Modular Construction and Analysis of Multi-Round Straightline Extractability Compilers

This thesis investigates the feasibility of a generic, modular compiler that treats an existing three-move straight-line extractability compiler as a black-box building block and extends it to multi-round public-coin protocols. We introduce a recursive compiler that compresses an interactive multi-round protocol layer by layer and analyze how its security and efficiency properties propagate through this recursion. The analysis demonstrates that while the framework successfully preserves completeness, zero knowledge, and knowledge soundness, the modularity incurs a substantial cost. The repetition parameters required at each recursive level cause an exponential blowup in both runtime and communication complexity, restricting the compiler’s efficiency to protocols with a strictly constant number of rounds. Furthermore, preserving the zero-knowledge property requires the input protocol to satisfy 2-Stage special Honest Verifier Zero-Knowledge, a stronger form of special Honest-Verifier Zero-Knowledge introduced in this work. Ultimately, this thesis provides a clean theoretical framework for modular straight-line extractability, but exposes the asymptotic performance gap between our flexible black-box construction and specialized monolithic transformations.