Speed-Stacking: Fast Sublinear Zero-Knowledge Proofs for Disjunctions

Building on recent disjunctive compilers for zero-knowledge (e.g. Goel et al. [EUROCRYPT'22]) we propose a new compiler that, when applied to sublinear-sized proofs, can result in sublinear-size disjunctive zero-knowledge with sublinear proving times (without meaningfully increasing proof sizes). Our key observation is that simulation in sublinear-size zero-knowledge proof systems can be much faster (both concretely and asymptotically) than the honest prover. We study applying our compiler to two classes of O(log n)-round protocols: interactive oracle proofs, specifically Aurora [EUROCRYPT'19] and Fractal [EU-ROCRYPT'20], and folding arguments, specifically Compressed Σ-protocols [CRYPTO'20, CRYPTO'21] and Bulletproofs [S&P'18]. This study validates that the compiler can lead to significant savings. For example, applying our compiler to Fractal enables us to prove a disjunction of ℓ clauses, each of size N , with only O((N + ℓ) • polylog(N )) computation, versus O(ℓN • polylog(N )) when proving the disjunction directly. We also find that our compiler offers a new lens through which to understand zero-knowledge proofs, evidenced by multiple examples of protocols with the same "standalone" complexity that each behave very differently when stacked.