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Small Low-Depth Circuits for Cryptographic Applications.

Joan Boyar1, Magnus Gausdal Find2, René Peralta2

  • 1Department of Mathematics and Computer Science University of Southern Denmark, joan@imada.sdu.dk.

Cryptography and Communications : Discrete Structures, Boolean Functions and Sequences
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Summary

New techniques create smaller, lower-depth cryptographic circuits over GF(2). These methods optimize linear components using depth-constrained linear optimization (DCLO) and a See-Saw approach for improved efficiency.

Keywords:
Boolean functionsSee-Saw Methodcircuit depthcircuit sizecryptographic functionsdepth-constrained circuit optimization

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Area of Science:

  • Cryptography
  • Computer Science
  • Boolean Algebra

Background:

  • Cryptographic functions are often specified over the field GF(2).
  • Designing efficient circuits with low depth is crucial for performance.
  • Linear components significantly impact circuit size and depth.

Purpose of the Study:

  • To develop techniques for synthesizing small, low-depth circuits for cryptographic functions.
  • To optimize linear components within circuits using novel heuristics.
  • To apply these techniques to specific cryptographic applications and evaluate their effectiveness.

Main Methods:

  • Utilizing a new heuristic, depth-constrained linear optimization (DCLO), for creating small linear circuits.
  • Employing a See-Saw method to iteratively optimize upper and lower linear circuit components.
  • Applying depth constraints to input arrival and output restrictions.

Main Results:

  • Achieved new results for the Advanced Encryption Standard S-Box and binary polynomial multiplication.
  • Demonstrated improved circuit synthesis for finite field multiplication.
  • Constructed a 16-bit S-Box using GF(2^16) inversion, potentially smaller than existing alternatives.

Conclusions:

  • The presented techniques effectively reduce circuit size and depth for cryptographic functions over GF(2).
  • DCLO and the See-Saw method offer a powerful approach to optimizing linear circuit components.
  • The results show practical improvements in cryptographic circuit design, including novel S-Box constructions.