Advanced cryptography
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.
Ressources en bibliothèque
- Algorithmic cryptanalysis / Joux
- Communication security / Vaudenay
- A computational introduction to number theory and algebra / Shoup
Websites
Moodle Link
Videos
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Advanced cryptography
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional