# Applied Cryptography

CMPS 297AD/396AI

## Welcome

Welcome to the website for the Applied Cryptography course at the American University of Beirut! This page serves as a unified and self-sufficient source of truth on everything concerning your course.

Bookmark this website for the duration of the course and visit it regularly. All course news will be kept up to date on this website.

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### Course Description

Applied Cryptography explores the core theory of modern cryptography and how to apply these fundamental principles to build and analyze real-world secure systems. We start with foundational concepts—such as Kerckhoff's Principle, computational hardness, and provable security—before moving on to key cryptographic primitives like pseudorandom generators, block ciphers, and hash functions. Building on this solid groundwork, we will survey how these technologies power critical real-world deployments such as TLS, secure messaging protocols (e.g., Signal), and post-quantum cryptography. We will also delve into specialized topics like high-assurance cryptographic implementations, elliptic-curve-based systems, and zero-knowledge proofs to give you a complete understanding of contemporary cryptography's scope and impact. By the end of the semester, you will have gained both a rigorous theoretical perspective and practical hands-on experience, enabling you to evaluate, design, and implement cryptographic solutions.

Note: This website is an informal resource, and not a substitute for the AUB learning management system.

### Course Dates & Times

- Lecture Times: Tuesdays and Thursdays, 12:30 to 13:45
- Lecture Location: Nicely Hall, Room 320
- Lab Times: I don't know yet
- Lab Location: I don't know yet
- Term Dates: August 25th until December 13th, 2025.
- Instructor's Email: cmps-297ad-396ai@nadim.email
- Office Hours: Email me to make an appointment.

### Course Prerequisites

This course is intended for senior undergraduate students. Graduate students are also welcome to register provided that they are working on a research topic that is relevant to this course. The following prerequisites are optional but recommended:

- CMPS 215: Theory of Computation

If you want to understand whether you have the sufficient background for this course, review this revision chapter and try to do all the exercises.

### Important Links

- AUB Academic Calendar

## News

May 28th, 2025

### Part 1 materials are complete!

The course plan, readings, slides, problem sets and lab session proposals for Part 1 of the course are now all complete and available on this website!

Things may change during the semester as Part 1 is being taught, but the course is beginning to take real shape, and the materials should at the very least be able to provide prospective students with an idea of what to expect. Also, the course schedule for Part 2 now looks much more mature and substantial, and will likely only change minimally as the course is developed.

### Older News

Older news entries are kept for the academic year for archival purposes.

May 1st, 2025

### We have a course number!

I'm excited to announce that our course has been officially assigned the course numbers CMPS 297AD (undergraduate) and CMPS 396AI (graduate). Please use these numbers when registering for the class through the university system.

Please note that this website is still very much under construction! I'm not even set on the course schedule yet. Everything isn't final. Some things could be outright wrong. Feedback welcome.

## Materials

Every lecture will be accompanied by outside readings that expand on what is discussed in class or present the same material in a different way. Neither the readings nor the lectures are a replacement for each other; deeply understanding the material will likely require attendance as well as reading. It is possible to read before or after class, depending on your learning style.

Aside from the textbooks and materials, students will also require their own personal computer for various parts of this course. Linux, Mac and Windows computers are all suitable.

### Textbook

#### The Joy of Cryptography

Oregon State University, 2021

Mike Rosulek

Required. This textbook is the primary resource for our course and is available free of charge online.

Note: For this course, we will be using an updated edition of the textbook that is not yet released to the public. Professor Rosulek has been gracious enough to grant us access in advance — access will be shared privately with students during the course.

### Online Readings

Online readings provide essential supplementary material that expands on specific cryptographic concepts, vulnerabilities, and practical implementations discussed throughout the course.

