Post Quantum Cryptography

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

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Prerequisites

General knowledge of cryptography.

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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

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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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