Russell W. F. Lai, Giulio Malavolta, Viktoria Ronge
In their celebrated work, Groth and Sahai [EUROCRYPT'08, SICOMP' 12] constructed non-interactive zero-knowledge (NIZK) proofs for general bilinear group arithmetic relations, which spawned the entire subfield of structure-preserving cryptography. This branch of the theory of cryptography focuses on modular design of advanced cryptographic primitives. Although the proof systems of Groth and Sahai are a powerful toolkit, their efficiency hits a barrier when the size of the witness is large, as the proof size is linear in that of the witness. In this work, we revisit the problem of proving knowledge of general bilinear group arithmetic relations in zero-knowledge. Specifically, we construct a succinct zero-knowledge argument for such relations, where the communication complexity is logarithmic in the integer and source group components of the witness. Our argument has public-coin setup and verifier and can therefore be turned non-interactive using the Fiat-Shamir transformation in the random oracle model. For the special case of non-bilinear group arithmetic relations with only integer unknowns, our system can be instantiated in non-bilinear groups. In many applications, our argument system can serve as a drop-in replacement of Groth-Sahai proofs, turning existing advanced primitives in the vast literature of structure-preserving cryptography into practically efficient systems with short proofs.
Over the last few years, there has been a surge of new cryptographic results, including laconic oblivious transfer [13, 16], (anonymous/ hierarchical) identity-based encryption [9], trapdoor functions [19, 20], chosen-ciphertext security transformations [32, 33], designated-verifier zero-knowledge proofs [30, 34, 37], due to a beautiful framework recently introduced in the works of Cho et al. [13], and Dottling and Garg [14]. The primitive of one-way function with encryption (OWFE) [19, 20] and its relatives (chameleon encryption, one-time signatures with encryption, hinting PRGs, trapdoor hash encryption, batch encryption) [9, 14, 16, 17, 33] have been a centerpiece in all these results.
Identity-based mutual authentication and key agreement (ID-MAKA) between a mobile user and cloud service provider is necessary for accessing any cloud services. In recent years, there are a large number of ID-MAKA schemes had been proposed on mobile cloud computing services to make authentication and accessing process more usability, security, and scalability. In this paper, we propose a new ID-MAKA scheme for mobile cloud computing, which firstly achieves remote biometric-based authentication(remote servers authenticate user's biometrics), single sign-on (a single credential and single registration for accessing multiple servers) and center-less authentication(the registration center does not participate in the access procedure) in one scheme. In order to realize this target, we design a ZK-token based on ECC and cryptographic hash function, and then artfully employ it to introduce the fuzzy extractor technology and zero-knowledge technology into our scheme. Therefore, the user can access multiple cloud computing servers by registering only once in the registration center, and cloud computing servers can complete the biometric-based remote authentication and key agreement for the user without the registration center participating. In this way, our scheme greatly improves usability, scalability, and security compared to other existing solutions. We give a formal security proof for our scheme by using Real-Or-Random(RoR) model and Burrows-Abadi-Needham (BAN) logic to show that the present scheme is secure and security analysis for other known attacks. Finally, according to the experiment result, our scheme has lower computation and communication cost compared with most existing related schemes.
We study the foundations of secure computation in the blockchain-hybrid model, where a blockchain – modeled as a global functionality – is available as an Oracle to all the participants of a cryptographic protocol. We demonstrate both destructive and constructive applications of blockchains:
We show that classical rewinding-based simulation techniques used in many security proofs fail against blockchain-active adversaries that have read and post access to a global blockchain. In particular, we show that zero-knowledge (ZK) proofs with black-box simulation are impossible against blockchain-active adversaries.
Nevertheless, we show that achieving security against blockchain-active adversaries is possible if the honest parties are also blockchain active. We construct an \(\omega (1)\)-round ZK protocol with black-box simulation. We show that this result is tight by proving the impossibility of constant-round ZK with black-box simulation.
Finally, we demonstrate a novel application of blockchains to overcome the known impossibility results for concurrent secure computation in the plain model. We construct a concurrent self-composable secure computation protocol for general functionalities in the blockchain-hybrid model based on standard cryptographic assumptions.
We give the first construction of three-round non-malleable commitments from the almost minimal assumption of injective one-way functions. Combined with the lower bound of Pass (TCC 2013), our result is almost the best possible w.r.t. standard polynomial-time hardness assumptions (at least w.r.t. black-box reductions). Our results rely on a novel technique which we call 'bidirectional Goldreich-Levin extraction'. Along the way, we also obtain the first rewind secure delayed-input witness indistinguishable (WI) proofs from only injective one-way functions. We also obtain the first construction of an epsilon-extractable commitment scheme from injective one-way functions. We believe both of these to be of independent interest. In particular, as a direct corollary of our rewind secure WI construction, we are able to obtain a construction of 3-round promise zero-knowledge from only injective one-way functions.
