Rigid Vertex Operator Algebra Cryptography C: An Engineering Pathway for Vertex Operator Algebra Cryptography — Parameter Space, Computational Feasibility, and Security Boundaries

Abstract

The modular invariance and automorphism group rigidity of vertex operatoralgebras provide a profound mathematical foundation for constructing novel postquantum cryptographic systems. However, a significant theoretical and engineeringgap exists between mathematical theorems and deployable cryptosystems. Thispaper does not propose new cryptographic protocols but rather systematicallyexamines the core challenges encountered in engineering vertex operator algebracryptography: the discrete selection of parameter spaces and their quantitativerelationship with security strength, the computational resource requirements ofcandidate algebraic families (lattice vertex operator algebras, WZW models, andmoonshine vertex operator algebras), the assessment of security boundaries underquantum attack models, and the practical overhead of auxiliary mechanisms suchas zero-knowledge proofs. The objective is to provide a clear problem inventoryand a feasibility analysis framework for future research, rather than to claim anyimmediately usable security parameters. The article concludes by summarizing thecurrent technology readiness levels and identifying the key breakthroughs requiredto advance from a theoretical framework toward a practical system.