- Felix Linker, Ralf Sasse and David Basin, A Formal Analysis of Apple’s iMessage PQ3 Protocol, USENIX Security Symposium, 2025.
- Mathy Vanhoef and Frank Piessens, All Your Biases Belong To Us: Breaking RC4 in WPA-TKIP and TLS, USENIX Security Symposium, 2015.
- Benjamin Beurdouche, Karthikeyan Bhargavan, Antoine Delignat-Lavaud, Cédric Fournet, Markulf Kohlweiss, Alfredo Pironti, Pierre-Yves Strub and Jean-Karim Zinzindohoué, A Messy State of the Union: Taming the Composite State Machines of TLS, IEEE Symposium on Security and Privacy, 2015.
- Martin R. Albrecht and Kenneth G. Paterson, Analysing Cryptography in the Wild: A Retrospective, IEEE Security & Privacy, 2024.
- Martin R. Albrecht, Lenka Mareková, Kenneth G. Paterson, Eyal Ronen and Igors Stepanovs, Analysis of the Telegram Key Exchange, IACR Eurocrypt, 2025.
- Lucas Franceschino, Announcing the hax Playground, Cryspen, 2024.
- David Evans, Vladimir Kolesnikov and Mike Rosulek, A Pragmatic Introduction to Secure Multi-Party Computation, NOW Publishers, 2020.
- Christina Garman, Kenneth G. Paterson and Thyla Van der Merwe, Attacks Only Get Better: Password Recovery Attacks Against RC4 in TLS, USENIX Security Symposium, 2015.
- Nadim Kobeissi, Karthikeyan Bhargavan and Bruno Blanchet, Automated Verification for Secure Messaging Protocols and their Implementations: A Symbolic and Computational Approach, IEEE European Symposium on Security and Privacy, 2017.
- Théophile Wallez, A Verification Framework for Secure Group Messaging, PSL Université Paris, 2025.
- Ksenia Ermoshina, Harry Halpin and Francesca Musiani, Can Johnny Build a Protocol? Co-ordinating Developer and User Intentions for Privacy-Enhanced Secure Messaging Protocols, European Workshop on Systems Security, 2017.
- Greg Aloupis, Erik D. Demaine, Alan Guo and Giovanni Viglietta, Classic Nintendo Games are (Computationally) Hard, ACM Theoretical Computer Science, 2015.
- Platon Kotzias, Abbas Razaghpanah, Johanna Amann, Kenneth G. Paterson, Narseo Vallina-Rodriguez and Juan Caballero, Coming of Age: A Longitudinal Study of TLS Deployment, ACM IMC, 2018.
- Hugo Krawczyk, Cryptographic Extraction and Key Derivation: The HKDF Scheme, IACR Crypto, 2010.
- Franziskus Kiefer and Jonas Schneider-Bensch, Cryptographic Protocol Verification with hax, Cryspen, 2024.
- Christina Garman, Matthew Green, Gabriel Kaptchuk, Ian Miers and Michael Rushanan, Dancing on the Lip of the Volcano: Chosen Ciphertext Attacks on Apple iMessage, USENIX Security Symposium, 2016.
- Joppe W. Bos, J. Alex Halderman, Nadia Heninger, Jonathan Moore, Michael Naehrig and Eric Wustrow, Elliptic Curve Cryptography in Practice, Financial Cryptography and Data Security, 2014.
- Joseph Bonneau and Andrew Morrison, Finite-State Security Analysis of OTR Version 2, Stanford Computer Security Laboratory, 2006.
- Martin R. Albrecht, Benjamin Dowling and Daniel Jones, Formal Analysis of Multi-Device Group Messaging in WhatsApp, IACR Eurocrypt, 2025.
- Cas Cremers, Charlie Jacomme and Aurora Naska, Formal Analysis of Session-Handling in Secure Messaging: Lifting Security from Sessions to Conversations, USENIX Security Symposium, 2023.
- Karthikeyan Bhargavan, Charlie Jacomme, Franziskus Kiefer and Rolfe Schmidt, Formal Verification of the PQXDH Post-Quantum Key Agreement Protocol for End-to-End Secure Messaging, USENIX Security Symposium, 2024.
- Ange Albertini, Thai Duong, Shay Gueron, Stefan Kölbl, Atul Luykx, and Sophie Schmieg, How to Abuse and Fix Authenticated Encryption Without Key Commitment, USENIX Security Symposium, 2022.
- Michael Luby and Charles Rackoff, How To Construct Pseudorandom Permutations From Pseudorandom Functions, Society for Industrial and Applied Mathematics, 1988.
- Nick Sullivan, Killing RC4: The Long Goodbye, Cloudflare Blog, 2014.
- Apple Security Engineering and Architecture (SEAR), iMessage with PQ3: The new state of the art in quantum-secure messaging at scale, Apple Security Research, 2024.
- David Adrian, Karthikeyan Bhargavan, Zakir Durumeric, Pierrick Gaudry, Matthew Green, J. Alex Halderman, Nadia Heninger, Drew Springall, Emmanuel Thomé, Luke Valenta, Benjamin VanderSloot, Eric Wustrow, Santiago Zanella-Béguelin and Paul Zimmermann, Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice, ACM CCS, 2015.
- Cas Cremers, Niklas Medinger and Aurora Naska, Impossibility Results for Post-Compromise Security in Real-World Communication Systems, IEEE Symposium on Security and Privacy, 2025.
- Chris Alexander and Ian Goldberg, Improved User Authentication in Off-The-Record Messaging, Workshop on Privacy in the Electronic Society, 2007.
- Ian Martiny, Gabriel Kaptchuk, Adam Aviv, Dan Roche and Eric Wustrow, Improving Signal's Sealed Sender, Network and Distributed Systems Security Symposium, 2021.
- Henry de Valence, It's 255:19AM. Do you know what your validation criteria are?, hdevalence.ca, 2020.
- Matilda Backendal, Sebastian Clermont, Marc Fischlin and Felix Günther, Key Derivation Functions Without a Grain of Salt, IACR Eurocrypt, 2025.
- Daniel J. Bernstein, Karthikeyan Bhargavan, Shivam Bhasin, Anupam Chattopadhyay, Tee Kiah Chia, Matthias J. Kannwischer, Franziskus Kiefer, Thales B. Paiva, Prasanna Ravi and Goutam Tamvada, KyberSlash: Exploiting Secret-Dependent Division Timings in Kyber Implementations, IACR Transactions on Cryptographic Hardware and Embedded Systems, 2025.
- Nadhem J. Alfardan and Kenneth G. Paterson, Lucky Thirteen: Breaking the TLS and DTLS Record Protocols, IEEE Symposium on Security and Privacy, 2013.
- Whitfield Diffie and Martin E. Hellman, New Directions in Cryptography, IEEE Transactions on Information Theory, 1976.
- Paul Rösler, Christian Mainka and Jörg Schwenk, More is Less: On the End-to-End Security of Group Chats in Signal, WhatsApp, and Threema, IEEE European Symposium on Security and Privacy, 2018.
- Nikita Borisov, Ian Goldberg and Eric Brewer, Off-the-Record Communication, or, Why Not To Use PGP, Workshop on Privacy in the Electronic Society, 2004.
- Karthikeyan Bhargavan and Gaëtan Leurent, On the Practical (In-)Security of 64-bit Block Ciphers, ACM CCS, 2016.
- Nadhem AlFardan, Daniel J. Bernstein, Kenneth G. Paterson, Bertram Poettering and Jacob C. N. Schuldt, On the Security of RC4 in TLS, USENIX Security Symposium, 2013.
- Tibor Jager, Jörg Schwenk and Juraj Somorovsky, Practical Invalid Curve Attacks on TLS-ECDH, ESORICS, 2015.
- Itsik Mantin, Predicting and Distinguishing Attacks on RC4 Keystream Generator, IACR Eurocrypt, 2005.
- Cas Cremers and Dennis Jackson, Prime, Order Please! Revisiting Small Subgroup and Invalid Curve Attacks on Protocols using Diffie-Hellman, IEEE CSF, 2019.
- Project Everest Team, Project Everest: Perspectives from Developing Industrial-Grade High-Assurance Software, Microsoft Research, 2025.
- Matthew McPherrin, Reflections on a Year of Sunlight, Let's Encrypt Blog, 2025.
- Richard Barnes, Karthikeyan Bhargavan, Benjamin Lipp and Christopher Wood, RFC 9810: Hybrid Public Key Encryption, RFC Editor, 2022.
- Daniel J. Bernstein and Tanja Lange, SafeCurves: choosing safe curves for elliptic-curve cryptography, SafeCurves, 2017.
- Joël Alwen, Binyi Chen, Krzysztof Pietrzak, Leonid Reyzin and Stefano Tessaro, Scrypt Is Maximally Memory-Hard, IACR Eurocrypt, 2017.
- Hugo Krawczyk, SIGMA: the 'SIGn-and-MAc' Approach to Authenticated Diffie-Hellman and its Use in the IKE Protocols, IACR Crypto, 2003.
- Manuel Barbosa, Gilles Barthe, Karthikeyan Bhargavan, Bruno Blanchet, Cas Cremers, Kevin Liao and Bryan Parno, SoK: Computer-Aided Cryptography, IEEE Symposium on Security and Privacy, 2021.
- Tarek Galal, The Curves of ZoKrates, tgalal.com, 2025.
- Marc Stevens, Elie Bursztein, Pierre Karpman, Ange Albertini and Yarik Markov, The First Collision for Full SHA-1, IACR Crypto, 2017.
- Zakir Durumeric, James Kasten, David Adrian, J. Alex Halderman, Michael Bailey, Frank Li, Nicholas Weaver, Johanna Amann, Jethro Beekman, Mathias Payer and Vern Paxson, The Matter of Heartbleed, ACM IMC, 2014.
- Philip Rogaway, The Moral Character of Cryptographic Work, IACR Cryptology ePrint Archive, 2016.
- Ran Canetti, Oded Goldreich and Shai Halevi, The Random Oracle Model Methodology, Revisited, Journal of the ACM, 2004.
- Bodo Möller, Thai Duong and Krzysztof Kotowicz, This POODLE Bites: Exploiting the SSL 3.0 Fallback, Google, 2014.
- Nicolas Gailly, Kelsey Melissaris and Yolan Romailler, tlock: Practical Timelock Encryption from Threshold BLS, IACR Cryptology ePrint Archive, 2023.
- Mark Russinovich, Manuel Costa, Cédric Fournet, David Chisnall, Antoine Delignat-Lavaud, Sylvan Clebsch, Kapil Vaswani and Vikas Bhatia, Toward Confidential Cloud Computing, Communications of the ACM, 2021.
- Karthikeyan Bhargavan and Gaëtan Leurent, Transcript Collision Attacks: Breaking Authentication in TLS, IKE and SSH, Network and Distributed Systems Security Symposium, 2016.
- Karthikeyan Bhargavan, Antoine Delignat-Lavaud, Cédric Fournet, Alfredo Pironti and Pierre-Yves Strub, Triple Handshakes and Cookie Cutters: Breaking and Fixing Authentication over TLS, IEEE Symposium on Security and Privacy, 2014.
- Yevgeniy Dodis, Daniel Jost, Shuichi Katsumata, Thomas Prest and Rolfe Schmidt, Triple Ratchet: A Bandwidth Efficient Hybrid-Secure Signal Protocol, IACR Eurocrypt, 2025.
- Karthikeyan Bhargavan, Bruno Blanchet and Nadim Kobeissi, Verified Models and Reference Implementations for the TLS 1.3 Standard Candidate, IEEE Symposium on Security and Privacy, 2017.
- David Balbás, Daniel Collins and Phillip Gajland, WhatsUpp with Sender Keys? Analysis, Improvements and Security Proofs, IACR Asiacrypt, 2023.
- Scott Fluhrer, Itsik Mantin and Adi Shamir, Weaknesses in the Key Scheduling Algorithm for RC4, Selected Areas in Cryptography, 2001.
- Alma Whitten and J. D. Tygar, Why Johnny Can't Encrypt: A Usability Evaluation of PGP 5.0, Security and Usability: Designing Secure Systems that People Can Use, O'Reilly, 2005.
- Scott Ruoti, Jeff Andersen, Daniel Zappala and Kent Seamons, Why Johnny Still, Still Can't Encrypt: Evaluating the Usability of a Modern PGP Client, arXiv, 2015.
- Manuel Barbosa, Deirdre Connolly, João Diogo Duarte, Aaron Kaiser, Peter Schwabe, Karolin Varner and Baas Westerban, X-Wing: The Hybrid KEM You’ve Been Looking For, IACR Communications in Cryptology, 2024.
- More to be added soon!

