Zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) allows a party, known as the prover, to convince another verifier, that he knows private value $v$ , without revealing it, such notation="LaTeX">$F(u,v)=y$ for so...

Zero-knowledge succinct non-interactive arguments (zk-SNARKs) rely on knowledge assumptions for their security. Meanwhile, as the complexity and scale of cryptographic systems continues to grow, composition secure protocols is vital importance. The current gold standards composable security, Universal Composability Constructive Cryptography frameworks cannot capture assumptions, core proofs pro...

Gennaro, Gentry, Parno, and Raykova (GGPR) introduced Quadratic Arithmetic Programs (QAPs) as a way of representing arithmetic circuits in a form amendable to highly efficient cryptographic protocols [11], particularly for verifiable computation and succinct non-interactive arguments [12]. Subsequently, Parno, Gentry, Howell, and Raykova introduced an improved cryptographic protocol (and implem...

Large computations, when amenable to distributed parallel execution, are often executed on computer clusters, for scalability and cost reasons. Such computations are used in many applications, including, to name but a few, machine learning, webgraph mining, and statistical machine translation. Oftentimes, though, the input data is private and only the result of the computation can be published....

This paper classifies all snarks up to order $36$ and explains the reasons for their uncolourability. The crucial part of our approach is a computer-assisted structural analysis cyclically $5$-connected critical snarks, which justified by fact that every other snark can be constructed from them series simple operations while preserving Our results reveal most analysed are built pieces Petersen ...

We propose a new approach for privacy-preserving and verifiable convolutional neural network (CNN) testing in distrustful multi-stakeholder environment. The is aimed to enable that CNN model developer convinces xmlns:xlink="http://www.w3.org/1999/xlink">user of the truthful performance over...

Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to approximate certain linear algebraic parameters, as well as to model the spread of diseases and information in social networks. In this paper, we introduce and study the connected forcing process – a restriction of z...

The Earth’s tectonic plates are strong, viscoelastic shells which make up the outermost part of a thermally convecting, predominantly viscous layer; at the boundaries between plates the rheology is thought to be dominated by brittle processes. Brittle failure of the lithosphere occurs when stresses are high. In order to build a realistic simulation of the planet’s evolution, the complete viscoe...