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% UQO Working Paper 34 — Beyond the Square-Root Barrier
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\newcommand{\WPnumber}{34}
\newcommand{\WPtitle}{Beyond the Square-Root Barrier: Automated Discovery of Algebraic and Algorithmic Shortcuts in Bitcoin Cryptography}
\newcommand{\WPsubtitle}{A hypothesis-driven, reproducible study of secp256k1, ECDSA, BIP340 Schnorr and SHA-256 with machine-checked identities and controlled negative results}
\newcommand{\WPdate}{November 2026}
\newcommand{\WPversion}{1.0}
\newcommand{\WPabstract}{\input{sections/abstract}}
\newcommand{\WPkeywords}{elliptic curve discrete logarithm; secp256k1; Pollard rho; endomorphisms; ECDSA; Schnorr signatures; BIP340; SHA-256; SAT-based cryptanalysis; automated mathematical discovery; Lean 4; reproducibility}
\newcommand{\WPjel}{C63, C88, D83 (MSC 2020: 94A60, 11T71, 11G20, 68V15, 68W30)}
\newcommand{\WPauthor}{Simon-Pierre Boucher}
\newcommand{\WPaffiliation}{%
  Département des sciences administratives\\
  Université du Québec en Outaouais%
}
\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca}
\newcommand{\WPaddress}{%
  Gatineau -- Pavillon Alexandre-Taché\\
  283, boulevard Alexandre-Taché\\
  Gatineau, Québec, Canada J9A 1L8%
}

\begin{document}
\input{sections/titlepage}
\tableofcontents
\newpage
\input{sections/01_introduction}
\input{sections/02_foundations}
\input{sections/03_literature}
\input{sections/04_secp256k1}
\input{sections/05_dlog_algorithms}
\input{sections/06_signatures}
\input{sections/07_sha256}
\input{sections/08_discovery_framework}
\input{sections/09_experimental_design}
\input{sections/10_results}
\input{sections/11_formal_negative}
\input{sections/12_implications}
\input{sections/13_limitations}
\input{sections/14_conclusion}
\newpage
\bibliography{references}
\input{appendix/appendix}
\end{document}