### Interactive Learning Tools

Interactive learning tools provide hands-on learning experiences that help reinforce cryptographic concepts through visualization, simulation, and practical application in ways that complement traditional reading materials.

- ASecuritySite.com: Tons of informal resources regarding many different encryption schemes and protocols.
- Visual One-Time Pad: An interactive tool for understanding the one-time pad encryption algorithm.
- Rijndael Cipher: animation explaining AES's internal structure.
- Verifpal: Cryptographic protocol analysis for students and engineers.
- ProofFrog: Tool for verifying cryptographic proofs written in the style of The Joy of Cryptography.
- Noise Explorer: an online engine for reasoning about Noise Protocol Framework Handshake Patterns.
- The New Illustrated TLS Connection: Every byte of a TLS connection explained and reproduced.
- Protocol Ladder: Computer-aided cryptographic proofs of simple protocols, formalized in different tools.
- hax Playground: Formally verify your Rust code by translating it into F* and other languages.
- More to be added soon!

## Syllabus and Course Schedule

A PDF copy of the Fall 2025 syllabus is available.

### Part 1: Provable Security

Part 1 explores the theoretical underpinnings of modern cryptography through the lens of provable security. Starting with introductory concepts and perfect secrecy in the one-time pad, we progressively build a rigorous framework for understanding and analyzing cryptographic primitives. We examine fundamental building blocks like pseudorandom generators, functions, and permutations, then advance to encryption schemes secure against increasingly powerful adversaries—from passive eavesdroppers to active attackers who can manipulate ciphertexts. The section also covers essential cryptographic tools including collision-resistant hash functions, digital signatures, and key exchange protocols. Throughout these topics, we emphasize formal security definitions, reduction proofs, and the connections between theoretical security guarantees and practical implementations. By the end of this section, students will have developed a comprehensive understanding of provable security techniques that form the foundation for analyzing and designing secure cryptographic systems.

Slides Topic 1.1

#### Introduction

This introduction establishes the foundation for the entire course by covering the scope, objectives, and structure of applied cryptography. We'll discuss key themes that will recur throughout the semester, including the balance between theory and practice, the importance of formal security definitions, and the evolution of cryptographic thinking. Students will gain a clear understanding of what to expect from the course and how the various topics connect to form a coherent framework for secure system design.

##### Required Readings

- The Joy of Cryptography, Chapter 0: Review of Concepts & Notation.

Slides Topic 1.2 Midterm

#### One-Time Pad & The Provable Security Mindset

This topic introduces the concept of perfect secrecy through the One-Time Pad (OTP) encryption system and explores its mathematical proof of unconditional security. While theoretically unbreakable, we'll examine the severe practical limitations that make OTP challenging to deploy in real-world systems, including key generation, distribution, and management problems. The topic then transitions to Kerckhoff's fundamental principle—that a cryptosystem should remain secure even if everything about the system, except the key, is public knowledge. We'll discuss how this principle has shaped modern cryptographic design philosophy and why security through obscurity fails as a long-term strategy for protecting sensitive information.

##### Required Readings

- The Joy of Cryptography, Chapter 0: Review of Concepts & Notation.
- The Joy of Cryptography, Chapter 1: One-Time Pad & The Provable Security Mindset.

Slides Topic 1.3 Midterm

#### Provable Security & Computational Cryptography

This topic begins by delving into the rigorous mathematical frameworks that allow cryptographers to provide formal security guarantees for cryptographic schemes. We'll examine how precise definitions of security properties create a foundation for meaningful analysis, and explore various adversarial models that capture different threat scenarios. The concept of reduction—proving that breaking a scheme is at least as hard as solving some well-studied mathematical problem—will be thoroughly explored. We then transition to modern computational cryptography, moving from unconditional security to a more practical approach where security is defined against computationally bounded adversaries. Students will learn about indistinguishability as a fundamental security concept, the bad-event technique for security proofs, and birthday probabilities in cryptographic attacks. The session provides essential mathematical foundations for understanding modern cryptographic security, including quantitative intuition about large numbers (like 2128) and tiny probabilities (like 2-80) that define practical security boundaries, preparing students for subsequent topics in pseudorandomness.

##### Required Readings

- The Joy of Cryptography, Chapter 2: Rudiments of Provable Security.
- The Joy of Cryptography, Chapter 4: Modern Computational Cryptography.

Slides Topic 1.4 Midterm

#### Pseudorandomness

This topic explores three fundamental pseudorandom primitives that enable practical cryptography. Pseudorandom generators (PRGs) solve one-time pad's key length limitation by expanding short seeds into longer outputs indistinguishable from random. Pseudorandom functions (PRFs) extend this by creating massive virtual dictionaries mapping inputs to pseudorandom outputs, allowing parties with a shared secret to derive unlimited pseudorandom data. Pseudorandom permutations (PRPs), also called block ciphers, provide both forward and inverse operations indistinguishable from random permutations. We'll examine key constructions including GGM (building PRFs from PRGs), the Feistel network (building invertible PRPs from non-invertible PRFs), and the PRF-PRP switching lemma that enables interchangeability in security proofs. Throughout, we'll emphasize crucial security principles like the PRF "Golden Rule" of preventing input repetition.

##### Required Readings

- The Joy of Cryptography, Chapter 5: Pseudorandom Generators.
- The Joy of Cryptography, Chapter 6: Pseudorandom Functions.
- The Joy of Cryptography, Chapter 7: Pseudorandom Permutations.

##### Optional Readings

- Michael Luby and Charles Rackoff, How To Construct Pseudorandom Permutations From Pseudorandom Functions, Society for Industrial and Applied Mathematics, 1988.

