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Refined Application of the XL Algorithm within the Algebraic Approach to the Regular Syndrome Decoding Problem
eprint.iacr.orgpaper

Refined Application of the XL Algorithm within the Algebraic Approach to the Regular Syndrome Decoding Problem

Furue and Aikawa build and analyze algebraic attacks on the Regular Syndrome Decoding Problem (RSDP), which underlies code-based post-quantum schemes. They extend the Wang et al. hybrid algorithm to allow an arbitrary XL solving degree d, and add two variants: an XFL-based one (partial Gaussian elimination plus variable guessing) and a WXL-based one that exploits Macaulay matrix sparsity. Complexity analysis shows the WXL variant with d>2 wins for small block size β, while the original hybrid wins as β grows. This matters for setting RSDP-based scheme parameters.

TL;DR Improved XL-based algebraic attacks (XFL and WXL variants, arbitrary degree) on the Regular Syndrome Decoding Problem, with complexity comparisons across parameters.
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Organisations named here

  • Macaulay matrix
  • Regular Syndrome Decoding Problem
  • Syndrome Decoding Problem
  • Wang et al. hybrid algorithm
  • WXL
  • XFL

Technologies named here

  • XL algorithm
  • XFL-based method
  • WXL-based method

Techniques named here

  • Algebraic approach to the Regular Syndrome Decoding Problem
  • XFL-based variant
  • WXL-based variant

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