Parisian Master of Research in Computer Science
Master Parisien de Recherche en Informatique (MPRI)

Preuves de protocoles de sécurité / proofs of security protocols (48h, 6 ECTS)

Responsable / Teacher in charge: Bruno Blanchet (Inria, Prosecco team).

Intervenants en 2023-2024 / Teachers for 2023-2024

  • David Pointcheval (12h)
  • Bruno Blanchet (12h)
  • Adrien Koutsos (12h)
  • Aymeric Fromherz (12h)

First lecture: Tuesday Sept. 12th at 8:45 - Room 381F in building Halle aux Farines; next courses in Room 1002 in Sophie Germain Building.

Objectifs / Goals of the course

Ce cours s'adresse à la fois aux étudiants intéressés par la logique, la concurrence, la sémantique et à ceux intéressés par la cryptographie. En effet, il étudie les protocoles cryptographiques en utilisant des outils formels (calculs de processus, sémantique, typage, logique, ...).

Les protocoles cryptographiques sont des programmes distribués qui visent à sécuriser des communications et transactions en utilisant des primitives cryptographiques. La conception des protocoles cryptographiques est difficile: de nombreuses erreurs ont été découvertes dans des protocoles après leur publication. Il est donc particulièrement important de pouvoir obtenir des preuves que ces protocoles sont sûrs.

Deux modèles des protocoles ont été considérés: le modèle symbolique et le modèle calculatoire. Cette année, nous considérerons seulement le modèle calculatoire, qui est le plus précis et qui est utilisé dans les preuves manuelles des cryptographes. Nous présenterons les techniques de preuves associées. Nous considérerons aussi leur mise en oeuvre, en montrant des outils de preuve automatique ou interactive dans ce modèle, et en les appliquant à la vérification de programmes qui implémentent des primitives ou protocoles cryptographiques.

Ce cours sera l'occasion d'adapter et d'utiliser des outils formels, comme les calculs de processus, la sémantique, le typage et la logique, au cas particulier de l'étude des protocoles cryptographiques.

This course targets both students interested in logic, concurrence, semanticsm and those interested in cryptography. Indeed, it studies cryptographic protocols using formal tools (process calculi, semantics, typing, logic, ...).

Cryptographic protocols are distributed programs which aim at securing communications and transactions by the means of cryptographic primitives. The design of cryptographic protocols is difficult: numerous errors have been discovered in protocols after their publication. It is therefore particularly important to be able to obtain proofs that protocols are secure.

Two models of the protocols have been considered: the formal model and the computational model. This year, we will only consider the computational model, which is the most precise and the one used in the manual proofs of cryptographers. We shall present the associated proof techniques. We shall also consider their implementation, by showing automatic or interactive proof tools in this model, and by applying them to the verification of programs that implement cryptographic primitives or protocols.

This course will be an opportunity to adapt and use formal tools, such as process calculi, semantics, and logic to the particular case of the study of cryptographic protocols.

Programme du cours / Course program

1. Computational cryptography (D. Pointcheval)

  • Security proofs in the computational model
  • Game-based proofs and public-key encryption
  • Signatures
  • Protocols

2. Mechanizing game-based computational security proofs (B. Blanchet)

  • The tool CryptoVerif
  • Small example: Full Domain Hash signature scheme
  • Practical exercises using CryptoVerif

3. A first-order logic for computational indistinguishability (A. Koutsos)

  • Expressing protocol security as a FO unsatisfiability problem
  • A sound set of inference rules for computational indistinguishability
  • Application: the Private Authentication protocol (unlinkability)
  • Correspondence properties: temporal properties and related inference rules
  • Application: the Basic Hash protocol (authentication)

4. Verification of protocol implementations (A. Fromherz)

  • The F* tool ( verifying purely-functional and effectful programs
  • Non-interference and Side-Channel Attacks
  • Verifying C and assembly implementations with Low* and Vale
  • Simple cryptographic protocol implementations in F*: signatures, MACs, stateful encryption, RPC, encrypt-then-mac, etc.
  • On the formal verification of a complete HTTPS stack (

Planning provisoire / Preliminary schedule

Sept. 12 D. Pointcheval Slides: Provable Security in the Computational Model
Sept. 19 D. Pointcheval Slides: The Case of Public Key Encryption
Sept. 26 D. Pointcheval Slides: The Case of Signatures
Oct. 3 D. Pointcheval Slides: Application to Authenticated Key Exchange
Oct. 10 B. Blanchet CryptoVerif enc-then-MAC.ocv fdh.ocv
Oct. 17 B. Blanchet correspondences tutorial
Oct. 24 B. Blanchet CV2ML tutorial continued
Oct. 31 B. Blanchet composition results tutorial continued Solutions
Nov. 7 B. Blanchet Revisions A possible solution
Nov. 14 D. Pointcheval Revisions
Nov. 28 D. Pointcheval/B. Blanchet Exam. The only allowed document will be one two-sided A4 sheet of paper (handwritten or printed).
Dec. 5 A. Koutsos Slides for week 1 to 3
Dec. 12 A. Koutsos continue on slides of lecture 1, exercice sheet 1
Dec. 19 No course
Jan. 9 A. Koutsos continues on slides of lecture 1
Jan. 16 A. Koutsos Slides for week 4
Jan. 23 A. Fromherz Slides: Introduction to F*, F* file: Integer Sum, F* file: List Reversal
Jan. 30 A. Fromherz Slides: Side-Channels and Non-Interference
Feb. 6 A. Fromherz Slides: Low-level Verification and HACL*, F* file: Stateful Sum, F* file: Stateful Factorial
Feb. 13 A. Fromherz Slides: End-to-End Verification: Vale, DY*, and Noise*
Feb. 20 A. Koutsos / A. Fromherz Revisions
Feb. 27 A. Koutsos / A. Fromherz Exam. The only allowed document will be one two-sided A4 sheet of paper (handwritten or printed).