Slides Topic 1.5 Midterm

#### Chosen-Plaintext & Chosen-Ciphertext Attacks

This topic explores advanced security models for symmetric-key encryption, beginning with chosen-plaintext attack (CPA) security, where ciphertexts must be indistinguishable from random strings. We'll examine why deterministic encryption cannot achieve this security level and explore solutions including randomized PRF-based schemes and block cipher modes like CBC and CTR, while explaining why ECB mode remains fundamentally insecure. The topic then advances to chosen-ciphertext attacks (CCA), where adversaries can decrypt chosen ciphertexts, demonstrating how even CPA-secure schemes like CTR mode remain vulnerable due to their malleability. We'll analyze practical format-oracle attacks that exploit information leakage during decryption to recover entire plaintexts, and examine how preventing adversaries from creating valid modified ciphertexts is essential for achieving comprehensive CCA security in real-world systems.

##### Required Readings

- The Joy of Cryptography, Chapter 8: Chosen-Plaintext Attacks.
- The Joy of Cryptography, Chapter 9: Chosen-Ciphertext Attacks.

##### Optional Readings

- Bodo Möller, Thai Duong and Krzysztof Kotowicz, This POODLE Bites: Exploiting the SSL 3.0 Fallback, Google, 2014.
- Nadhem J. Alfardan and Kenneth G. Paterson, Lucky Thirteen: Breaking the TLS and DTLS Record Protocols, IEEE Symposium on Security and Privacy, 2013.
- Christina Garman, Matthew Green, Gabriel Kaptchuk, Ian Miers and Michael Rushanan, Dancing on the Lip of the Volcano: Chosen Ciphertext Attacks on Apple iMessage, USENIX Security Symposium, 2016.
- Ange Albertini, Thai Duong, Shay Gueron, Stefan Kölbl, Atul Luykx, and Sophie Schmieg, How to Abuse and Fix Authenticated Encryption Without Key Commitment, USENIX Security Symposium, 2022.

Slides Topic 1.6 Midterm

#### Collision-Resistant Hash Functions

This topic explores collision-resistant hash functions, cryptographic primitives that convert arbitrary-length inputs to fixed-length outputs while making it computationally infeasible to find colliding inputs. We'll examine three essential properties—collision resistance, preimage resistance, and second preimage resistance—while exploring practical applications in password storage, data integrity verification, and proof-of-work systems. The topic introduces the counterintuitive birthday paradox, demonstrating why collisions can be found after approximately square-root-many attempts rather than brute force. We'll survey hash function evolution from broken algorithms like MD5 and SHA-1 to modern standards like SHA-2, SHA-3, and BLAKE3, while analyzing vulnerabilities including precomputation attacks using rainbow tables and length extension weaknesses in Merkle-Damgård constructions. The topic covers critical defensive techniques including properly salting hashes and implementing specialized password hashing algorithms like PBKDF2 and memory-hard functions such as Scrypt, which resist hardware acceleration attacks by requiring significant memory resources, providing comprehensive guidance for secure hash function implementation in real-world systems.

##### Required Readings

- The Joy of Cryptography, Chapter 10: Collision-Resistant Hash Functions.
- The Joy of Cryptography, Chapter 12: Random Oracles and Other Idealized Models.

##### Optional Readings

- Marc Stevens, Elie Bursztein, Pierre Karpman, Ange Albertini and Yarik Markov, The First Collision for Full SHA-1, IACR Crypto, 2017.
- Joël Alwen, Binyi Chen, Krzysztof Pietrzak, Leonid Reyzin and Stefano Tessaro, Scrypt Is Maximally Memory-Hard, IACR Eurocrypt, 2017.
- Ran Canetti, Oded Goldreich and Shai Halevi, The Random Oracle Model Methodology, Revisited, Journal of the ACM, 2004.

Slides Topic 1.7 Midterm

#### Hard Problems & Diffie-Hellman

This topic explores computational hardness problems that form the cornerstone of modern public-key cryptography, with particular focus on the discrete logarithm problem that underpins Diffie-Hellman key exchange. We'll examine how complexity theory provides a framework for classifying problems based on their computational difficulty, covering fundamental complexity classes including P, NP, and the famous unsolved P vs. NP problem. The topic then investigates the discrete logarithm problem in detail, analyzing its computational complexity and known algorithms, before exploring how this hard problem enables the revolutionary Diffie-Hellman protocol that allows two parties to establish a shared secret over an insecure channel. We'll examine the mathematical foundations of DH using modular exponentiation in prime fields, the computational hardness assumptions (CDH and DDH) that underpin its security, and protocol variants including anonymous and authenticated DH. The topic concludes by analyzing practical implementation considerations, security pitfalls, and how theoretical hardness assumptions translate into real-world cryptographic security.

##### Required Readings

- Jean-Philippe Aumasson, Serious Cryptography, 2nd Edition. Chapter 9: Hard Problems, No Starch Press, 2024.
- Jean-Philippe Aumasson, Serious Cryptography, 2nd Edition. Chapter 11: Diffie-Hellman, No Starch Press, 2024.

##### Optional Readings

- Whitfield Diffie and Martin E. Hellman, New Directions in Cryptography, IEEE Transactions on Information Theory, 1976.
- Greg Aloupis, Erik D. Demaine, Alan Guo and Giovanni Viglietta, Classic Nintendo Games are (Computationally) Hard, ACM Theoretical Computer Science, 2015.

Slides Topic 1.8 Midterm

#### Elliptic Curves & Digital Signatures

This topic explores elliptic curve cryptography (ECC), an approach that provides stronger security with smaller keys than traditional cryptosystems like RSA. We'll examine the mathematical foundations of elliptic curves and their group structure supporting point addition and scalar multiplication operations. The topic covers the elliptic curve discrete logarithm problem (ECDLP) that underpins ECC's security, and how it enables efficient implementations of key exchange (ECDH) and digital signatures (ECDSA and EdDSA/Ed25519). We'll analyze the advantages of ECC, including faster signing operations and significantly shorter keys and signatures compared to RSA, while examining critical implementation considerations that affect security. The topic concludes with guidance on selecting appropriate curves, comparing standardized options like NIST curves and Curve25519, and exploring potential vulnerabilities including invalid curve attacks, randomness failures, and interoperability challenges in modern ECC deployments.

##### Required Readings

- Jean-Philippe Aumasson, Serious Cryptography, 2nd Edition. Chapter 12: Elliptic Curves, No Starch Press, 2024.

##### Optional Readings

- Daniel J. Bernstein and Tanja Lange, SafeCurves: choosing safe curves for elliptic-curve cryptography, SafeCurves, 2017.
- Tibor Jager, Jörg Schwenk and Juraj Somorovsky, Practical Invalid Curve Attacks on TLS-ECDH, ESORICS, 2015.
- Henry de Valence, It's 255:19AM. Do you know what your validation criteria are?, hdevalence.ca, 2020.
- Joppe W. Bos, J. Alex Halderman, Nadia Heninger, Jonathan Moore, Michael Naehrig and Eric Wustrow, Elliptic Curve Cryptography in Practice, Financial Cryptography and Data Security, 2014.

### Part 2: Real-World Cryptography

Part 2 shifts from theoretical foundations to practical applications, examining how cryptographic principles are implemented in real-world systems. We begin with secure messaging protocols that provide forward secrecy and post-compromise security through ratcheting mechanisms, then explore authenticated key exchange protocols that secure communications against active adversaries. The section covers advanced concepts like zero-knowledge proofs that enable proving knowledge without revealing secrets, and post-quantum cryptography designed to resist attacks from quantum computers. We examine critical infrastructure protocols like TLS that secure internet communications, cloud security applications of cryptography, and analyze significant cryptographic failures to extract valuable design lessons. The course then investigates formal verification and high-assurance implementations that provide mathematical guarantees of security, specialized cryptography in cryptocurrencies, secure multiparty computation enabling joint computation without revealing inputs, and privacy-preserving technologies that protect sensitive information while enabling useful computation. By connecting theoretical foundations to practical systems, students will develop the knowledge needed to evaluate, implement, and design secure cryptographic solutions for complex real-world environments.

