110 http://isa.epfl.ch/imoniteur_ISAP/ itffichecours.txt?path=EPFL.Etu.FicheCours.HeaderFR itffichecours.txt?path=EPFL.Etu.FicheCours.GlobalNav_js fr 2026 84482813 2936286 84482813 2305107546 2305107546 0 1 Mineurs MINEUR !itffichecours.htm?ww_i_matiere=3204340051&ww_x_anneeAcad=2305107546&ww_i_section=84482813&ww_i_niveau=2936286 1696552884 1696552963 2024-2025 COURSE BOOKLET CS-459 Foundations of probabilistic proofs Foundations of probabilistic proofs Lecturers Chiesa Alessandro Language of teaching English Cursus Applied Mathematics(2024-2025, MA-ING - Master 2023)
Applied Mathematics(2024-2025, MA-ING - Master 2024)
Communication Systems - master program(2024-2025, SC - Master EPFL 2023)
Communication Systems - master program(2024-2025, SC - Master EPFL 2024)
Computer Science - Cybersecurity(2024-2025, IN-CS - Master 2023)
Computer Science - Cybersecurity(2024-2025, IN-CS - Master 2024)
Computer Science(2024-2025, IN - Master 2023)
Computer Science(2024-2025, IN - Master 2024)
Cyber security minor(2024-2025, Information security minor 2024-25)
Mathematics - master program(2024-2025, MATH - Master 2023)
Mathematics - master program(2024-2025, MATH - Master 2024)
SemesterMand.OptionFilières
Hx
MA1, MA3xA
MA1, MA3xD I
MA1, MA3xD
 Credits 6 Session Winter Workload 180h Exam During the semester Number of positions Semester Fall Weeks 14 Hours 5 weekly
Courses 4 weekly
Exercises 1 weekly
Study planSemesterMand.OptionFilières
Cyber security 2024-25MA1xD
Cyber security 2024-25MA3xD
Informatique 2024-25MA1xD I
Informatique 2024-25MA3xD I
Ingénierie Mathématiques 2024-25MA1xA
Ingénierie Mathématiques 2024-25MA3xA
Mathématiques 2024-25MA1xA
Mathématiques 2024-25MA3xA
Mineur : Cyber security 2024-25Hx
Systèmes de communication 2024-25MA1xD I
Systèmes de communication 2024-25MA3xD I
Cursus Sem. Type
Computer science MA1, MA3 Opt.
Cyber security minor H Opt.
Cybersecurity MA1, MA3 Opt.
Ing.-math MA1, MA3 Opt.
Mathématicien MA1, MA3 Opt.
SC master EPFL MA1, MA3 Opt.
Summary Probabilistic proof systems (eg PCPs and IPs) have had a tremendous impact on theoretical computer science, as well as on real-world secure systems. They underlie delegation of computation protocols and hardness of approximation. This course covers the foundations of probabilistic proof systems. Content

Proofs are at the foundations of mathematics, and verifying the correctness of a mathematical proof is a fundamental computational task. (The P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.) The complexity-theoretic study of proof verification has led to new notions of mathematical proofs, such as Interactive Proofs, Probabilistically Checkable Proofs, and others.


Probabilistic proofs are a powerful tool for proving hardness of approximation results, and are an essential building block to achieve delegation of computation (protocols that enable super fast verification of long computations, such as SNARKs). Via these applications, probabilistic proofs have had a tremendous impact on theoretical computer science and, more recently, are playing an exciting role in applied cryptography, computer security, and blockchain technology (e.g., they help secure billions of dollars in transactionds per day).


This course provides an introduction to probabilistic proofs and the beautiful mathematics underlying them.
Covered topics include arithmetization, the sumcheck protocol, zero knowledge, doubly-efficient interactive proofs, linearity testing, low-degree testing, proof composition, succinct verification, and more.


This courses assumes basic familiarity with algorithms (asymptotic notation and analysis of algorithms), complexity theory (computation models and simple complexity classes), and some algebra (finite fields and their properties).

 Learning Prerequisites Important concepts to start the course

- Basic knowledge of discrete probability.
- Basic knowledge of finite fields and their properties.
- Basic knowledge of algorithms (asymptotic notation and analysis of algorithms).
- Basic knowledge of computational complexity (Turing machines; boolean circuits; complexity classes; reductions, familiarity with the classes P and NP; probabilistic computation and the class BPP).

 Teaching methods

Two weekly lectures that include definitions, theorems, and proofs. One weekly recitation to guide students through exercises. Weekly problem sets to reinforce the material.

 Assessment methods
  • Homework 60%
  • Presentation projet 30%
  • Project report 10%

 

