Rate-1 Non-Interactive Arguments for Batch-NP and Applications

We present a rate-$1$ construction of a publicly verifiable non-interactive argument system for batch-$\mathsf{NP}$ (also called a BARG), under the LWE assumption. Namely, a proof corresponding to a batch of $k$ NP statements each with an $m$-bit witness, has size $m + \mathsf{poly}(\lambda,\log k)$. In contrast, prior work either relied on non-standard knowledge assumptions, or produced proofs of size $m \cdot \mathsf{poly}(\lambda,\log k)$ (Choudhuri, Jain, and Jin, STOC 2021, following Kalai, Paneth, and Yang 2019). We show how to use our rate-$1$ BARG scheme to obtain the following results, all under the LWE assumption in the standard model: - A multi-hop BARG scheme for $\mathsf{NP}$. - A multi-hop aggregate signature scheme. - An incrementally verifiable computation (IVC) scheme for arbitrary $T$-time deterministic computations with proof size $\mathsf{poly}(\lambda,\log T)$. Prior to this work, multi-hop BARGs were only known under non-standard knowledge assumptions or in the random oracle model; aggregate signatures were only known under indistinguishability obfuscation (and RSA) or in the random oracle model; IVC schemes with proofs of size $\mathsf{poly}(\lambda,T^{\epsilon})$ were known under a bilinear map assumption, and with proofs of size $\mathsf{poly}(\lambda,\log T)$ were only known under non-standard knowledge assumptions or in the random oracle model

The B.G. News November 12, 1957

The BGSU campus student newspaper November 12, 1957. Volume 42 - Issue 13https://scholarworks.bgsu.edu/bg-news/2387/thumbnail.jp

Subtractive Sets over Cyclotomic Rings:Limits of Schnorr-like Arguments over Lattices

We study when (dual) Vandermonde systems of the form ${V}_T^{{(\intercal)}} \cdot \vec{z} = s\cdot \vec{w}$ admit a solution $\vec{z}$ over a ring $\mathcal{R}$, where ${V}_T$ is the Vandermonde matrix defined by a set $T$ and where the slack $s$ is a measure of the quality of solutions. To this end, we propose the notion of $(s,t)$-subtractive sets over a ring $\mathcal{R}$, with the property that if $S$ is $(s,t)$-subtractive then the above (dual) Vandermonde systems defined by any $t$-subset $T \subseteq S$ are solvable over $\mathcal{R}$. The challenge is then to find large sets $S$ while minimising (the norm of) $s$ when given a ring $\mathcal{R}$. By constructing families of $(s,t)$-subtractive sets $S$ of size $n =$ poly over cyclotomic rings $\mathcal{R} = \mathbb{Z}[\zeta_{p^\ell}]$ for prime $p$, we construct Schnorr-like lattice-based proofs of knowledge for the SIS relation ${A} \cdot \vec{x} = s \cdot \vec{y} \bmod q$ with $O(1/n)$ knowledge error, and $s = 1$ in case $p =$ poly. Our technique slots naturally into the lattice Bulletproof framework from Crypto\u2720, producing lattice-based succinct arguments for NP with better parameters. We then give matching impossibility results constraining $n$ relative to $s$, which suggest that our Bulletproof-compatible protocols are optimal unless fundamentally new techniques are discovered. Noting that the knowledge error of lattice Bulletproofs is $\Omega(\log k/n)$ for witnesses in $\mathcal{R}^k$ and subtractive set size $n$, our result represents a barrier to practically efficient lattice-based succinct arguments in the Bulletproof framework. Beyond these main results, the concept of $(s,t)$-subtractive sets bridges group-based threshold cryptography to lattice settings, which we demonstrate by relating it to distributed pseudorandom functions

