Chapter 2
Core Cryptographic Foundations for Access Control
What makes decentralized access control not only possible but provably secure? This chapter uncovers the cryptographic bedrock underlying modern, distributed access management: from the theory of key systems to the advanced techniques allowing large-scale, trust-minimized collaboration. Readers will build a rigorous understanding of the mathematical constructs and key management protocols that empower secure, resilient, and programmable access control in adversarial environments.
2.1 Symmetric and Asymmetric Key Systems
Cryptographic systems are fundamentally categorized into symmetric-key and asymmetric-key schemes, distinguished by their mathematical structures and key management paradigms. At their core, both methods rely on complex algebraic functions and hardness assumptions, yet they embody distinct design principles and operational trade-offs that influence their security guarantees and system integration.
Mathematical Foundations
Symmetric-key cryptography employs a single secret key shared by both communicating parties. The central mathematical construct is a bijective function
where M,
