Advanced cryptography

COM-501 / 6 crédits

Langue: Anglais

Remark: This course is a "depth" for Cyber Security master program and Cyber Security minor.

Summary

This course reviews some failure cases in public-key cryptography. It introduces some cryptanalysis techniques. It also presents fundamentals in cryptography such as interactive proofs. Finally, it presents some techniques to validate the security of cryptographic primitives.

Content

The cryptograhic zoo: definitions, cryptographic primitives, math, algorithms, complexity
Cryptographic security models: security notions for encryption and authentication, game reduction techniques, RSA and Diffie-Hellman security notions
Public-key cryptanalysis: side channels, low RSA exponents, discrete logarithm, ElGamal signature
Interactive proofs: NP-completeness, interactive systems, zero-knowledge
Symmetric-key cryptanalysis: differential and linear cryptanalysis, hypothesis testing, decorrelation
Proof techniques: random oracles, leftover-hash lemma, Fujisaki-Okamoto transform

Keywords

cryptography, cryptanalysis, interactive proof, security proof

Learning Prerequisites

Required courses

Cryptography and security (COM-401)

Important concepts to start the course

Cryptography
Mathematical reasoning
Number theory and probability theory
Algorithmics
Complexity

Learning Outcomes

By the end of the course, the student must be able to:

Assess / Evaluate the security deployed by cryptographic schemes
Prove or disprove security
Justify the elements of cryptographic schemes
Analyze cryptographic schemes
Implement attack methods
Model security notions

Teaching methods

ex-cathedra

Expected student activities

active participation during the course
take notes during the course
do the exercises during the exercise sessions
complete the regular tests and homework
read the material from the course
self-train using the provided material
do the midterm exam and final exam

Assessment methods

Mandatory continuous evaluation:

homework (30%)
regular graded tests (30%)
midterm exam (40%)

Final exam averaged (same weight) with the contiuous evaluation, but with final grade between final_exam-1 and final_exam+1.

Supervision

Office hours	No
Assistants	Yes
Forum	Yes
Others	Lecturers and assistants are available upon appointment.

Resources

Bibliography

Communication security: an introduction to cryptography. Serge Vaudenay. Springer 2004.
A computational introduction to number theory and algebra. Victor Shoup. Cambridge University Press 2005.
Algorithmic cryptanalysis. Antoine Joux. CRC 2009.