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A Simple Deterministic Algorithm for Systems of Quadratic Polynomials over

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... 2. By utilizing a simple version of the crossbred algorithm [JV17] proposed in [BDT22] to solve an overdefined quadratic equation system, our attacks on 3-round LowMC require negligible memory and can achieve better time-memory tradeoffs than Dinur's algorithm [Din21]. ...
... In our attacks, we will adopt a simple version of the crossbred algorithm [JV17] to solve an overdefined system of quadratic equations, which is described in [BDT22]. This algorithm fits very well with our attacks on LowMC for its simplicity to bound the time complexity and to implement in practice. ...
... The first attack is a new and simple guess-and-determine (GnD) attack on 3-round LowMC by using Banik et al.'s strategy [BBDV20] to linearize the 3-bit S-box, where we solve a system of quadratic equations with the standard linearization technique. The second attack is a much simpler yet more efficient GnD attack on 3-round LowMC by using a naive guess strategy to linearize the 3-bit S-box, where we solve quadratic equations with the simplified version of the crossbred algorithm [BDT22]. The third attack is for full-round (4-round) LowMC, where we still adopt the naive guess strategy but use Dinur's algorithm [Din21] to solve equations of degree 4. ...
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Chapter
After initial publication of the book, various errors were identified that needed correction. The following corrections have been updated within the current version, along with all known typographical errors.
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GeMSS: A Great Multivariate Short Signature
  • Antoine Casanova
  • Jean-Charles Faugère
  • Gilles Macario-Rat
  • Jacques Patarin
  • Ludovic Perret
  • Jocelyn Ryckeghem
Antoine Casanova, Jean-Charles Faugère, Gilles Macario-Rat, Jacques Patarin, Ludovic Perret, and Jocelyn Ryckeghem. GeMSS: A Great Multivariate Short Signature. Research report, UPMC -Paris 6 Sorbonne Universités ; INRIA Paris Research Centre, MAMBA Team, F-75012, Paris, France ; LIP6 -Laboratoire d'Informatique de Paris 6, December 2017. URL: https://hal.inria.fr/hal-01662158.
A Crossbred Algorithm for Solving Boolean Polynomial Systems
  • Antoine Joux
  • Vanessa Vitse
Antoine Joux and Vanessa Vitse. A Crossbred Algorithm for Solving Boolean Polynomial Systems. In NuTMiC, volume 10737 of Lecture Notes in Computer Science, pages 3-21. Springer, 2017. https://eprint.iacr.org/2017/ 372.pdf.