Blind zkSNARKs

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Abstract
In this paper, we show for the first time it is practical to privately delegate proof generation of zkSNARKs to a single server for computations of up to 2^20 R1CS constraints. We achieve this by computing zkSNARK proof generation over homomorphic ciphertexts, an approach we call blind zkSNARKs. We formalize the concept of blind proofs, analyze their cryptographic properties and show that the resulting blind zkSNARKs remain sound when compiled using BCS compilation. Our work follows the framework proposed by Garg et al. (Crypto'24) and improves the instantiation presented by Aranha et al. (Asiacrypt'24), which implements only the FRI subprotocol. By delegating proof generation, we are able to reduce client computation time from 10 minutes to mere seconds, while server computation time remains limited to 20 minutes. We also propose a practical construction for vCOED supporting constraint sizes four orders of magnitude larger than the current state-of-the-art verifiable FHE-based approaches. These results are achieved by optimizing Fractal for the GBFV homomorphic encryption scheme, including a novel method for making homomorphic NTT evaluation packing-friendly by computing it in two dimensions. Furthermore, we make the proofs publicly verifiable by appending a zero-knowledge Proof of Decryption (PoD). We propose a new construction for PoDs optimized for low proof generation time, exploiting modulus and ring switching in GBFV and using the Schwartz-Zippel lemma for proof batching; these techniques might be of independent interest. Finally, we implement the latter protocol in C and report on execution time and proof sizes.

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