International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Omkant Pandey

Publications

Year
Venue
Title
2021
CRYPTO
Towards a Unified Approach to Black-Box Constructions of Zero-Knowledge Proofs 📺
Xiao Liang Omkant Pandey
General-purpose zero-knowledge proofs for all $\NP$ languages greatly simplify secure protocol design. However, they inherently require the code of the underlying relation. If the relation contains black-box calls to a cryptographic function, the code of that function must be known to use the ZK proof, even if both the relation and the proof require only black-box access to the function. Rosulek (Crypto'12) shows that non-trivial proofs for even simple statements, such as membership in the range of a one-way function, require non-black-box access. We propose an alternative approach to bypass Rosulek's impossibility result. Instead of asking for a ZK proof directly for the given one-way function $f$, we seek to construct a {\em new} one-way function $F$ given only black-box access to $f$, {\em and} an associated ZK protocol for proving non-trivial statements, such as range membership, over its output. We say that $F$, along with its proof system, is a {\em proof-based} one-way function. We similarly define proof-based versions of other primitives, specifically pseudo-random generators and collision-resistant hash functions. We show how to construct proof-based versions of each of the primitives mentioned above from their ordinary counterparts under mild but necessary restrictions over the input. More specifically, \begin{itemize} \item We first show that if the prover entirely chooses the input, then proof-based pseudo-random generators cannot be constructed from ordinary ones in a black-box manner, thus establishing that some restrictions over the input are necessary. \item We next present black-box constructions handling inputs of the form $(x,r)$ where $r$ is chosen uniformly by the verifier. This is similar to the restrictions in the widely used Goldreich-Levin theorem. The associated ZK proofs support range membership over the output as well as arbitrary predicates over prefixes of the input. \end{itemize} Our results open up the possibility that general-purpose ZK proofs for relations that require black-box access to the primitives above may be possible in the future without violating their black-box nature by instantiating them using proof-based primitives instead of ordinary ones.
2021
CRYPTO
Compact Ring Signatures from Learning With Errors 📺
Ring signatures allow a user to sign a message on behalf of a ``ring'' of signers, while hiding the true identity of the signer. As the degree of anonymity guaranteed by a ring signature is directly proportional to the size of the ring, an important goal in cryptography is to study constructions that minimize the size of the signature as a function of the number of ring members. In this work, we present the first compact ring signature scheme (i.e., where the size of the signature grows logarithmically with the size of the ring) from the (plain) learning with errors (LWE) problem. The construction is in the standard model and it does not rely on a trusted setup or on the random oracle heuristic. In contrast with the prior work of Backes \etal~[EUROCRYPT'2019], our scheme does not rely on bilinear pairings, which allows us to show that the scheme is post-quantum secure assuming the quantum hardness of LWE. At the heart of our scheme is a new construction of compact and statistically witness-indistinguishable ZAP arguments for NP $\cap$ coNP, that we show to be sound based on the plain LWE assumption. Prior to our work, statistical ZAPs (for all of NP) were known to exist only assuming \emph{sub-exponential} LWE. We believe that this scheme might find further applications in the future.
2018
JOFC
2018
EUROCRYPT
2017
EUROCRYPT
2017
EUROCRYPT
2017
CRYPTO
2016
EUROCRYPT
2016
CRYPTO
2016
TCC
2016
TCC
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
TCC
2015
TCC
2015
TCC
2015
TCC
2015
CRYPTO
2014
CRYPTO
2014
TCC
2014
EPRINT
2014
EPRINT
2013
PKC
2013
CRYPTO
2012
EUROCRYPT
2012
EUROCRYPT
2010
TCC
2009
CRYPTO
2008
EUROCRYPT
2008
EPRINT
Non-black-box Techniques Are Not Necessary for Constant Round Non-malleable Protocols
Omkant Pandey
Recently, non-black-box techniques have enjoyed great success in cryptography. In particular, they have led to the construction of \emph{constant round} protocols for two basic cryptographic tasks (in the plain model): non-malleable zero-knowledge (NMZK) arguments for NP, and non-malleable commitments. Earlier protocols, whose security proofs relied only on black-box techniques, required non-constant (e.g., $O(\log n)$) number of rounds. Given the inefficiency (and complexity) of existing non-black-box techniques, it is natural to ask whether they are \emph{necessary} for achieving constant-round non-malleable cryptographic protocols. In this paper, we answer this question in the \emph{negative}. Assuming the validity of a recently introduced assumption, namely the \emph{Gap Discrete Logarithm} (Gap-DL) assumption [MMY06], we construct a constant round \emph{simulation-extractable} argument system for NP, which implies NMZK. The Gap-DL assumption also leads to a very simple and natural construction of \emph{non-interactive non-malleable commitments}. In addition, plugging our simulation-extractable argument in the construction of Katz, Ostrovsky, and Smith [KOS03] yields the first $O(1)$-round secure multiparty computation with a dishonest majority using only black-box techniques. Although the Gap-DL assumption is relatively new and non-standard, in addition to answering some long standing open questions, it brings a new approach to non-malleability which is simpler and very natural. We also demonstrate that \odla~holds unconditionally against \emph{generic} adversaries.
2008
CRYPTO
2007
EPRINT
Private Locally Decodable Codes
We consider the problem of constructing efficient locally decodable codes in the presence of a computationally bounded adversary. Assuming the existence of one-way functions, we construct {\em efficient} locally decodable codes with positive information rate and \emph{low} (almost optimal) query complexity which can correctly decode any given bit of the message from constant channel error rate $\rho$. This compares favorably to our state of knowledge locally-decodable codes without cryptographic assumptions. For all our constructions, the probability for any polynomial-time adversary, that the decoding algorithm incorrectly decodes any bit of the message is negligible in the security parameter.
2007
EPRINT
Precise Concurrent Zero Knowledge
\emph{Precise zero knowledge} introduced by Micali and Pass (STOC'06) guarantees that the view of any verifier $V$ can be simulated in time closely related to the \emph{actual} (as opposed to worst-case) time spent by $V$ in the generated view. We provide the first constructions of precise concurrent zero-knowledge protocols. Our constructions have essentially optimal precision; consequently this improves also upon the previously tightest non-precise concurrent zero-knowledge protocols by Kilian and Petrank (STOC'01) and Prabhakaran, Rosen and Sahai (FOCS'02) whose simulators have a quadratic worst-case overhead. Additionally, we achieve a statistically-precise concurrent zero-knowledge property---which requires simulation of unbounded verifiers participating in an unbounded number of concurrent executions; as such we obtain the first (even non-precise) concurrent zero-knowledge protocols which handle verifiers participating in a super-polynomial number of concurrent executions.
2006
EPRINT
Attribute-Based Encryption for Fine-Grained Access Control of Encrypted Data
As more sensitive data is shared and stored by third-party sites on the Internet, there will be a need to encrypt data stored at these sites. One drawback of encrypting data, is that it can be selectively shared only at a coarse-grained level (i.e., giving another party your private key). We develop a new cryptosystem for fine-grained sharing of encrypted data that we call Key-Policy Attribute-Based Encryption (KP-ABE). In our cryptosystem, ciphertexts are labeled with sets of attributes and private keys are associated with access structures that control which ciphertexts a user is able to decrypt. We demonstrate the applicability of our construction to sharing of audit-log information and broadcast encryption. Our construction supports delegation of private keys which subsumes Hierarchical Identity-Based Encryption (HIBE).

Program Committees

PKC 2020
Eurocrypt 2017
PKC 2016
TCC 2016