Polyhedra Research

Zero-knowledge, Infinite innovation

Resources to learn about Polyhedra Network - recent updates, research, videos, and whitepapers

Academic Papers

Zero-knowledge Proof

Scalability is one of the key issues hindering the deployment of blockchains in many applications. ZKPs have been proposed and adopted by many projects trying to solve these problems but often proof generation is a bottleneck solved by deploying powerful machines with TBs of memory.

MissileProof

MissileProof

MissileProof is a succinct range proof for vectors that achieves constant proof size and verification time. Polyhedra can leverage MissileProof for efficient anonymous payments and asset auditing. The core components of MissileProof are a novel sumcheck and zerocheck for bivariate polynomials, resulting in a proof size of less than 1KB.

Virgo

Virgo

Virgo presents a powerful zero-knowledge argument scheme for layered arithmetic circuits without trusted setup based on Libra. It enjoys a fast prover as well as competitive proof size and fast verification time. Experiments show that it only takes 53 seconds to generate a proof for a circuit computing a Merkle tree with 256 leaves, at least an order of magnitude faster than all other succinct zero-knowledge argument schemes.

Virgo ++

Virgo ++

Virgo++ generalizes the interactive proof of GKR protocol for layered circuits to arbitrary circuits, while preserving the optimal prover complexity that is strictly linear to the size of the circuits. Not only does our new protocol achieve optimal prover complexity asymptotically, but it is also efficient in practice. Our experiments show that it only takes less than one second to generate the proof for a circuit with more than a million gates, which is 13 times faster than the original interactive proof protocol on the corresponding layered circuit.

Orion

Orion

Orion is the latest proof system that utilizes the most recent advancements in the area. The system significantly reduces the proof generation time with practical proof size and verification time. The system is best suited for off-chain applications and zkEVMs.

Libra

Libra

Libra is a high performance proof system that achieves high speed by directly making an algorithm breakthrough without doing any trade-off. The system has been implemented, modified and optimized in our company’s core codebase. Our experiments show that the new implementation beats other proof systems by an order of magnitude.

Gemini

Gemini

Gemini, a hardware-friendly zero-knowledge proof system, will help Polyhedra accelerate proof generation by leveraging specialized hardware. The Gemini prover has multiple configurations with different time and memory tradeoffs, which can be selected depending on the execution environment and the proved statement. The output proof is independent of the chosen configuration. In a space-efficient configuration, the Gemini prover uses a logarithmic amount of memory, enabling super-fast hardware with limited memory.

Interoperability & Other Applications

With thousands of new blockchains being created every year it is more important than ever for application developers to have access to secure, efficient, trust-minimized solutions for sending accurate data between blockchains. We have done extensive research on how to increase security and efficiency of cross-chain interactions without the introduction of additional trust assumptions.

zkBridge

zkBridge

zkBridge is a fully trustless, efficient, and secure foundation for Web3 interoperability. Join our ecosystem for the future of Web3 empowered by zkBridge.

Ghostor

Ghostor

Ghostor is an anonymous, decentralized data-sharing system. Ghostor serves as the data availability layer for Polyhedra, which hides user identities from the server and allows users to detect server-side integrity violations.

Merkle^2

Merkle^2

Merkle^2 is a low-latency transparency log system that helps Polyhedra achieve efficient certificate and identity management. Merkle^2 leverages a new multi-dimensional, authenticated data structure that nests two types of Merkle trees. As a result, both monitoring and lookup can be achieved within polylogarithmic time.

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