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Polynomial Multiplication with FFT (fast Fourier transform)
Research
The cost of polynomial multiplication (including division) would quadratically depend on the input size if computed naively. Such dependence is not desirable for the efficiency of SNARKs and directly impacts proving performance. For Parasol, this directly impacts throughput on Solana. At perpetual market scale, the gap between a quadratic and a near-linear algorithm compounds quickly.
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Polynomial Multiplication with FFT (fast Fourier transform)
Research
May 14, 2026
Asymptotics vs concrete performance
Research
May 13, 2026
How to prove EdDSA verification at scale - PART 2: Field-agnostic Proof Systems
Research
April 30, 2026
How to prove EdDSA verification at scale - PART 1: Limitations of zkVMs
Research
April 29, 2026
zkVMs: Offloading Computation for Programs in Mainstream Languages
Research
April 29, 2026
Why ZK Isn’t Really About Zero Knowledge - Part II: How Proofs Actually Work
Research
April 10, 2026
Why ZK Isn’t Really About Zero Knowledge - Part I: The Foundations Behind ZK Proofs
Research
April 10, 2026
Polynomial Commitment Schemes: FRI and KZG for Fast & Succinct Zero-Knowledge Proofs
Research
April 10, 2026
What Is Plonk...And Why?
Research
April 10, 2026
Inside ZK Systems: From Interactive Proofs to SNARKs
Research
April 10, 2026
Transaction Ordering in On-Chain Perpetual Markets
Research
April 10, 2026
Introducing Parasol: The Engine Making Solana the Onchain Perps Machine
Announcements
April 10, 2026