 Resources Moodle Link Informatique, 2024-2025, Master semestre 1 Computer Science, 2024-2025, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 1 MA1 HIVER Master semester 1 MA1 Informatique IN Computer Science IN
Informatique IN Computer Science IN
D I optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique, 2024-2025, Master semestre 3 Computer Science, 2024-2025, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 3 MA3 HIVER Master semester 3 MA3 Informatique IN Computer Science IN
Informatique IN Computer Science IN
D I optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique - Cybersecurity, 2024-2025, Master semestre 1 Computer Science - Cybersecurity, 2024-2025, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 1 MA1 HIVER Master semester 1 MA1 Informatique - Cybersecurity IN_CS Computer Science - Cybersecurity IN_CS
Informatique IN Computer Science IN
D optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique - Cybersecurity, 2024-2025, Master semestre 3 Computer Science - Cybersecurity, 2024-2025, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 3 MA3 HIVER Master semester 3 MA3 Informatique - Cybersecurity IN_CS Computer Science - Cybersecurity IN_CS
Informatique IN Computer Science IN
D optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Ingénierie mathématique, 2024-2025, Master semestre 1 Applied Mathematics, 2024-2025, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 1 MA1 HIVER Master semester 1 MA1 Ingénierie mathématique ING_MATH Applied Mathematics ING_MATH
Mathématiques MA Mathematics MA
A optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Ingénierie mathématique, 2024-2025, Master semestre 3 Applied Mathematics, 2024-2025, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 3 MA3 HIVER Master semester 3 MA3 Ingénierie mathématique ING_MATH Applied Mathematics ING_MATH
Mathématiques MA Mathematics MA
A optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Mathématiques - master, 2024-2025, Master semestre 1 Mathematics - master program, 2024-2025, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 1 MA1 HIVER Master semester 1 MA1 Mathématiques - master MATH Mathematics - master program MATH
Mathématiques MA Mathematics MA
A optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Mathématiques - master, 2024-2025, Master semestre 3 Mathematics - master program, 2024-2025, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 3 MA3 HIVER Master semester 3 MA3 Mathématiques - master MATH Mathematics - master program MATH
Mathématiques MA Mathematics MA
A optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Systèmes de communication - master, 2024-2025, Master semestre 1 Communication Systems - master program, 2024-2025, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 1 MA1 HIVER Master semester 1 MA1 Systèmes de communication - master SC_EPFL Communication Systems - master program SC_EPFL
Systèmes de communication SC Communication Systems SC
D I optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Systèmes de communication - master, 2024-2025, Master semestre 3 Communication Systems - master program, 2024-2025, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Master semestre 3 MA3 HIVER Master semester 3 MA3 Systèmes de communication - master SC_EPFL Communication Systems - master program SC_EPFL
Systèmes de communication SC Communication Systems SC
D I optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
Cyber security minor, 2024-2025, Semestre automne Cyber security minor, 2024-2025, Autumn semester Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2024-2025 Semestre automne H HIVER Autumn semester H Cyber security minor MIN_IN_SEC Cyber security minor MIN_IN_SEC
optionnel optional
4 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Chiesa Alessandro 348124
Informatique IN Computer Science IN
3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs 6
Pendant le semestre During the semester Crédit Credits 6 Session hiver Session winter HIV HIV
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FO_fin HTML_debut &#951; HTML_fin JS_debut \x26#951; JS_fin CODE72092805 BOOLEAN_Symbol BaliseJS_debut \x5bETA\x5d BaliseJS_fin Balise_debut [ETA] Balise_fin FO_debut [inline]=&#919; FO_fin HTML_debut &#919; HTML_fin JS_debut \x26#919; JS_fin BALISE_SOULIGNER BOOLEAN_Symbol BaliseJS_debut \x5bu\x5d BaliseJS_fin \x5b\x2fu\x5d Balise_debut [u] Balise_fin [/u] FO_debut text-decoration=underline FO_fin text-decoration=none HTML_debut <u> HTML_fin </u> JS_debut \x3cu\x3e JS_fin \x3c\x2fu\x3e CODE72092388 BOOLEAN_Symbol BaliseJS_debut \x5bpsi\x5d BaliseJS_fin Balise_debut [psi] Balise_fin FO_debut [inline]=&#968; FO_fin HTML_debut &#968; HTML_fin JS_debut \x26#968; JS_fin CODE72092541 BOOLEAN_Symbol BaliseJS_debut \x5bPSI\x5d BaliseJS_fin Balise_debut [PSI] Balise_fin FO_debut [inline]=&#936; FO_fin HTML_debut &#936; HTML_fin JS_debut \x26#936; JS_fin CODE140502511 BOOLEAN_Symbol 1 BaliseJS_debut \x5brho\x5d BaliseJS_fin Balise_debut [rho] Balise_fin FO_debut [inline]=&#961; FO_fin HTML_debut &#961; HTML_fin JS_debut \x26#961; JS_fin CODE140504636 BOOLEAN_Symbol 1 BaliseJS_debut \x5bRHO\x5d BaliseJS_fin Balise_debut [RHO] Balise_fin FO_debut [inline]=&#929; FO_fin HTML_debut &#929; HTML_fin JS_debut \x26#929; JS_fin CODE148292791 BOOLEAN_Symbol BaliseJS_debut \x5bepsilon\x5d BaliseJS_fin Balise_debut [epsilon] Balise_fin FO_debut [inline]=&#949; FO_fin HTML_debut &#949; HTML_fin JS_debut \x26#949; JS_fin CODE169976220 BOOLEAN_Symbol BaliseJS_debut \x5blig\x5d BaliseJS_fin Balise_debut [lig] Balise_fin FO_debut [inline]=&#x203A;&#160;&#160; FO_fin HTML_debut &#x203A;&#160;&#160; HTML_fin JS_debut \x26#x203A;\x26#160;\x26#160; JS_fin CODE148292899 BOOLEAN_Symbol BaliseJS_debut \x5bEPSILON\x5d BaliseJS_fin Balise_debut [EPSILON] Balise_fin FO_debut [inline]=&#917; FO_fin HTML_debut &#917; HTML_fin JS_debut \x26#917; JS_fin BALISETXT_SAUT BOOLEAN_Symbol BaliseJS_debut \x5bbr\x2f\x5d BaliseJS_fin Balise_debut [br/] Balise_fin FO_debut FO_fin HTML_debut <br/> HTML_fin JS_debut \x3cbr\x2f\x3e JS_fin 3204340051 Foundations of probabilistic proofs Foundations of probabilistic proofs anglais Chiesa Alessandro 348124 244047873