Non-interactive Zero Knowledge Proofs in the Random Oracle Model

In this paper we use strong one-time signatures schemes and adaptive Non-Interactive Zero-Knowledge (NIZK) proof systems to construct an efficient unbounded simulation-sound NIZK proof system, assuming the existence of one-way permutation and pseudorandom generator. Furthermore, we can obtain an unbounded non-malleable NIZK proof system when replacing the adaptive NIZK proof systems in our construction with adaptive NIZK proof of knowledge.KeywordsSignature SchemeProof SystemReference StringChoose Ciphertext AttackCommon Reference StringThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Direct Anonymous Attestation (DAA) is a special signature scheme that enables remote authentication of a user while preserving privacy under the user's control. Thus, in this paper, based on existing schemes and mechanisms, we firstly construct a DAA signature scheme which is proven secure without random oracles. By making certain reasonable assumptions and employing the techniques of non-interactive zero-knowledge(NIZK) proof system and Two-Party Computation(2PC) scheme, we prove that our scheme satisfies anonymous and untraceable, and compares with existing DAA schemes in the aspects of security and efficiency.

Privacy concerns of smart contracts are a major roadblock preventing their wider adoption. A promising approach to protect private data is hiding it with cryptographic primitives and then enforcing correctness of state updates by Non-Interactive Zero-Knowledge (NIZK) proofs. Unfortunately, NIZK statements are less expressive than smart contracts, forcing developers to keep some functionality in the contract. This results in scattered logic, split across contract code and NIZK statements, with unclear privacy guarantees. To address these problems, we present the zkay language, which introduces privacy types defining owners of private values. zkay contracts are statically type checked to (i) ensure they are realizable using NIZK proofs and (ii) prevent unintended information leaks. Moreover, the logic of zkay contracts is easy to follow by just ignoring privacy types. To enforce zkay contracts, we automatically transform them into contracts equivalent in terms of privacy and functionality, yet executable on public blockchains. We evaluated our approach on a proof-of-concept implementation generating Solidity contracts and implemented 10 interesting example contracts in zkay. Our results indicate that zkay is practical: On-chain cost for executing the transformed contracts is around 1M gas per transaction (~0.50US$) and off-chain cost is moderate.

We show new lower bounds and impossibility results for general (possibly non-black-box) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a constant-round zero-knowledge strong proof (or argument) of knowledge (as defined by Goldreich, 2001) for a nontrivial language; 2. There does not exist a two-round zero-knowledge proof system with perfect completeness for an NP-complete language; 3. There does not exist a constant-round public-coin proof system for a nontrivial language that is resettable zero knowledge. This result also extends to bounded resettable zero knowledge. In contrast, we show that under reasonable assumptions, there does exist such a (computationally sound) argument system that is bounded-resettable zero knowledge.

Many of the recent advanced lattice-based \(\varSigma \)-/public-coin honest verifier (HVZK) interactive protocols based on the techniques developed by Lyubashevsky (Asiacrypt’09, Eurocrypt’12) can be transformed into a non-interactive zero-knowledge (NIZK) proof in the random oracle model (ROM) using the Fiat-Shamir transform. Unfortunately, although they are known to be secure in the classical ROM, existing proof techniques are incapable of proving them secure in the quantum ROM (QROM). Alternatively, while we could instead rely on the Unruh transform (Eurocrypt’15), the resulting QROM secure NIZK will incur a large overhead compared to the underlying interactive protocol.

In a non-interactive zero-knowledge (NIZK) proof, a prover can non-interactively convince a verifier of a statement without revealing any additional information. Thus far, numerous constructions of NIZKs have been provided in the common reference string (CRS) model (CRS-NIZK) from various assumptions, however, it still remains a long standing open problem to construct them from tools such as pairing-free groups or lattices. Recently, Kim and Wu (CRYPTO’18) made great progress regarding this problem and constructed the first lattice-based NIZK in a relaxed model called NIZKs in the preprocessing model (PP-NIZKs). In this model, there is a trusted statement-independent preprocessing phase where secret information are generated for the prover and verifier. Depending on whether those secret information can be made public, PP-NIZK captures CRS-NIZK, designated-verifier NIZK (DV-NIZK), and designated-prover NIZK (DP-NIZK) as special cases. It was left as an open problem by Kim and Wu whether we can construct such NIZKs from weak paring-free group assumptions such as DDH. As a further matter, all constructions of NIZKs from Diffie-Hellman (DH) type assumptions (regardless of whether it is over a paring-free or paring group) require the proof size to have a multiplicative-overhead \(|C| \cdot \mathsf {poly}(\kappa )\), where |C| is the size of the circuit that computes the \(\mathbf {NP}\) relation.

One important property of group signatures is forward-security, which prevents an attacker in possession of a group signing key to forge signatures produced in the past. In case of exposure of one group member’s signing key, group signatures lacking forward-security need to invalidate all group public and secret keys (by re-initializing the whole system) but also invalidate all previously issued group signatures. Most of the existing forward-secure group signatures (FS-GS) are built from number-theoretic security assumptions which are vulnerable to quantum computers. The only post-quantum secure FS-GS scheme is built from lattices by Ling et al. (PQCrypto 19) in the random oracle model, following the classical framework of encrypt-then-prove, thus using non-interactive zero-knowledge (NIZK) proofs. In this work, we achieve the first FS-GS from lattices in the standard model. Our starting point is the group signature of Katsumada and Yamada (Eurocrypt 19) which replaces NIZK by attribute-based signatures (ABS), thus removing the need for random oracles. We first modify the underlying ABS of Tsabary (TCC 17) to equip it with forward-security property. We then prove that by plugging it back in the group signature framework of Katsumada and Yamada (Eurocrypt 19), we can design a FS-GS scheme secure in the standard model with public key and signature size constant in the number of users. Our constant size is achieved by relying on complexity leveraging, which further implies relying on the subexponential hardness of the Short Integers Solution (SIS) assumption.