Exam conditions:

  • session 1: 3 hours written exam, at the same time and in the same room as the course
  • session 2: 3 hours written exam, at the same time and in the same room as the course

Langue / Language policy

The lecture notes (or slides when relevant) are in English.

The lecture will be in English as soon as one non-French speaking student attends. Otherwise, it will be given in French.

Supports de cours / Lecture notes

You can find here some material related to the class: Slides & Exercises by D. Pointcheval The slides will be made available online on the course web page.

Pré-requis / Prerequisites

Pas de pré-requis particulier, mais on s'appuiera sur les pré-requis généraux du MPRI (sémantique, logique, typage, ...).

No specific prerequisites. We will however rely on the general prerequisites of the MPRI (semantics, logic, typing...).

Cours liés / Related courses

Concurrence / Concurrency (2-3): Il est recommandé de suivre le cours 2-3, car les modèles présentés dans la 1ère partie du cours sont des modèles de la concurrence (même s'ils sont différents de ceux du cours 2-3). It is recommended to attend course 2-3, since the formal models presented in the first part of the course are models of concurrency (although different from those of course 2-3).

Techniques en cryptographie et cryptoanalyse / Techniques in Cryptography and Cryptanalysis (2-12-1) Les preuves de sécurité dans le modèle calculatoire seront utilisées dans le cours 2-12-1. Le cours 2-30 sera donc une introduction essentielle pour le cours 2-12-1. Computational security proofs will be used in course 2-12-1. Course 2-30 will therefore be a useful introduction for course 2-12-1.

Algorithmes arithmétiques pour la cryptologie / Algorithmic number theory for cryptology (2-12-2),
Systèmes polynomiaux, calcul formel et applications / Polynomial systems, formal computation, and applications (2-13-1)
and Codes correcteurs d'erreurs et applications à la cryptographie / Error correcting codes and applications to cryptography (2-13-2): These 3 courses study the validity of some algorithmic assumptions used in security proofs.

Bibliographie / Bibliography

M. Abadi and B. Blanchet. Analyzing security protocols with secrecy types and logic of programs. Journal of the ACM, 52(1):102–­146, Jan. 2005.

M. Abadi and C. Fournet. Mobile values, new names, and secure communication. In 28th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL'01), pages 104–­115, London, United Kingdom, Jan. 2001. ACM Press.

D. Ahman, C. Hriţcu, K. Maillard, G. Martínez, G. Plotkin, J. Protzenko, A. Rastogi, N. Swamy. Dijkstra Monads for Free, In 44th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL). To appear, January 2017.

M. Arapinis, S. Delaune, and S. Kremer. From one session to many : Dynamic tags for security protocols. In Proc. Logic for Programming, Artificial Intelligence, and Reasoning, 15th International Conference, LPAR 2008, pages 128-­142, 2008.

D. Baelde, S. Delaune, C. Jacomme, A. Koutsos, S. Moreau. An Interactive Prover for Protocol Verification in the Computational Model. IEEE Symposium on Security and Privacy, S&P 2021. Paper.

G. Bana, H. Comon-Lundh. A Computationally Complete Symbolic Attacker for Equivalence Properties. ACM CCS 2014. Paper.

B. Blanchet. A computationally sound mechanized prover for security protocols. In IEEE Symposium on Security and Privacy, pages 140­–154, Oakland, California, May 2006. Extended version available as ePrint Report 2005/401.

B. Blanchet and D. Pointcheval. Automated security proofs with sequences of games. In C. Dwork, editor, Advances in Cryptology ­ CRYPTO 2006, pages 537–­554, Santa Barbara, CA, Aug. 2006.

H. Comon-Lundh. Soundness of abstract cryptography. Lecture notes, Part 1. Available here, 2007.

H. Comon-Lundh, V. Cortier, and E. Zalinescu. Deciding security properties of cryptographic protocols. Application to key cycles. Transaction on Computational Logic, 2009. Available here.

H. Comon, A. Koutsos. Formal Computational Unlinkability Proofs of RFID Protocols. 30th IEEE Computer Security Foundations Symposium, CSF 2017. Paper.

D. Pointcheval. Advanced Course on Contemporary Cryptology, chapter Provable Security for Public-Key Schemes, pages 133­–189. Advanced Courses CRM Barcelona. (248 pages).

V. Shoup. Sequences of games : a tool for taming complexity in security proofs. Manuscript. Available here.

N. Swamy, C. Hriţcu, C. Keller, A. Rastogi, A. Delignat-Lavaud, S. Forest, K. Bhargavan, C. Fournet, P.-Y. Strub, M. Kohlweiss, J.-K. Zinzindohoue, S. Zanella-Béguelin. Dependent Types and Multi-Monadic Effects in F*, In 43nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), ACM, 2016.

Some more references on attacks and verification of TLS can be found here:

Equipe pédagogique / Possible lecturers

Karthikeyan Bhargavan DR INRIA
Bruno Blanchet DR INRIA
Aymeric Fromherz ISFP INRIA
Adrien Koutsos CR INRIA
David Pointcheval DR ENS Paris - DIENS
Universités partenaires Université Paris-Diderot
Université Paris-Saclay
ENS Cachan École polytechnique Télécom ParisTech
Établissements associés Université Pierre-et-Marie-Curie CNRS INRIA CEA