasing the effectiveness of the differential security analyses of SIMON.

Abstract

The exponential growth in the number of Internet of Things (IoT) devices has seen the introduction of several Lightweight Encryption Algorithms (LEA). While LEAs are designed to enhance the integrity, privacy and security of data collected and transmitted by IoT devices, it is hazardous to assume that all LEAs are secure and exhibit similar levels of protection. To improve encryption strength, cryptanalysts and algorithm designers routinely probe LEAs using various cryptanalysis techniques to identify vulnerabilities and limitations of LEAs. Despite recent improvements in the efficiency of cryptanalysis utilising heuristic methods and a Partial Difference Distribution Table (PDDT), the process remains inefficient, with the random nature of the heuristic inhibiting reproducible results. However, the use of a PDDT presents opportunities to identify relationships between differentials utilising knowledge graphs, leading to the identification of efficient paths throughout the PDDT. This paper introduces the novel use of knowledge graphs to identify intricate relationships between differentials in the SIMON LEA, allowing for the identification of optimal paths throughout the differentials, and increasing the effectiveness of the differential security analyses of SIMON.

Cryptanalysis of the SIMON Cypher Using Neo4j

TL;DR

The novel use of knowledge graphs are introduced to identify intricate relationships between differentials in the SIMON LEA, allowing for the identification of optimal paths throughout the differentials, and increasing the effectiveness of the differential security analyses of SIMON.

Abstract

The exponential growth in the number of Internet of Things (IoT) devices has seen the introduction of several Lightweight Encryption Algorithms (LEA). While LEAs are designed to enhance the integrity, privacy and security of data collected and transmitted by IoT devices, it is hazardous to assume that all LEAs are secure and exhibit similar levels of protection. To improve encryption strength, cryptanalysts and algorithm designers routinely probe LEAs using various cryptanalysis techniques to identify vulnerabilities and limitations of LEAs. Despite recent improvements in the efficiency of cryptanalysis utilising heuristic methods and a Partial Difference Distribution Table (PDDT), the process remains inefficient, with the random nature of the heuristic inhibiting reproducible results. However, the use of a PDDT presents opportunities to identify relationships between differentials utilising knowledge graphs, leading to the identification of efficient paths throughout the PDDT. This paper introduces the novel use of knowledge graphs to identify intricate relationships between differentials in the SIMON LEA, allowing for the identification of optimal paths throughout the differentials, and increasing the effectiveness of the differential security analyses of SIMON.
Paper Structure (13 sections, 1 theorem, 7 equations, 7 figures, 2 algorithms)

This paper contains 13 sections, 1 theorem, 7 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem
  3. Contribution
  4. Structure of the Paper
  5. Preliminaries
  6. Description of the SIMON Cypher
  7. Calculating Differential Probabilities
  8. Partial Difference Distribution Tables
  9. Methodology
  10. PDDT and Comma Separated Values File Generation
  11. Knowledge Graphs
  12. Results
  13. Conclusion and future research

Key Result

Proposition 1

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

Figures (7)

  • Figure 1: Our methodology: 1) Create a PDDT from the full distribution of differentials. 2) Import the PDDT to Neo4j database. 3) Create knowledge graph using Neo4j. 4) Analyse relationships between differentials using Neo4j.
  • Figure 2: SIMON round function
  • Figure 3: 240 nodes connected by 960 relationships in Neo4j. Enlarged views of \ref{['fig:zoom_a']} and \ref{['fig:zoom_b']} are presented below.
  • Figure 4: Enlarged views of neighbourhoods \ref{['fig:zoom_a']} and \ref{['fig:zoom_b']}.
  • Figure 5: The same knowledge graph com ID in Figure \ref{['fig:nodes_by_id']}, output differential in Figure \ref{['fig:nodes_by_output']} and weight in Figure \ref{['fig:nodes_by_weight']}.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Proposition 1