Jan 24

Deep Dive into the Sumcheck Protocol with Justin Thaler

We invited Justin Thaler (@SuccinctJT) to give a talk to our research team… If you’re interested in Sumcheck Protocol, this is must-see TV 📺 🦁 Follow our Journey Twitter: https://twitter.com/Ingo_zk Github: https://github.com/ingonyama-zk YouTube: https://www.youtube.com/@ingo_zk Join us: https://www.ingonyama.com/careers LinkedIn: https://www.linkedin.com/company/ingonyama/

Zero Knowledge Proofs

1 min read

Deep Dive into the Sumcheck Protocol with Justin Thaler

Zero Knowledge Proofs

1 min read

Deep Dive into the Sumcheck Protocol with Justin Thaler

We invited Justin Thaler (@SuccinctJT) to give a talk to our research team…

If you’re interested in Sumcheck Protocol, this is must-see TV 📺 🦁

Justin Thaler & Ingonyama Research team

Follow our Journey

Twitter: https://twitter.com/Ingo_zk

Github: https://github.com/ingonyama-zk

YouTube: https://www.youtube.com/@ingo_zk

Join us: https://www.ingonyama.com/careers

LinkedIn: https://www.linkedin.com/company/ingonyama/

Jan 15

Multi-Precision Fast Modular Multiplication

by Ido Atlas, Tomer Solberg, and Yuval Domb The Barrett-Domb modular multiplication is a low-complexity, hardware-friendly modular multiplication algorithm based on the novel Barrett modular reduction scheme. In this work, we introduce a multi-precision, GPU/CPU friendly version of the Barrett-Domb algorithm. We show that our scheme is competitive with the…

Zero Knowledge Proofs

2 min read

Multi-Precision Fast Modular Multiplication

Zero Knowledge Proofs

2 min read

Dec 28, 2022

Hardware-friendliness of HyperPlonk

by Omer Shlomovits In this note we provide the hardware perspective on HyperPlonk. We focus on the main building block, the Multivariate SumCheck protocol and compare its computational and memory complexity to that of an NTT (Number Theoretic Transform). Read this article on HackMD: https://hackmd.io/@omershlo/rJhgKJPtj Background — HyperPlonk Plonk is one of the…

Zero Knowledge Proofs

7 min read

Zero Knowledge Proofs

7 min read

Dec 21, 2022

Zero Knowledge Proofs and the Metaverse

by Elan Neiger In the first week of December, 2022, the term “Metaverse” placed second in the Oxford English Dictionary’s competition for Word of the Year, a vote cast by over 300k people signifying a word or expression believed to have lasting cultural significance reflecting the ethos and moods of…

Zero Knowledge Proofs

11 min read

Zero Knowledge Proofs

11 min read

Dec 21, 2022

The Z Games: Pushing ZK Provers to the Extreme

A competition for accelerating real-world ZK provers, inspired by ZPRIZE and the X Games Welcome to the first edition of the Z Games: Accelerating Aleo Incentivized Testnet! Aleo is a blockchain for privacy-preserving applications, powered by Zero Knowledge. Aleo provers participate in AleoBFT to submit coinbase puzzle solutions and earn rewards. …

Aleo

3 min read

The Z Games: Pushing ZK Provers to the Extreme

Aleo

3 min read

Dec 13, 2022

Goldilocks NTT Trick

by Tomer Solberg Polynomial arithmetic is at the heart of modern Zero Knowledge Proving (ZKP) systems. The Number Theoretic Transform (NTT) is a crucial tool in facilitating efficient computational complexity over large polynomials encountered in ZKPs. NTTs are dominated by the number of field multiplications. In this short note we focus on the specific case of NTT in the 64 bit Goldilocks field. Following the simple observation that 2⁴⁸ is a root of unity, we show that expressing the first few roots of unity in terms of powers of 2, allows modular multiplications to be replaced with simple bit-shift operations, resulting in a significant cost saving for NTT.

Zkp

1 min read

Zkp

1 min read

Goldilocks NTT Trick

by Tomer Solberg

Polynomial arithmetic is at the heart of modern Zero Knowledge Proving (ZKP) systems. The Number Theoretic Transform (NTT) is a crucial tool in facilitating efficient computational complexity over large polynomials encountered in ZKPs. NTTs are dominated by the number of field multiplications.

In this short note we focus on the specific case of NTT in the 64 bit Goldilocks field. Following the simple observation that 2⁴⁸ is a root of unity, we show that expressing the first few roots of unity in terms of powers of 2, allows modular multiplications to be replaced with simple bit-shift operations, resulting in a significant cost saving for NTT.

Read the Paper on our Github here: https://github.com/ingonyama-zk/papers/blob/main/goldilocks_ntt_trick.pdf

Follow our Journey

Twitter: https://twitter.com/Ingo_zk

Github: https://github.com/ingonyama-zk

YouTube: https://www.youtube.com/@ingo_zk

Join us: https://www.ingonyama.com/#careers-section

Dec 4, 2022

Down the Rabbit Hole: Optimizing AWS F1 Direct Memory Access (DMA)

by Tony Wu When implementing a system involving both software and hardware components, unforeseen issues always seem to occur at the interfaces. Today we will look at one such pain points that occurs when transferring large amounts of data from a software application running on a typical x86 host machine…

Fpga

11 min read

Down the Rabbit Hole: Optimizing AWS F1 Direct Memory Access (DMA)

Fpga

11 min read

Nov 23, 2022

Sparkworks - Native Hardware Acceleration in Arkworks

TL;DR: We demonstrate integration of our cloud-ZK FPGA acceleration by running Arkworks Groth16 over the BN254 curve This work can easily be extended to support other primitives in the Arkworks framework and various System/HW configurations This is a joint work with Geometry research Background Cloud-ZK is our toolkit for developing ZKP acceleration…

Zero Knowledge Proofs

5 min read

Sparkworks - Native Hardware Acceleration in Arkworks

Zero Knowledge Proofs

5 min read

Nov 15, 2022

NTT Mini: Exploring Winograd’s Heuristic for Faster NTT

by Carol Danvers “Pushing the Limits on NTT Computation” Abstract: We report on the Winograd-based implementation for the Number Theoretical Transform. It uses less multiplications than the better-known Cooley-Tuckey alternative. This optimization is important for very high order finite-fields. Unfortunately, the Winograd scheme is difficult to generalize for arbitrary sizes and is only known for small-size transforms. We open-source our hardware implementation for size 32 based on [1].

Zkp

1 min read

Zkp

1 min read

NTT Mini: Exploring Winograd’s Heuristic for Faster NTT

by Carol Danvers

“Pushing the Limits on NTT Computation”

Abstract:

We report on the Winograd-based implementation for the Number Theoretical Transform. It uses less multiplications than the better-known Cooley-Tuckey alternative. This optimization is important for very high order finite-fields. Unfortunately, the Winograd scheme is difficult to generalize for arbitrary sizes and is only known for small-size transforms. We open-source our hardware implementation for size 32 based on [1].