Adversary Models for Configuration Space Cryptography: Formal Security Proofs and Game-Based Definitions

This paper develops formal adversary models for Configuration Space Cryptography (CSC), establishing game-based security definitions analogous to IND-CPA and IND-CCA frameworks in conventional cryptography. We define a five-class taxonomy of adversary capabilities—from passive observers to partial mapping compromise—and prove security bounds against each class under explicit cryptographic assumptions. The central result demonstrates that CSC achieves IND-CSC-CPA security with advantage bound Adv(A) ≤ 1/|C| + Adv_PRF + negl(λ). We analyze graceful degradation under partial compromise and establish conditions under which multi-layer attacks remain computationally infeasible.