Slides Topic 2.1 Final

#### Transport Layer Security

This topic examines the Transport Layer Security (TLS) protocol, the backbone of secure communication on the internet that secures billions of connections daily. We'll explore the evolution from SSL to modern TLS 1.3, analyzing the protocol architecture, handshake process, and the cryptographic primitives deployed at each stage. The session covers key exchange mechanisms, authentication methods, and the cipher suites that provide confidentiality and integrity protections. Students will learn about certificate validation, trust models, and the public key infrastructure (PKI) that underpins TLS security. We'll also investigate significant vulnerabilities that have affected TLS implementations throughout its history, including FREAK, Logjam, Heartbleed, and POODLE, analyzing how these vulnerabilities arose and the mitigations developed in response. The topic concludes with practical deployment considerations, performance optimizations like session resumption and 0-RTT, and the security trade-offs encountered when configuring TLS in production environments.

##### Required Readings

- Jean-Philippe Aumasson, Serious Cryptography, 2nd Edition. Chapter 13: TLS, No Starch Press, 2024.

##### Optional Readings

- Matthew McPherrin, Reflections on a Year of Sunlight, Let's Encrypt Blog, 2025.
- Bodo Möller, Thai Duong and Krzysztof Kotowicz, This POODLE Bites: Exploiting the SSL 3.0 Fallback, Google, 2014.
- Nadhem J. Alfardan and Kenneth G. Paterson, Lucky Thirteen: Breaking the TLS and DTLS Record Protocols, IEEE Symposium on Security and Privacy, 2013.
- Philip Rogaway, The Moral Character of Cryptographic Work, IACR Cryptology ePrint Archive, 2016.
- David Adrian, Karthikeyan Bhargavan, Zakir Durumeric, Pierrick Gaudry, Matthew Green, J. Alex Halderman, Nadia Heninger, Drew Springall, Emmanuel Thomé, Luke Valenta, Benjamin VanderSloot, Eric Wustrow, Santiago Zanella-Béguelin and Paul Zimmermann, Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice, ACM CCS, 2015.
- Karthikeyan Bhargavan, Antoine Delignat-Lavaud, Cédric Fournet, Alfredo Pironti and Pierre-Yves Strub, Triple Handshakes and Cookie Cutters: Breaking and Fixing Authentication over TLS, IEEE Symposium on Security and Privacy, 2014.
- Benjamin Beurdouche, Karthikeyan Bhargavan, Antoine Delignat-Lavaud, Cédric Fournet, Markulf Kohlweiss, Alfredo Pironti, Pierre-Yves Strub and Jean-Karim Zinzindohoué, A Messy State of the Union: Taming the Composite State Machines of TLS, IEEE Symposium on Security and Privacy, 2015.
- Karthikeyan Bhargavan and Gaëtan Leurent, On the Practical (In-)Security of 64-bit Block Ciphers, ACM CCS, 2016.
- Karthikeyan Bhargavan and Gaëtan Leurent, Transcript Collision Attacks: Breaking Authentication in TLS, IKE and SSH, Network and Distributed Systems Security Symposium, 2016.
- Zakir Durumeric, James Kasten, David Adrian, J. Alex Halderman, Michael Bailey, Frank Li, Nicholas Weaver, Johanna Amann, Jethro Beekman, Mathias Payer and Vern Paxson, The Matter of Heartbleed, ACM IMC, 2014.

Slides Topic 2.2 Final

#### The Story of RC4

This topic presents a biographical narrative of RC4 (Rivest Cipher 4), tracing its remarkable journey from promising youth to eventual downfall in cryptographic history. We'll examine RC4's birth as a proprietary stream cipher at RSA Security in 1987, its meteoric rise to become the most widely deployed stream cipher in the world, and its golden era powering protocols like WEP, SSL, and TLS due to its simplicity and performance advantages. The topic then chronicles RC4's gradual decline as researchers uncovered a series of increasingly devastating weaknesses, starting with the 2001 Fluhrer-Mantin-Shamir attack on WEP, through the 2013 discovery of extensive biases in RC4-generated keystreams that enabled practical attacks against TLS, culminating in the 2015 "Bar Mitzvah" and RC4 NOMORE attacks that could recover passwords and other sensitive information from encrypted connections. We'll analyze how the security community responded to these revelations, including browser vendors' gradual restriction of RC4 ciphersuites and the IETF's eventual formal prohibition of RC4 in TLS in 2015, while drawing broader lessons about cryptographic lifecycle management, the importance of formal security analysis, and how the story of RC4 exemplifies both the evolution of cryptanalytic techniques and the challenges of maintaining backward compatibility in security protocols.

##### Required Readings

- None.

##### Optional Readings

- Scott Fluhrer, Itsik Mantin and Adi Shamir, Weaknesses in the Key Scheduling Algorithm for RC4, Selected Areas in Cryptography, 2001.
- Itsik Mantin, Predicting and Distinguishing Attacks on RC4 Keystream Generator, IACR Eurocrypt, 2005.
- Platon Kotzias, Abbas Razaghpanah, Johanna Amann, Kenneth G. Paterson, Narseo Vallina-Rodriguez and Juan Caballero, Coming of Age: A Longitudinal Study of TLS Deployment, ACM IMC, 2018.
- Nadhem AlFardan, Daniel J. Bernstein, Kenneth G. Paterson, Bertram Poettering and Jacob C. N. Schuldt, On the Security of RC4 in TLS, USENIX Security Symposium, 2013.
- Christina Garman, Kenneth G. Paterson and Thyla Van der Merwe, Attacks Only Get Better: Password Recovery Attacks Against RC4 in TLS, USENIX Security Symposium, 2015.
- Bodo Möller, Thai Duong and Krzysztof Kotowicz, This POODLE Bites: Exploiting the SSL 3.0 Fallback, Google, 2014.
- Nick Sullivan, Killing RC4: The Long Goodbye, Cloudflare Blog, 2014.
- Mathy Vanhoef and Frank Piessens, All Your Biases Belong To Us: Breaking RC4 in WPA-TKIP and TLS, USENIX Security Symposium, 2015.

Slides Topic 2.3 Final

#### Secure Messaging

This topic traces the evolution of secure messaging from early failures to modern protocols, examining how cryptographic innovation has shaped private communication. We begin with PGP's usability challenges and fundamental limitations, understanding why "Johnny Can't Encrypt" despite decades of effort. The topic then explores Off-the-Record (OTR) messaging's revolutionary features—forward secrecy through ephemeral keys, deniable authentication via MACs instead of signatures, and automatic key exchange—demonstrating how synchronous protocols solved many of PGP's problems. We dive deep into authenticated key exchange protocols like SIGMA, examining how they prevent man-in-the-middle attacks while maintaining identity protection. The discussion covers proper key derivation functions (HKDF) for deriving multiple keys from shared secrets, addressing the shortcomings of ad-hoc approaches. We then transition to Signal's asynchronous messaging architecture, analyzing X3DH key exchange and the Double Ratchet's elegant combination of symmetric and Diffie-Hellman ratcheting. The topic critically examines post-compromise security's promises versus reality, revealing through formal analysis why perfect healing is impossible in practical systems that must handle state loss. We also contrast Signal's approach with alternatives like Telegram's controversial design choices. Throughout, we'll analyze the fundamental trade-offs between security guarantees, usability, and real-world deployment constraints that shape how billions of messages are protected daily. We'll also examine modern extensions including secure group messaging protocols like MLS (Messaging Layer Security) that scale encrypted conversations to thousands of participants.

