International Association for Cryptologic Research

International Association
for Cryptologic Research


Yi Deng

Affiliation: Chinese Academy of Sciences, CN


On the Security of Classic Protocols for Unique Witness Relations
We revisit the problem of whether the known classic constant-round public-coin argument/proof systems are witness hiding for languages/distributions with unique witnesses. Though strong black-box impossibility results are known, we provide some less unexpected positive results on the witness hiding security of these classic protocols:We give sufficient conditions on a hard distribution over unique witness NP relation for which all witness indistinguishable protocols (including all public-coin ones, such as ZAPs, Blum protocol and GMW protocol) are indeed witness hiding. We also show a wide range of cryptographic problems with unique witnesses satisfy these conditions, and thus admit constant-round public-coin witness hiding proof system.For the classic Schnorr protocol (for which the distribution of statements being proven seems not to satisfy the above sufficient conditions), we develop an embedding technique and extend the result of Bellare and Palacio to base the witness hiding property of the Schnorr protocol in the standalone setting on a relaxed version of one-more like discrete logarithm (DL) assumption, which essentially assumes there does not exist instance compression scheme for the DL problem, and show that breaking this assumption would lead to some surprising consequences, such as zero knowledge protocols for the AND-DL language with extremely efficient communication and highly non-trivial hash combiner for hash functions based on the DL problem. Similar results hold for the Guillou-Quisquater protocol.
On Resettably-Sound Resttable Zero Knowledege Arguments
Yi Deng Dongdai Lin
We study the simultaneous resettability problem, namely whether resettably-sound resettable ZK arguments for non-trivial languages exist (posed by Barak et al. [BGGL FOCS'01]), in both the plain model and the bare public-key (BPK for short) model. Under general hardness assumptions, we show: 1. in the BPK model, there exist constant-round (full-fledged) resettably-sound resettable ZK arguments for NP. This resolves a main problem in this model that remained open since the Micali and Reyzin's identification of notions of soundness [MR Crypto 2001] in the BPK model. the plain model, there exist constant-round (unbounded) resettably-sound class-bounded resettable ZK (as defined by Deng and Lin in [DL Eurocrypt 2007]) arguments for NP. This improves the previous result of Deng and Lin [Eurocrypt 2007] in that the DL construction for class-bounded resettable ZK argument achieves only a weak notion of resettable-soundness. The crux of these results is a construction of constant-round instance-dependent (full-fledged) resettably-sound resettable WI argument of knowledge (IDWIAOK for short) for any NP statement of the form x_0\in L_0 or x_1\in L_1, a notion also introduced by Deng and Lin [Eurocrypt 2007], whose construction, however, obtains only weak resettable-soundness when x_0\notin L_0. Our approach to the simultaneous resettability problem in the BPK model is to make a novel use of IDWIAOK, which gives rise to an elegant structure we call \Sigma-puzzles. Given the fact that all previously known resettable ZK arguments in the BPK model can be achieved in the plain model when ignoring round complexity, we believe this approach will shed light on the simultaneous resettability problem in the plain model.
Resettable Zero Knowledge in the Bare Public-Key Model under Standard Assumption
Yi Deng Dongdai Lin
In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for $\mathcal{NP}$ in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in $\mathcal{NP}$ in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.
Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model
We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks. As negative results in the area of concurrent non-malleable zero-knowledge imply that protocols in the standard setting (i.e., under no setup assumptions) can only be given for trivial languages, researchers have studied such protocols in models with setup assumptions, such as the common reference string (CRS) model. This model assumes that a reference string is honestly created at the beginning of all interactions and later available to all parties (an assumption that is satisfied, for instance, in the presence of a trusted party). A growing area of research in Cryptography is that of reducing the setup assumptions under which certain cryptographic protocols can be realized. In an effort to reduce the setup assumptions required for efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks, we consider a model, which we call the Authenticated Public-Key (APK) model. The APK model seems to significantly reduce the setup assumptions made by the CRS model (as no trusted party or honest execution of a centralized algorithm are required), and can be seen as a slightly stronger variation of the Bare Public-Key (BPK) model from \cite{CGGM,MR}, and a weaker variation of the registered public-key model used in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK model. Our main result is a constant-round concurrent non-malleable zero-knowledge argument of knowledge for any polynomial-time relation (associated to a language in $\mathcal{NP}$), under the (minimal) assumption of the existence of a one-way function family. We also show time-efficient instantiations of our protocol, in which the transformation from a 3-round honest-verifier zero-knowledge argument of knowledge to a 4-round concurrently non-malleable zero-knowledge argument of knowledge for the same relation incurs only $\mathcal{O}(1)$ (precisely, a {\em small} constant) additional modular exponentiations, based on known number-theoretic assumptions. Furthermore, the APK model is motivated by the consideration of some man-in-the-middle attacks in models with setup assumptions that had not been considered previously and might be of independent interest. We also note a negative result with respect to further reducing the setup assumptions of our protocol to those in the (unauthenticated) BPK model, by showing that concurrently non-malleable zero-knowledge arguments of knowledge in the BPK model are only possible for trivial languages.

Program Committees

PKC 2019