Epistemic Logics for Cryptographic Protocols and Zero-Knowledge Proofs
Mateo C. Jaramillo

Abstract:
This thesis presents an epistemic logic for modeling Zero-Knowledge proofs and other cryptographic protocols. We consider multi-agent interactions where a prover convinces a verifier of some proposition φ, with the verifier learning nothing more than the validity of φ. By enriching existing cryptographic variants of DEL with notions of probability, we introduce a cryptographic probability logic (CPL) that is capable of modeling cryptographic primitives such as encryption and passive adversaries while also capturing the concepts of interactive proofs and simulations. Within our presentation, we analyze multiple protocols including RSA encryption and a zero-knowledge proof for the NP-Complete problem of graph 3-coloring.