##### Required Readings

- The Joy of Cryptography, Chapter 17: Encrypted Messaging & Ratcheting.

##### Optional Readings

- Alma Whitten and J. D. Tygar, Why Johnny Can't Encrypt: A Usability Evaluation of PGP 5.0, Security and Usability: Designing Secure Systems that People Can Use, O'Reilly, 2005.
- Scott Ruoti, Jeff Andersen, Daniel Zappala and Kent Seamons, Why Johnny Still, Still Can't Encrypt: Evaluating the Usability of a Modern PGP Client, arXiv, 2015.
- Ksenia Ermoshina, Harry Halpin and Francesca Musiani, Can Johnny Build a Protocol? Co-ordinating Developer and User Intentions for Privacy-Enhanced Secure Messaging Protocols, European Workshop on Systems Security, 2017.
- Nikita Borisov, Ian Goldberg and Eric Brewer, Off-the-Record Communication, or, Why Not To Use PGP, Workshop on Privacy in the Electronic Society, 2004.
- Hugo Krawczyk, SIGMA: the 'SIGn-and-MAc' Approach to Authenticated Diffie-Hellman and its Use in the IKE Protocols, IACR Crypto, 2003.
- Hugo Krawczyk, Cryptographic Extraction and Key Derivation: The HKDF Scheme, IACR Crypto, 2010.
- Matilda Backendal, Sebastian Clermont, Marc Fischlin and Felix Günther, Key Derivation Functions Without a Grain of Salt, IACR Eurocrypt, 2025.
- Joseph Bonneau and Andrew Morrison, Finite-State Security Analysis of OTR Version 2, Stanford Computer Security Laboratory, 2006.
- Chris Alexander and Ian Goldberg, Improved User Authentication in Off-The-Record Messaging, Workshop on Privacy in the Electronic Society, 2007.
- Nadim Kobeissi, Karthikeyan Bhargavan and Bruno Blanchet, Automated Verification for Secure Messaging Protocols and their Implementations: A Symbolic and Computational Approach, IEEE European Symposium on Security and Privacy, 2017.
- Cas Cremers, Charlie Jacomme and Aurora Naska, Formal Analysis of Session-Handling in Secure Messaging: Lifting Security from Sessions to Conversations, USENIX Security Symposium, 2023.
- Cas Cremers, Niklas Medinger and Aurora Naska, Impossibility Results for Post-Compromise Security in Real-World Communication Systems, IEEE Symposium on Security and Privacy, 2025.
- Ian Martiny, Gabriel Kaptchuk, Adam Aviv, Dan Roche and Eric Wustrow, Improving Signal's Sealed Sender, Network and Distributed Systems Security Symposium, 2021.
- Martin R. Albrecht, Lenka Mareková, Kenneth G. Paterson, Eyal Ronen and Igors Stepanovs, Analysis of the Telegram Key Exchange, IACR Eurocrypt, 2025.
- Martin R. Albrecht, Benjamin Dowling and Daniel Jones, Formal Analysis of Multi-Device Group Messaging in WhatsApp, IACR Eurocrypt, 2025.
- Paul Rösler, Christian Mainka and Jörg Schwenk, More is Less: On the End-to-End Security of Group Chats in Signal, WhatsApp, and Threema, IEEE European Symposium on Security and Privacy, 2018.
- David Balbás, Daniel Collins and Phillip Gajland, WhatsUpp with Sender Keys? Analysis, Improvements and Security Proofs, IACR Asiacrypt, 2023.
- Richard Barnes, Karthikeyan Bhargavan, Benjamin Lipp and Christopher Wood, RFC 9810: Hybrid Public Key Encryption, RFC Editor, 2022.
- Théophile Wallez, A Verification Framework for Secure Group Messaging, PSL Université Paris, 2025.

Slides Topic 2.4

#### Applied Cryptography in Cloud Security

This topic explores how cryptographic principles and techniques are applied to secure cloud computing environments, focusing on the unique challenges of protecting data and applications in distributed, multi-tenant infrastructures. We'll examine key management strategies for distributed systems, including hierarchical key management, key rotation policies, and hardware security modules (HSMs) in cloud deployments. The topic covers confidential computing technologies that use hardware-based trusted execution environments and memory encryption to protect data in use. Students will learn about tokenization systems that replace sensitive data with non-sensitive equivalents, and encryption schemes optimized for cloud storage including convergent encryption and client-side encryption models. We'll investigate secret management at scale, analyzing secure vaults, dynamic credential generation, and secure secret distribution in containerized environments. The topic also explores cryptographic access control mechanisms like attribute-based encryption and practical implementations of end-to-end encryption in cloud services, examining how these technologies can maintain confidentiality even when the cloud provider itself isn't fully trusted.

##### Required Readings

- Mark Russinovich, Manuel Costa, Cédric Fournet, David Chisnall, Antoine Delignat-Lavaud, Sylvan Clebsch, Kapil Vaswani and Vikas Bhatia, Toward Confidential Cloud Computing, Communications of the ACM, 2021.
- More to be added soon!

Slides Topic 2.5 Final

#### High-Assurance Cryptography

This topic examines methodologies for developing cryptographic implementations with high assurance of correctness and security, moving beyond traditional testing approaches to formal verification and rigorous proof techniques. We'll explore the spectrum of formal methods applied to cryptography, from lightweight verification using refinement types to comprehensive mathematical proofs of functional correctness and security properties. The topic covers verification frameworks and tools including F*, Coq, Lean, and ProVerif, examining how they can be applied to verify cryptographic implementations against their specifications and security definitions. Students will learn about verified cryptographic libraries like HACL*, EverCrypt, and initiatives from organizations like Cryspen that bring formal verification to practical cryptography. We'll also discuss the challenges in formally verifying cryptographic code, including the gap between mathematical specifications and efficient implementations, side-channel resistance verification, and performance considerations. The topic concludes with case studies of successful verification projects that have produced high-assurance cryptographic implementations deployed in critical systems.

##### Required Readings

- Manuel Barbosa, Gilles Barthe, Karthikeyan Bhargavan, Bruno Blanchet, Cas Cremers, Kevin Liao and Bryan Parno, SoK: Computer-Aided Cryptography, IEEE Symposium on Security and Privacy, 2021.
- More to be added soon!

##### Optional Readings

- Project Everest Team, Project Everest: Perspectives from Developing Industrial-Grade High-Assurance Software, Microsoft Research, 2025.
- Martin R. Albrecht and Kenneth G. Paterson, Analysing Cryptography in the Wild: A Retrospective, IEEE Security & Privacy, 2024.
- Théophile Wallez, A Verification Framework for Secure Group Messaging, PSL Université Paris, 2025.
- Franziskus Kiefer and Jonas Schneider-Bensch, Cryptographic Protocol Verification with hax, Cryspen, 2024.
- Lucas Franceschino, Announcing the hax Playground, Cryspen, 2024.
- Daniel J. Bernstein, Karthikeyan Bhargavan, Shivam Bhasin, Anupam Chattopadhyay, Tee Kiah Chia, Matthias J. Kannwischer, Franziskus Kiefer, Thales B. Paiva, Prasanna Ravi and Goutam Tamvada, KyberSlash: Exploiting Secret-Dependent Division Timings in Kyber Implementations, IACR Transactions on Cryptographic Hardware and Embedded Systems, 2025.

