Homomorphic Encryption (HE) allows computations on encrypted data without decryption. It can be used where the users' information are to be processed by an untrustful server, and has been a popular choice in privacy-preserving applications. However, in order to obtain meaningful results, we have to assume an honest-but-curious server, i.e., it will faithfully follow what was asked to do. If the server is malicious, there is no guarantee that the computed result is correct. The notion of verifiable HE (vHE) is introduced to detect malicious server's behaviors, but current vHE schemes are either more than four orders of magnitude slower than the underlying HE operations (Atapoor et. al, CIC 2024) or fast but incompatible with server-side private inputs (Chatel et. al, CCS 2024). In this work, we propose a vHE framework ZHE: efficient Zero-Knowledge Proofs (ZKPs) that prove the correct execution of HE evaluations while protecting the server's private inputs. More precisely, we first design two new highly-efficient ZKPs for modulo operations and (Inverse) Number Theoretic Transforms (NTTs), two of the basic operations of HE evaluations. Then we build a customized ZKP for HE evaluations, which is scalable, enjoys a fast prover time and has a non-interactive online phase. Our ZKP is applicable to all Ring-LWE based HE schemes, such as BGV and CKKS. Finally, we implement our protocols for both BGV and CKKS and conduct extensive experiments on various HE workloads. Compared to the state-of-the-art works, both of our prover time and verifier time are improved; especially, our prover cost is only roughly 27–36× more expensive than the underlying HE operations, this is two to three orders of magnitude cheaper than state-of-the-arts.

Single Input Functionality (SIF) is a special case of MPC, where only one distinguished party called dealer holds the secret input. SIF allows the dealer to complete a computation task and send to other parties their respective outputs without revealing any additional information about its secret input. SIF has many applications, including multiple-verifier zero-knowledge and verifiable relation sharing, etc. Recently, several works devote to round-efficient realization of SIF, and achieve 2-round communication in the honest majority setting (Applebaum et al., Crypto 2022; Baum et al., CCS 2022; Yang and Wang, Asiacrypt 2022). In this work, we focus on concrete efficiency and propose the first practical construction for SIF against a dishonest majority in the preprocessing model; moreover, the online phase of our protocol is only 2-round and is highly efficient, as it requires no cryptographic operations and achieves information theoretical security. For SIF among 5 parties, our scheme takes 152.34ms (total) to evaluate an AES-128 circuit with 7.36ms online time. Compared to the state-of-the-art (honest majority) solution (Baum et al., CCS 2022), our protocol is roughly 2 × faster in the online phase, although more preprocessing time is needed. Compared to the state-of-the-art generic MPC against a dishonest majority (Wang et al., CCS 2017; Cramer et al., Crypto 2018), our protocol outperforms them with respect to both total running time and online running time.

Non-interactive zero-knowledge proof or argument (NIZK) systems are widely used in many security sensitive applications to enhance computation integrity, privacy and scalability. In such systems, a prover wants to convince one or more verifiers that the result of a public function is correctly computed without revealing the (potential) private input, such as the witness. In this work, we introduce a new notion, called scriptable SNARK, where the prover and verifier(s) can specify the function (or language instance) to be proven via a script. We formalize this notion in UC framework and provide a generic trusted hardware based solution. We then instantiate our solution in both SGX and Trustzone with Lua script engine. The system can be easily used by typical programmers without any cryptographic background. The benchmark result shows that our solution is better than all the known SNARK proof systems w.r.t. prover’s running time (1000 times faster), verifier’s running time, and the proof size. In addition, we also give a lightweight scriptable SNARK protocol for hardware with limited state, e.g., Θ ( λ ) bits. Finally, we show how the proposed scriptable SNARK can be readily deployed to solve many well-known problems in the blockchain context, e.g. verifier’s dilemma, fast joining for new players, etc.