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Documents authored by Strub, Pierre-Yves

Document
DOI: 10.4230/LIPIcs.ITP.2026.9
Functional Correctness of an Optimized Modular Inversion Algorithm

Authors: Assia Mahboubi, Guillaume Melquiond, Pierre-Yves Strub, and Tomás Vallejos Parada

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
This article describes the first mechanized proof of functional correctness of an algorithm due to Pornin (2020), for computing modular inverses via an optimized extended binary GCD algorithm. This algorithm is widely used in cryptography applications, due to its speed and constant-timeness. But this speed comes from the use of approximate computations during its loop iterations. In particular, the pen-and-paper proof of the fact that sufficiently many loop iterations were performed is especially intricate (and the originally published version was actually wrong), which negatively impacts the trust in the applications that rely on the algorithm. In this work, we expand the notes provided in the original description by Pornin into a complete formal proof. We discuss the challenges raised by its mechanization, which eventually relies on the collaboration of deductive program verification and interactive theorem proving through the use of the tools Rocq and Why3.
Cite as

Assia Mahboubi, Guillaume Melquiond, Pierre-Yves Strub, and Tomás Vallejos Parada. Functional Correctness of an Optimized Modular Inversion Algorithm. In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mahboubi_et_al:LIPIcs.ITP.2026.9,
  author =	{Mahboubi, Assia and Melquiond, Guillaume and Strub, Pierre-Yves and Vallejos Parada, Tom\'{a}s},
  title =	{{Functional Correctness of an Optimized Modular Inversion Algorithm}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.9},
  URN =		{urn:nbn:de:0030-drops-269839},
  doi =		{10.4230/LIPIcs.ITP.2026.9},
  annote =	{Keywords: deductive program verification, modular inversion algorithm, formal verification, Rocq, Why3}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.8
Unsolvability of the Quintic Formalized in Dependent Type Theory

Authors: Sophie Bernard, Cyril Cohen, Assia Mahboubi, and Pierre-Yves Strub

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
In this paper, we describe an axiom-free Coq formalization that there does not exists a general method for solving by radicals polynomial equations of degree greater than 4. This development includes a proof of Galois' Theorem of the equivalence between solvable extensions and extensions solvable by radicals. The unsolvability of the general quintic follows from applying this theorem to a well chosen polynomial with unsolvable Galois group.
Cite as

Sophie Bernard, Cyril Cohen, Assia Mahboubi, and Pierre-Yves Strub. Unsolvability of the Quintic Formalized in Dependent Type Theory. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bernard_et_al:LIPIcs.ITP.2021.8,
  author =	{Bernard, Sophie and Cohen, Cyril and Mahboubi, Assia and Strub, Pierre-Yves},
  title =	{{Unsolvability of the Quintic Formalized in Dependent Type Theory}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.8},
  URN =		{urn:nbn:de:0030-drops-139038},
  doi =		{10.4230/LIPIcs.ITP.2021.8},
  annote =	{Keywords: Galois theory, Coq, Mathematical Components, Dependent Type Theory, Abel-Ruffini, General quintic}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.102
*-Liftings for Differential Privacy

Authors: Gilles Barthe, Thomas Espitau, Justin Hsu, Tetsuya Sato, and Pierre-Yves Strub

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
Recent developments in formal verification have identified approximate liftings (also known as approximate couplings) as a clean, compositional abstraction for proving differential privacy. There are two styles of definitions for this construction. Earlier definitions require the existence of one or more witness distributions, while a recent definition by Sato uses universal quantification over all sets of samples. These notions have different strengths and weaknesses: the universal version is more general than the existential ones, but the existential versions enjoy more precise composition principles. We propose a novel, existential version of approximate lifting, called *-lifting, and show that it is equivalent to Sato's construction for discrete probability measures. Our work unifies all known notions of approximate lifting, giving cleaner properties, more general constructions, and more precise composition theorems for both styles of lifting, enabling richer proofs of differential privacy. We also clarify the relation between existing definitions of approximate lifting, and generalize our constructions to approximate liftings based on f-divergences.
Cite as

Gilles Barthe, Thomas Espitau, Justin Hsu, Tetsuya Sato, and Pierre-Yves Strub. *-Liftings for Differential Privacy. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 102:1-102:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{barthe_et_al:LIPIcs.ICALP.2017.102,
  author =	{Barthe, Gilles and Espitau, Thomas and Hsu, Justin and Sato, Tetsuya and Strub, Pierre-Yves},
  title =	{{*-Liftings for Differential Privacy}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{102:1--102:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.102},
  URN =		{urn:nbn:de:0030-drops-74358},
  doi =		{10.4230/LIPIcs.ICALP.2017.102},
  annote =	{Keywords: Differential Privacy, Probabilistic Couplings, Formal Verification}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.107
A Program Logic for Union Bounds

Authors: Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, and Pierre-Yves Strub

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms, the union bound allows flexible and compositional reasoning over possible ways an algorithm may go wrong. It also enables a clean separation between reasoning about probabilities and reasoning about events, which are expressed as standard first-order formulas in our logic. Notably, assertions in our logic are non-probabilistic, even though we can conclude probabilistic facts from the judgments. Our logic can also prove accuracy properties for interactive programs, where the program must produce intermediate outputs as soon as pieces of the input arrive, rather than accessing the entire input at once. This setting also enables adaptivity, where later inputs may depend on earlier intermediate outputs. We show how to prove accuracy for several examples from the differential privacy literature, both interactive and non-interactive.
Cite as

Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, and Pierre-Yves Strub. A Program Logic for Union Bounds. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 107:1-107:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{barthe_et_al:LIPIcs.ICALP.2016.107,
  author =	{Barthe, Gilles and Gaboardi, Marco and Gr\'{e}goire, Benjamin and Hsu, Justin and Strub, Pierre-Yves},
  title =	{{A Program Logic for Union Bounds}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{107:1--107:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.107},
  URN =		{urn:nbn:de:0030-drops-62425},
  doi =		{10.4230/LIPIcs.ICALP.2016.107},
  annote =	{Keywords: Probabilistic Algorithms, Accuracy, Formal Verification, Hoare Logic, Union Bound}
}
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