Inspired by the work of Ghadafi and Groth (ASIACRYPT 2017) on a certain type of computational hardness assumptions in cyclic groups (which they call ``target assumptions''), we initiate an analogous work on another type of hardness assumptions, namely the ``knowledge-of-exponent'' assumptions (KEAs). Originally introduced by Damgard to construct practical encryption schemes secure against chosen ciphertext attacks, KEAs have subsequently been used primarily to construct succinct non-interactive arguments of knowledge (SNARKs), and proved to be inherent to such constructions. Since SNARKs (and their zero-knowledge variant, zk-SNARKs) are already used in practice in such systems as the Zcash digital currency, it can be expected that the use of KEAs will increase in the future, which makes it important to have a good understanding of those assumptions. Using a proof technique first introduced by Bellare and Palacio (but acknowledged by them as being due to Halevi), we first investigate the internal structure of the q-power knowledge-of-exponent (q-PKE) family of assumptions introduced by Groth, which is thus far the most general variant of KEAs. We then introduce a generalisation of the q-PKE family, and show that it can be simplified.
We address the problem of speeding up isogeny computation for supersingular elliptic curves over finite fields using untrusted computational resources like third party servers or cloud service providers (CSPs). We first propose new, efficient and secure delegation schemes. This especially enables resource-constrained devices (e.g. smart cards, RFID tags, tiny sensor nodes) to effectively deploy post-quantum isogeny-based cryptographic protocols. To the best of our knowledge, these new schemes are the first attempt to generalize the classical secure delegation schemes for group exponentiations and pairing computation to an isogeny-based post-quantum setting. Then, we apply these secure delegation subroutines to improve the performance of supersingular isogeny-based zero-knowledge proofs of identity. Our experimental results show that, at the 128-bit quantum-security level, the proving party only needs about 3% of the original protocol cost, while the verifying party's effort is fully reduced to comparison operations. Lastly, we also apply our delegation schemes to decrease the computational cost of the decryption step for the NIST postquantum standardization candidate SIKE.
After the work of Impagliazzo and Rudich (STOC, 1989), the black box framework has become one of the main research domain of cryptography. However black box techniques say nothing about non-black box techniques such as making use of zero-knowledge proofs. Brakerski et al. introduced a new black box framework named augmented black box framework, in which they gave a zero-knowledge proof oracle in addition to a base primitive oracle (TCC, 2011). They showed a construction of a non-interactive zero knowledge proof system based on a witness indistinguishable proof system oracle. They presented augmented black box construction of chosen ciphertext secure public key encryption scheme based on chosen plaintext secure public key encryption scheme and augmented black box separation between one-way function and key agreement.
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.
Muhammed F. Esgin, Raymond K. Zhao, Ron Steinfeld, Joseph K. Liu · 5 authors
We introduce MatRiCT, an efficient RingCT protocol for blockchain confidential transactions, whose security is based on post-quantum'' (module) lattice assumptions. The proof length of the protocol is around two orders of magnitude shorter than the existing post-quantum proposal, and scales efficiently to large anonymity sets, unlike the existing proposal. Further, we provide the first full implementation of a post-quantum RingCT, demonstrating the practicality of our scheme. In particular, a typical transaction can be generated in a fraction of a second and verified in about 23 ms on a standard PC. Moreover, we show how our scheme can be extended to provide auditability, where a user can select a particular authority from a set of authorities to reveal her identity. The user also has the ability to select no auditing and all these auditing options may co-exist in the same environment. The key ingredients, introduced in this work, of MatRiCT are 1) the shortest to date scalable ring signature from standard lattice assumptions with no Gaussian sampling required, 2) a novel balance zero-knowledge proof and 3) a novel extractable commitment scheme from (module) lattices. We believe these ingredients to be of independent interest for other privacy-preserving applications such as secure e-voting. Despite allowing 64-bit precision for transaction amounts, our new balance proof, and thus our protocol, does not require a range proof on a wide range (such as 32- or 64-bit ranges), which has been a major obstacle against efficient lattice-based solutions. Further, we provide new formal definitions for RingCT-like protocols, where the real-world blockchain setting is captured more closely. The definitions are applicable in a generic setting, and thus are believed to contribute to the development of future confidential transaction protocols in general (not only in the lattice setting).
Jun Zhou, Kim‐Kwang Raymond Choo, Zhenfu Cao, Xiaolei Dong
Outsourced pattern matching delegates the task of finding all positions pattern$P$appears in text$T$to the cloud from resource-constrained devices. Unfortunately, it has brought a series of security and privacy issues. Most of the state-of-the-art either disclosed text/pattern privacy or exploited the computationally-intensive techniques of public key fully homomorphic encryption (FHE), commitment schemes and zero knowledge proof to achieve both text/pattern privacy and verifiability. To address these issues, as a building block, an efficient privacy preserving verifiable outsourced discrete fourier transform protocol OVFT is first devised based on any one-way trapdoor permutation (OWTP). Based on OVFT, we propose an efficient secure verifiable outsourced polynomial multiplication protocol OPVML which is further exploited in designing our final protocol PVOPM for verifiable privacy-preserving outsourced pattern matching. Without exploiting public key FHE, the proposed PVOPM achieves both verifiability and text/pattern privacy against the collusion between the cloud and malicious receiver/sender, by generating authentication proofs of constant size and executing constant times of any one-way trapdoor permutation, independent to both the text size$n$and the pattern size$m$. Finally, formal security proof under universal composable (UC) model and extensive evaluations demonstrate the efficiency and practicability of our proposed PVOPM.