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Dimensional e\(\textsf{ROS}\)ion: Improving the \(\textsf{ROS}\) Attack with Decomposition in Higher Bases

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Antoine Joux
Julian Loss
Giacomo Santato
Published in
Theory of Cryptography
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the cryptographic problem of finding random inhomogeneities in an overdetermined solvable system of linear equations, a challenge central to the security of various interactive signature schemes. The authors revisit and enhance the polynomial attack from previous research, introducing a novel approach that leverages decompositions in higher bases to improve efficiency. Key topics include the binary decomposition attack, the benefits of ternary decomposition, and the development of a base-n decomposition attack. The paper also explores the generalized attack, combining Wagner's subexponential algorithm with the new polynomial method to further enhance cryptanalytic capabilities. Practical implementations and detailed technical overviews are provided, demonstrating the attack's effectiveness against blind Schnorr signatures and other cryptographic schemes. The chapter concludes with a discussion on the implications for affected schemes and the potential for future research in this area.
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previous chapter The Pseudorandomness of Legendre Symbols Under the Quadratic-Residuosity Assumption
next chapter Threshold Signatures from One-Way Functions
Title
Dimensional eion: Improving the  Attack with Decomposition in Higher Bases
Authors
Antoine Joux
Julian Loss
Giacomo Santato
Copyright Year
2026
Book
Theory of Cryptography

Print ISBN: 978-3-032-12295-7

Electronic ISBN: 978-3-032-12296-4

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-12296-4_11
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