Recent work has produced interactive Zero Knowledge (ZK) proof systems that can express proofs as arbitrary C programs (Heath et al., 2021, henceforth referred to as ZEE); these programs can be executed by a simulated ZK processor that runs in the 10KHz range. In this work, we demonstrate that such proof systems are amenable to high degrees of parallelism. Our epoch parallelism-based approach allows the prover and verifier to divide the ZK proof into pieces such that each piece can be executed on a different machine. These proof snippets can then be glued together, and the glued parallel proofs are equivalent to the original sequential proof. We implemented and we experimentally evaluate an epoch parallel version of the ZEE proof system. By running the prover and verifier each across 31 2-core machines, we achieve a ZK processor that runs at up to 394KHz. This allowed us to run a benchmark involving the Linux program bzip2, which would have required at least 11 days with the former ZEE system, in only 8.5 hours.

Devising a fair-exchange protocol for digital goods has been an appealing line of research in the past decades. The Zero-Knowledge Contingent Payment (ZKCP) protocol first achieves fair exchange in a trustless manner with the aid of the Bitcoin network and zero-knowledge proofs. However, it incurs setup issues and substantial proving overhead, and has difficulties handling complicated validation of large-scale data. In this paper, we propose an improved solution ZKCPlus for practical and flexible fair exchange. ZKCPlus incorporates a new commit-and-prove non-interactive zero-knowledge (CP-NIZK) argument of knowledge under standard discrete logarithmic assumption, which is prover-efficient for data-parallel computations. With this argument we avoid the setup issues of ZKCP and reduce seller's proving overhead, more importantly enable the protocol to handle complicated data validations. We have implemented a prototype of ZKCPlus and built several applications atop it. We rework a ZKCP's classic application of trading sudoku solutions, and ZKCPlus achieves 21-67 times improvement in seller efficiency than ZKCP, with only milliseconds of setup time and 1 MB public parameters. In particular, our CP-NIZK argument shows an order of magnitude higher proving efficiency than the zkSNARK adopted by ZKCP. We also built a realistic application of trading trained CNN models. For a 3-layer CNN containing 8,620 parameters, it takes less than 1 second to prove and verify an inference computation, and also about 1 second to deliver the parameters, which is very promising for practical use.

This paper presents zero knowledge proofs, their cryptographic significance and applications. It presents a basic classification: interactive and noninteractive zero knowledge proofs. It presents and compares three protocols of non-interactive zero knowledge proofs: ZK-SNARK, ZK-STARK and Bulletproofs. It presents the quadratic residue problem and proofs it with both interactive and non-interactive zero knowledge proofs. The non-interactive protocol used to prove the quadratic residue problem is ZK-SNARK. The proof is implemented in the Python programming language, using python-snark library.

In this paper we propose a two-round authenticated key agreement protocol using non-interactive zero-knowledge (NIZK) proofs. Essentially, a NIZK proof allows a prover to convince a verifier about the correctness of a statement without interaction. An obvious application of this is in a two-round key agreement protocol where each participant proves non-interactively the knowledge of the private key and a shared secret. Our key agreement protocol is based on this idea and is secure assuming the hardness of the Diffie-Hellman problem (DHP) and another related problem in bilinear maps.

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.

Non-interactive zero-knowledge (NIZK) proofs for algebraic relations in a group, such as the Groth-Sahai proofs, are an extremely powerful tool in pairing-based cryptography. A series of recent works focused on obtaining very efficient NIZK proofs for linear spaces in a weaker quasi-adaptive model. We revisit recent quasi-adaptive NIZK constructions, providing clean, simple, and improved constructions via a conceptually different approach inspired by recent developments in identity-based encryption. We then extend our techniques also to linearly homomorphic structure-preserving signatures, an object both of independent interest and with many applications.

Malleability for cryptography is not necessarily an opportunity for attack; in many cases it is a potentially useful feature that can be exploited. In this work, we examine notions of malleability for non-interactive zero-knowledge (NIZK) proofs. We start by defining a malleable proof system, and then consider ways to meaningfully control the malleability of the proof system, as in many settings we would like to guarantee that only certain types of transformations can be performed. As our motivating application, we consider a shorter proof for verifiable shuffles. Our controlled-malleable proofs allow us for the first time to use one compact proof to prove the correctness of an entire multi-step shuffle. Each authority takes as input a set of encrypted votes and a controlled-malleable NIZK proof that these are a shuffle of the original encrypted votes submitted by the voters; it then permutes and re-randomizes these votes and updates the proof by exploiting its controlled malleability. As another application, we generically use controlled-malleable proofs to realize a strong notion of encryption security. Finally, we examine malleability in existing proof systems and observe that Groth-Sahai proofs are malleable. We then go beyond this observation by characterizing all the ways in which they are malleable, and use them to efficiently instantiate our generic constructions from above; this means we can instantiate our proofs and all their applications using only the Decision Linear (DLIN) assumption.

The cutting-edge technology, namely Cloud of Things (CoT) has shaped the existing business process into a new orientation in terms of performance, usability, and reliability. Among different business processes, online education is one of the prime areas where CoT can be used to make it more agile in the context of performance and usability. In this endeavor, a novel methodology has been proposed for an online higher education framework based on CoT. The proposed framework is made agile using Service Oriented Architecture (SOA). Furthermore, in order to make the proposed framework more reliable, a Zero Knowledge Proof (ZKPF) system has been introduced here. The proposed ZKPF algorithm is based on the Hadamard matrix. Experimental results have shown to lay bare the effectiveness of the proposed algorithms.