Slides Topic 2.6

#### Cryptocurrency Cryptography

This topic explores the cryptographic foundations of blockchain systems and cryptocurrencies, examining how traditional cryptographic primitives are combined in novel ways to create decentralized trust systems. We'll investigate the core components of blockchain protocols, including hash functions in proof-of-work mechanisms, digital signatures for transaction authentication, and Merkle trees for efficient verification. The topic covers the cryptographic aspects of Bitcoin, Ethereum, and other significant blockchain platforms, analyzing their security models, consensus mechanisms, and vulnerability mitigations. Students will learn about specialized cryptographic constructions in cryptocurrencies, including zero-knowledge proofs for privacy coins, threshold signatures for multi-signature wallets, and timelock puzzles for conditional transactions. We'll also discuss emerging cryptographic challenges in blockchain systems, including quantum resistance considerations, layer-2 scaling solutions with unique security properties, and the cryptographic foundations of newer consensus mechanisms like proof-of-stake that aim to address energy consumption concerns while maintaining security guarantees.

##### Required Readings

- Jean-Philippe Aumasson, Serious Cryptography, 2nd Edition. Chapter 15: Cryptocurrency Cryptography, No Starch Press, 2024.

Slides Topic 2.7 Final

#### Post-Quantum Cryptography

This topic explores post-quantum cryptography, which addresses the threat quantum computers pose to current cryptographic systems. We'll examine how quantum algorithms like Shor's can break widely-used public-key cryptography based on factoring and discrete logarithms, while Grover's algorithm reduces symmetric-key security by effectively halving key lengths. The topic introduces the Learning With Errors (LWE) problem as a foundation for post-quantum cryptography, explaining how its computational hardness against quantum attacks makes it suitable for building secure cryptographic primitives. We'll analyze practical LWE-based key exchange protocols that form the basis for NIST's standardized post-quantum schemes like ML-KEM. Students will understand both the theoretical foundation of quantum-resistant cryptography and the practical considerations for implementing these systems in real-world applications, preparing them for the transition to a post-quantum cryptographic landscape.

##### Required Readings

- The Joy of Cryptography, Chapter 20: Post-Quantum Cryptography.

##### Optional Readings

- Manuel Barbosa, Deirdre Connolly, João Diogo Duarte, Aaron Kaiser, Peter Schwabe, Karolin Varner and Baas Westerban, X-Wing: The Hybrid KEM You’ve Been Looking For, IACR Communications in Cryptology, 2024.
- Apple Security Engineering and Architecture (SEAR), iMessage with PQ3: The new state of the art in quantum-secure messaging at scale, Apple Security Research, 2024.
- Felix Linker, Ralf Sasse and David Basin, A Formal Analysis of Apple’s iMessage PQ3 Protocol, USENIX Security Symposium, 2025.
- Karthikeyan Bhargavan, Charlie Jacomme, Franziskus Kiefer and Rolfe Schmidt, Formal Verification of the PQXDH Post-Quantum Key Agreement Protocol for End-to-End Secure Messaging, USENIX Security Symposium, 2024.
- Yevgeniy Dodis, Daniel Jost, Shuichi Katsumata, Thomas Prest and Rolfe Schmidt, Triple Ratchet: A Bandwidth Efficient Hybrid-Secure Signal Protocol, IACR Eurocrypt, 2025.

Slides Topic 2.8 Final

#### Zero-Knowledge Proofs

This topic explores zero-knowledge proofs, which enable proving possession of secret information without revealing anything about the secret itself. We'll examine how these interactive protocols can authenticate a party's identity while maintaining deniability—allowing someone to prove they know a private key without creating evidence that could later convince others. The topic begins with the Schnorr identification protocol, which demonstrates this paradoxical capability through a clever three-move interaction. We'll then generalize to sigma protocols, a powerful class of interactive proofs with completeness, special soundness, and honest-verifier zero-knowledge properties. The topic covers several practical examples, including proofs of discrete log equality and complex logical conditions using AND/OR compositions. Finally, we'll explore how interactive proofs can be transformed into non-interactive proofs and digital signatures through the Fiat-Shamir transformation, which replaces the verifier with a cryptographic hash function. This transformation creates powerful primitives like Schnorr signatures but necessarily sacrifices the deniability property that makes interactive zero-knowledge proofs unique.

##### Required Readings

- The Joy of Cryptography, Chapter 19: Zero-Knowledge Proofs.

##### Optional Readings

- Tarek Galal, The Curves of ZoKrates, tgalal.com, 2025.
- Chris Alexander and Ian Goldberg, Improved User Authentication in Off-The-Record Messaging, Workshop on Privacy in the Electronic Society, 2007.

Slides Topic 2.9

#### Secure Multiparty Computation

This topic explores Secure Multiparty Computation (MPC), a powerful cryptographic paradigm that enables multiple parties to jointly compute functions over their private inputs without revealing those inputs to each other. We'll examine the theoretical foundations of MPC, including feasibility results, security models, and the distinctions between semi-honest and malicious adversaries. The topic covers core MPC techniques including Yao's garbled circuits, secret sharing schemes like Shamir's threshold method, and oblivious transfer protocols that enable secure two-party computation. Students will learn about practical MPC frameworks and implementations such as SCALE-MAMBA, MP-SPDZ, and EMP-toolkit, analyzing their performance characteristics and security guarantees. We'll investigate applications of MPC across various domains, including private data analysis, secure auctions, privacy-preserving machine learning, and confidential financial systems. The topic also addresses performance optimizations like preprocessing, circuit minimization, and communication-efficient protocols that make MPC increasingly practical for real-world use. We'll conclude with case studies of deployed MPC systems, examining how these technologies overcome real-world implementation challenges to enable secure collaboration while maintaining strict privacy guarantees.

##### Required Readings

- David Evans, Vladimir Kolesnikov and Mike Rosulek, A Pragmatic Introduction to Secure Multi-Party Computation (Chapter 1), NOW Publishers, 2020.

Slides Topic 2.10

#### Creative Cryptography

This topic explores timelock encryption, a fascinating cryptographic innovation that enables messages to be encrypted such that they can only be decrypted after a predetermined time has elapsed. We'll examine both the theoretical foundations and practical implementation of timelock encryption using the League of Entropy, an existing threshold network that implements threshold BLS signatures within Boneh and Franklin's identity-based encryption (IBE) framework. The topic demonstrates how this network, which broadcasts BLS signatures for each time interval (round number), effectively functions as a decentralized key custodian that periodically publishes private keys for an IBE system where identities correspond to specific time periods. We'll analyze the elegant design that requires cryptographic operations only from encryptors and decryptors while allowing the threshold network to remain unmodified and unaware of the timelock functionality. Students will gain hands-on experience with an open-source implementation of this scheme and explore a production-ready web interface utilizing the League of Entropy's distributed randomness beacon service. This creative application of cryptography showcases how existing cryptographic primitives can be combined in innovative ways to enable entirely new functionalities, inspiring students to think beyond conventional applications as they develop their own cryptographic solutions.