Certifying Zero-Knowledge Circuits with Refinement Types

Zero-knowledge (ZK) proof systems have emerged as a promising solution for building security-sensitive applications. However, bugs in ZK applications are extremely difficult to detect and can allow a malicious party to silently exploit the system without leaving any observable trace. This paper presents Coda, a novel statically-typed language for building zero-knowledge applications. Critically, Coda makes it possible to formally specify and statically check properties of a ZK application through a rich refinement type system. One of the key challenges in formally verifying ZK applications is that they require reasoning about polynomial equations over large prime fields that go beyond the capabilities of automated theorem provers. Coda mitigates this challenge by generating a set of Coq lemmas that can be proven in an interactive manner with the help of a tactic library. We have used Coda to re-implement 79 arithmetic circuits from widely-used Circom libraries and applications. Our evaluation shows that Coda makes it possible to specify important and formally verify correctness properties of these circuits. Our evaluation also revealed 6 previously-unknown vulnerabilities in the original Circom projects

Algorithmic Regulation using AI and Blockchain Technology

This thesis investigates the application of AI and blockchain technology to the domain of Algorithmic Regulation. Algorithmic Regulation refers to the use of intelligent systems for the enabling and enforcement of regulation (often referred to as RegTech in financial services). The research work focuses on three problems: a) Machine interpretability of regulation; b) Regulatory reporting of data; and c) Federated analytics with data compliance. Uniquely, this research was designed, implemented, tested and deployed in collaboration with the Financial Conduct Authority (FCA), Santander, RegulAItion and part funded by the InnovateUK RegNet project. I am a co-founder of RegulAItion. / Using AI to Automate the Regulatory Handbook: In this investigation we propose the use of reasoning systems for encoding financial regulation as machine readable and executable rules. We argue that our rules-based “white-box” approach is needed, as opposed to a “black-box” machine learning approach, as regulators need explainability and outline the theoretical foundation needed to encode regulation from the FCA Handbook into machine readable semantics. We then present the design and implementation of a production-grade regulatory reasoning system built on top of the Java Expert System Shell (JESS) and use it to encode a subset of regulation (consumer credit regulation) from the FCA Handbook. We then perform an empirical evaluation, with the regulator, of the system based on its performance and accuracy in handling 600 “real- world” queries and compare it with its human equivalent. The findings suggest that the proposed approach of using reasoning systems not only provides quicker responses, but also more accurate results to answers from queries that are explainable. / SmartReg: Using Blockchain for Regulatory Reporting: In this investigation we explore the use of distributed ledgers for real-time reporting of data for compliance between firms and regulators. Regulators and firms recognise the growing burden and complexity of regulatory reporting resulting from the lack of data standardisation, increasing complexity of regulation and the lack of machine executable rules. The investigation presents a) the design and implementation of a permissioned Quorum-Ethereum based regulatory reporting network that makes use of an off-chain reporting service to execute machine readable rules on banks’ data through smart contracts b) a means for cross border regulators to share reporting data with each other that can be used to given them a true global view of systemic risk c) a means to carry out regulatory reporting using a novel pull-based approach where the regulator is able to directly “pull” relevant data out of the banks’ environments in an ad-hoc basis- enabling regulators to become more active when addressing risk. We validate the approach and implementation of our system through a pilot use case with a bank and regulator. The outputs of this investigation have informed the Digital Regulatory Reporting initiative- an FCA and UK Government led project to improve regulatory reporting in the financial services. / RegNet: Using Federated Learning and Blockchain for Privacy Preserving Data Access In this investigation we explore the use of Federated Machine Learning and Trusted data access for analytics. With the development of stricter Data Regulation (e.g. GDPR) it is increasingly difficult to share data for collective analytics in a compliant manner. We argue that for data compliance, data does not need to be shared but rather, trusted data access is needed. The investigation presents a) the design and implementation of RegNet- an infrastructure for trusted data access in a secure and privacy preserving manner for a singular algorithmic purpose, where the algorithms (such as Federated Learning) are orchestrated to run within the infrastructure of data owners b) A taxonomy for Federated Learning c) The tokenization and orchestration of Federated Learning through smart contracts for auditable governance. We validate our approach and the infrastructure (RegNet) through a real world use case, involving a number of banks, that makes use of Federated Learning with Epsilon-Differential Privacy for improving the performance of an Anti-Money-Laundering classification model