Overview
Post-quantum cryptography is no longer just a futuristic concept, but a necessity in the present day. Anyone who works in the field and ignores its principles and techniques could be left at a severe disadvantage. This course offers a comprehensive overview of post-quantum cryptography.
Day 1 explores quantum-based attacks, lattices, and their applications in schemes and key exchange. Day 2 delves into error-correcting codes, isogenies, and their security implications. Day 3 covers the MQ problem, various schemes, including oil and vinegar, rainbow, and their cryptanalysis.
Other candidates, such as hash-based signatures and MPC-in-the-head signatures, and side-channel attacks, are also discussed. Participants will gain a thorough understanding of post-quantum cryptography and its potential impact on modern cryptography.
High Level Overview of the class topics;
- Introduction to post-quantum cryptography
- Attacks on DLOG and factoring
- Lattices and related algorithms
- LWE and Regev's encryption scheme
- NTRU and NTRUPrime
- Codes and cryptosystems
- Isogenies and elliptic curves
- MQ problem and its variants
- Other candidates for PQC
- Side-channel attacks and countermeasures
Prerequisites
General knowledge of cryptography.
Delegates will learn how to
You will;
- Be able to evaluate the security of different cryptographic primitives
- Be able to select suitable cryptographic algorithms for their specific use case and deployment scenario
- Have practical experience implementing and using post-quantum cryptographic schemes
- Understand the mathematical foundations of post-quantum cryptography
- Be familiar with the state-of-the-art in post-quantum cryptography
- Possess knowledge and skills to defend against side-channel and physical attacks on cryptographic implementations
Outline
Day 1
Intro
Attacks Against DLOG and Factoring
- Shor's Algorithm
- NIST Competition
Lattices
- Definitions
- SVP, CVP, BDD
- Good and Bad Basis
- Babai Nearest Plane Algorithm
- GGH Schemes and Attack Against Digital Signature Scheme
- LWE
- Regev's Encryption Scheme
- Key Exchange from LWE
- Ring LWE
- Module LWE and LWR
- Frodo, Kyber, Saber
- NTRU and NTRUPrime
- SIS Problem, Hash Function, and Digital Signature from SIS
- Falcon
- Lyubashevskys's ID Scheme
- Dilithium
- IBE and FHE
Day 2
Codes
- Error Correcting Codes in General
- Goppa Codes, Decoding Algorithm
- McEliece Cryptosystem, Cryptanalysis History
- BIKE and HQC
- Niederreiter Cryptosystem, Syndrome Decoding
- Trapdoor One-Way Function
- Digital Signature Scheme Wave
- Rank Metric Codes and Cryptosystems
Isogenies
- Crash Course on Isogenies and Elliptic Curves
- CGL Hash Function and SIDH
- Security of SIDH, SIKE
- Group Actions, CSIDH, and Applications
- SQISign (High-Level Discussion)
Day 3
MQ
- MQ Problem
- Discussion about Its Hardness
- Linearization, Gröbner Basis (High-Level Discussion)
- Benchmarking Systems
- Imai-Matsumoto, Hidden Field Equations
- Variants of HFE
- Oil and Vinegar Scheme, Kipnis-Shamir Attack, UOV
- Rainbow and Cryptanalysis Results for Both UOV and Rainbow
- ID Scheme and GeMSS
Other Candidates
- Hash-Based Signatures (SPHINCS+)
- MPC-in-the-Head Signatures (Picnic)
Side-Channel Attacks
- Basic Attacks
- Countermeasures Against Physical and Implementation Attacks
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