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Code-Based Cryptography - session 1
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Infos du cours
Table of Contents
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Table of Contents
Introduction
Course Presentation
Guide: Learning Platform
Guide: Discussion Forums
Week 1: Error-Correcting Codes and Cryptography
1.1. Introduction I - Cryptography
1.2. Introduction II - Coding Theory
1.3. Encoding (Linear Transformation)
1.4. Parity Checking
1.5. Error Correcting Capacity
1.6. Decoding (A Difficult Problem)
1.7. Reed-Solomon Codes
1.8. Goppa Codes
1.9. McEliece Cryptosystem
Exercises Week 1
Course Documents & References
Week 2: McEliece Cryptosystem
Survey: profile and expectations
2.1. Formal Definition
2.2. Security-Reduction Proof
2.3. McEliece Assumptions
2.4. Notions of Security
2.5. Critical Attacks - Semantic Secure Conversions
2.6. Reducing the Key Size
2.7. Reducing the Key Size - LDPC codes
2.8. Reducing the Key Size - MDPC codes
2.9. Implementation
Exercice Week 2
Course Documents
Week 3: Message Attacks (ISD)
3.1. From Generic Decoding to Syndrome Decoding
3.2. Combinatorial Solutions: Exhaustive Search and Birthday Decoding
3.3. Information Set Decoding: the Power of Linear Algebra
3.4. Complexity Analysis
3.5. Lee and Brickell Algorithm
3.6. Stern/Dumer Algorithm
3.7. May, Meurer, and Thomae Algorithm
3.8. Becker, Joux, May, and Meurer Algorithm
3.9. Generalized Birthday Algorithm for Decoding
3.10. Decoding One Out of Many
Week 3 - Exercises
Course Documents & References
Week 4: Key Attacks
Survey: work time and satisfaction
4.1. Introduction
4.2. Support Splitting Algorithm
4.3. Distinguisher for GRS codes
4.4. Attack against subcodes of GRS codes
4.5. Error-Correcting Pairs
4.6. Attack against GRS codes
4.7. Attack against Reed-Muller codes
4.8. Attack against Algebraic Geometry codes
4.9. Goppa codes still resist
Week 4 - Exercises
Course Documents
Week 5: Other Cryptographic Constructions Relying on Coding Theory
5.1. Code-Based Digital Signatures
5.2. The Courtois-Finiasz-Sendrier (CFS) Construction
5.3. Attacks against the CFS Scheme
5.4. Parallel-CFS
5.5. Stern's Zero-Knowledge Identification Scheme
5.6. An Efficient Provably Secure One-Way Function
5.7. The Fast Syndrome-Based (FSB) Hash Function
Week 5 exercises
Course Documents
Survey: follow up on the Mooc and opinion