##### Required Readings

- Nicolas Gailly, Kelsey Melissaris and Yolan Romailler, tlock: Practical Timelock Encryption from Threshold BLS, IACR Cryptology ePrint Archive, 2023.

## Assignments & Lab Sessions

Check the Syllabus for detailed information on class grading criteria, as well as how lab sessions, problem sets and exams will be designed and presented.

### Problem Sets

Problem sets will be assigned periodically throughout the semester to reinforce and deepen your understanding of the lecture material. Each set will include a range of exercises—some focused on theoretical proofs and problem-solving, others requiring short coding tasks or computational experiments. These assignments are designed to bridge the gap between abstract cryptographic concepts and their concrete applications. You are encouraged to start working on each problem set early and to seek guidance during office hours or lab sessions if you encounter difficulties.

#### Problem Set 1: Provable Security Foundations

This problem set focuses on the fundamental concepts of provable security covered in the first three topics of the course. It consists of four main sections: Cryptographic Foundations, which tests your understanding of basic security goals and perfect secrecy; Provable Security, which explores library interchangeability and formal security proofs; Computational Cryptography, which examines computational security concepts, distinguishability, and the bad events technique; and Application of Cryptographic Principles, which challenges you to analyze block cipher modes, evaluate real-world implementations, and design secure protocols. The assignments blend theoretical analysis with practical applications, requiring you to demonstrate both mathematical reasoning and applied cryptographic thinking. A bonus challenge on the discrete logarithm problem offers extra credit for those wanting to explore advanced concepts.

#### Problem Set 2: Symmetric Cryptography

This problem set explores symmetric cryptography fundamentals covered in topics 1.4, 1.5 and 1.6, addressing four key areas: pseudorandomness, encryption security models, hash functions, and practical applications. In pseudorandomness, you'll analyze PRG constructions, PRF security requirements including the "Golden Rule," and Feistel cipher properties. The encryption security section examines why deterministic encryption fails CPA security, format oracle attacks against CPA-secure schemes, and authenticated encryption constructions including AES-GCM. The hash function component investigates collision resistance properties, construction methods like Merkle-Damgård versus Sponge, and specialized password hashing algorithms including memory-hard functions. Real-world case studies challenge you to apply these concepts to file storage systems, software update verification, and password management implementations.

#### Problem Set 3: Asymmetric Cryptography

This problem set covers concepts from topics 1.7 and 1.8 of the course, spanning three comprehensive areas: cryptographic hardness foundations, Diffie-Hellman security analysis, and elliptic curve implementation challenges. In cryptographic hardness, you'll analyze real-world implications of mathematical breakthroughs like P=NP and evaluate discrete logarithm security architectures including parameter selection and vulnerability assessment. The Diffie-Hellman section explores attack scenarios in hostile network environments, man-in-the-middle defenses, and protocol design challenges including SSH trust models. Elliptic curve security engineering examines curve selection controversies, invalid curve attacks, mobile performance optimization, and implementation vulnerabilities including side-channel attacks and nonce reuse scenarios. Finally, applied case studies challenge you to design complete key exchange protocols for secure messaging, analyze cryptocurrency signature scheme decisions, and architect enterprise-scale secure communication systems. Throughout, the assignments emphasize both mathematical security analysis and practical deployment considerations, requiring you to bridge theoretical cryptographic principles with real-world system design challenges.

#### Problem Set 4: Secure Channel Protocols

This problem set explores real-world cryptographic protocols covered in topics 2.1, 2.2, and 2.3, focusing on three critical areas: Transport Layer Security, the RC4 cryptanalysis story, and secure messaging protocols. In the TLS section, you'll analyze attack scenarios including legacy downgrade vulnerabilities and certificate authority compromises, while examining TLS 1.3's design decisions around forward secrecy, cryptographic agility, and enterprise monitoring challenges. The RC4 component investigates stream cipher vulnerabilities through WEP forensics and modern protocol analysis, emphasizing cryptographic lifecycle management and deprecation strategies. The secure messaging section compares PGP and Signal's design philosophies, analyzes authenticated key exchange protocols for security properties, and identifies subtle flaws in broken ratcheting protocols. Throughout, the assignments require you to balance theoretical security analysis with practical deployment considerations, examining real-world trade-offs in protocol design, migration strategies, and threat model assumptions. A bonus challenge offers deeper exploration into formal verification's impact on TLS 1.3, RC4's complete cryptanalytic timeline, or the convergence of modern messaging protocols.

### Lab Sessions

Lab sessions will be held weekly to serve as a hands-on complement to the lectures. During each lab, you will experiment with real-world libraries, and even simulate attacks or vulnerabilities to understand why certain security practices are necessary. These sessions will also help you become comfortable with relevant tools and environments, including formal analysis tools. Attendance is mandatory, and lab participation will be graded based on preparedness, engagement, and the successful completion of in-lab activities. Labs offer an excellent opportunity for collaborative problem-solving and immediate feedback on your work.

#### Lab 1: Designing a Password Manager

In this lab, you will design and implement a secure password manager application. You'll learn about secure password storage techniques, key derivation functions, and encryption methods for sensitive data. The lab will guide you through implementing features such as master password protection, secure password generation, and encrypted storage. You'll also analyze potential vulnerabilities in your system and implement countermeasures to protect against common attacks like password cracking and memory scraping.

#### Lab 2: Designing a Secure Messenger

This lab focuses on building a secure messaging application implementing end-to-end encryption. You'll work with cryptographic libraries to implement key exchange protocols, message encryption, and authentication mechanisms. The lab covers essential features like perfect forward secrecy, deniability, and secure group messaging. You'll also explore practical challenges such as key verification, metadata protection, and secure key storage on devices. By the end of this lab, you'll understand the cryptographic foundations behind modern secure messaging platforms like Signal.

#### Lab 3: Protocol Modeling and Verification with Verifpal and Tamarin

This lab introduces formal verification of security protocols using two complementary tools: Verifpal and Tamarin. You'll begin with Verifpal, a user-friendly tool designed for students, to model and analyze custom authentication and key exchange protocols. After gaining proficiency in identifying protocol vulnerabilities, you'll advance to Tamarin Prover to perform more sophisticated analyses with temporal properties and unbounded verification. Throughout the lab, you'll apply these tools to real-world protocols like TLS 1.3 fragments and Signal's X3DH, gaining practical experience in formal security verification. By the end of this lab, you'll understand how formal methods can mathematically prove security properties and detect subtle flaws that might otherwise remain hidden in manual security reviews.

#### Lab 4: Designing a Battleship Game Using Zero-Knowledge Systems

In this creative lab, you'll implement the classic Battleship game with a cryptographic twist using zero-knowledge proofs. You'll learn how two mutually distrustful parties can play a fair game without revealing their ship placements except when a hit occurs. The lab will guide you through designing commitment schemes, validity proofs for ship placement, and secure mechanisms for torpedo shots and hit verification—all without requiring a trusted third party. This practical application of zero-knowledge techniques demonstrates how cryptography can enable secure computation between untrusting parties in a tangible, engaging context.

#### Propose your own lab session!

Take the opportunity to propose and develop your own cryptographic project based on your interests and the concepts covered in the course! You might implement a novel protocol, create a secure application, perform a cryptanalysis of an existing system, or conduct formal verification of a protocol. Your proposal should include your project goals, the cryptographic primitives or techniques you'll explore, implementation details, and how you'll evaluate its security properties. This self-directed project allows you to delve deeper into an area of applied cryptography that particularly interests you while demonstrating your understanding of the course material in a creative and practical context.