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Optimizing implementations of linear layers using two and higher input XOR gates.

Meltem Kurt Pehlivanoğlu1, Mehmet Ali Demir1

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Summary
This summary is machine-generated.

Researchers developed new algorithms to optimize the design of lightweight block cipher components. These methods reduce the number of XOR gates and circuit depth, leading to more efficient and secure cryptographic designs.

Keywords:
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Area of Science:

  • Cryptography
  • Computer Engineering
  • Digital Circuit Design

Background:

  • Maximum distance separable (MDS) matrices are crucial for diffusion in block cipher linear layers.
  • Lightweight involutory MDS matrices offer security and performance benefits.
  • Efficient circuit implementations (linear straight-line programs) for MDS matrices are challenging.

Purpose of the Study:

  • To develop novel heuristic algorithms for optimizing XOR gate count and circuit depth in linear layers.
  • To design new, highly efficient involutory MDS matrices for block ciphers.
  • To improve circuit area efficiency for linear layers using multiple-input XOR gates.

Main Methods:

  • Proposed the Superior Boyar-Peralta (SBP) heuristic algorithm for optimizing two-input XOR gate circuits.
  • Introduced a depth-aware enhancement to the BDKCI heuristic for multiple-input XOR gates.
  • Designed and analyzed a new 4x4 involutory MDS matrix.

Main Results:

  • The SBP algorithm yielded a 4x4 involutory MDS matrix with 41 XOR gates and depth 3, outperforming previous bests.
  • The enhanced BDKCI algorithm achieved a more efficient AES MixColumn circuit (44 XOR gates/depth 3).
  • The new 4x4 involutory MDS matrix achieved an exceptionally low cost of 19 XOR gates/depth 3.

Conclusions:

  • The SBP and enhanced BDKCI algorithms significantly improve the efficiency of linear layer circuit design.
  • New MDS matrix designs offer state-of-the-art lightweight implementations.
  • Optimized linear layers contribute to more secure and performant block ciphers.