When Math Meets Auto Research with Bartosz Naskręcki

This week, Anna and Tarun are joined by Bartosz Naskręcki, mathematician and professor at Adam Mickiewicz University and researcher at the Centre for Credible AI, to explore how AI agents are transforming mathematical research. Bartosz shares his background in algebraic geometry and cryptography, and how he became involved in the ECDSA.fail competition. They discuss auto-research, the kinds of problems best suited to agent-driven exploration, and how collaborative competitions can accelerate discovery.   The conversation then turns to recent AI breakthroughs in mathematics, the challenges of verifying AI-generated proofs using tools like Lean, and the risk of AI research slop. Bartosz reflects on the changing role of mathematical intuition, the importance of keeping humans in the loop, and what these advances mean for the future of mathematics and the next generation of researchers.   Related Links Yukon.orgECDSA.fail ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor’s AlgorithmProving at Scale for Universal Algebra Mathematical discovery in the age of artificial intelligenceAI Grinding for Fun and CryptanalysisBartosz Naskręcki – Full Publication List FrontierMath: Benchmarking AI against advanced mathematical researchLeiden Declaration on Artificial Intelligence and MathematicsZK Podcast Episode 411: Auto Research on Yukon with Soubhik Deb      New from the Zero Knowledge Podcast and Succinct: the 2026 ZK Industry Report, a snapshot of ZK’s tech, research and real-world adoption. Free at zeroknowledge.fm/zk-industry-report-2026       **If you like what we do:** * Consider becoming a zkMesh+ Subscriber * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   Read transcript

This week, Anna and Nico catch up with Srinath Setty, researcher at Microsoft. They look back at his research since his work on Nova, spanning lattice-based folding, zero-knowledge identity proofs, and lookups and memory checking, much of which traces back to his 2019 work, Spartan. The bulk of the conversation is on Magnetar, his newly released zkVM. Built only on standard hash functions, it aims to be among the most secure general-purpose zkVMs, and it also turned out to be dramatically faster than many existing systems. Srinath explains how it’s put together, where the speed comes from, and what’s still left to build. Related links: Magnetar: High-speed post-quantum RV64 zkVM from standard hashesProof-based general-purpose computing with Magnetar(Microsoft Research blog)BinarySpartan: Spartan over binary fieldsSpartan: Efficient and general-purpose zkSNARKs without trusted setupNeo and SuperNeo: Post-quantum folding with pay-per-bit costs over small fieldsLatticeFold: A Lattice-based Folding Scheme and its Applications to Succinct Proof SystemsVega: Low-Latency Zero-Knowledge Proofs over Existing CredentialsUnlocking the lookup singularity with LassoJolt: SNARKs for Virtual Machines via LookupsTwist and Shout: Faster memory checking arguments via one-hot addressing and incrementsLigerito: A Small and Concretely Fast Polynomial Commitment SchemeArc: Accumulation for Reed-Solomon CodesWARP: Linear-Time Accumulation SchemesFlock: Fast Proving for Batch Boolean ComputationsZK Podcast: Nova and Beyond with Srinath SettyZK Podcast: Lattices, Folding, & Symphony with Binyi ChenZK Podcast: Episode 404 with Benedikt BünzZK Podcast: Episode 410 with Ron Rothblum     New from the Zero Knowledge Podcast and Succinct: the 2026 ZK Industry Report, a snapshot of ZK’s tech, research and real-world adoption. Free at zeroknowledge.fm/zk-industry-report-2026       **If you like what we do:** * Consider becoming a zkMesh+ Subscriber * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube Read transcript

This week, Anna is joined by Nico and Kobi to speak with Mathias Hall-Andersen and Giorgio Dell'Immagine from zkSecurity about zkGolf, a competition challenging humans and AI agents to build the most efficient, formally verified ZK circuits. They look back at ZK Hack puzzles and CTFs, exploring how AI is changing the nature of technical competitions. They then dive into Clean, zkSecurity's framework for writing and formally verifying circuits in Lean, and how an experiment using AI to optimize a SHA-256 circuit inspired zkGolf. They discuss how the zkGolf competition works, the breakthroughs and exploits participants have uncovered, how it compares to other AI-driven optimisation challenges, and what AI-assisted circuit development could mean for the future of ZK engineering and security audits.   Related Links   zkGolf Website Clean GitHub Repo Clean WebsiteLean Programming WebsiteZK HackYukon Website ZK Podcast: Auto Research on Yukon with Soubhik DebZK Podcast: Alex Ozdemir on where Theorem Provers and ZK meet ECDSA.fail  SNARK.fast Flock ChallengeThe Proximity Prize     Sovright builds the critical infrastructure that preserves your right to choose. Discover more at sovright.com.     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address Read transcript

This week, Anna and Guillermo chat with Josh Yang, CEO and co-founder of Brightlight Photonics, about the lasers that power quantum computers. Josh explains how lasers are used in neutral atom and other atom-based quantum systems to cool and move atoms, manipulate qubit states and read out results. They explore why these systems require so many different lasers and how today’s bulky, expensive optical setups can become a bottleneck as quantum computers scale. They also cover Brightlight’s work miniaturising the Ti:sapphire laser, a longstanding workhorse of quantum optics. Josh explains how integrated waveguides and semiconductor manufacturing techniques make this possible, the challenges of packaging and powering these tiny lasers, and how a more compact, versatile laser platform could better support quantum computing. This one is a departure from the usual topics covered on the show, but we hope you find it as fascinating as we did.   Related Links Brightlight PhotonicsJosh Yang Google Scholar ProfileEpisode 357: Quantum Engineering with Jelena VučkovićStanford Report: Chip-scale titanium-sapphire laser puts powerful technology in reach Titanium:Sapphire-on-insulator for broadband tunable lasers and high-power amplifiers on chipTitanium:sapphire-on-insulator integrated lasers and amplifiersMulti-dimensional data transmission using inverse-designed silicon photonics and microcombsBrightlight Photonics Images shared by Josh YangEpisode 400: Quantum Advances, Hybrid Signatures and SNARKs to the Rescue with Dan BonehEpisode 402: The Quantum Question Panel – Live from zkSummit14     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address Read transcript

This week, Anna, Tarun and Nico are joined by JP Aumasson, co-designer of BLAKE3, author of Serious Cryptography and cryptography engineer at Cloudflare. They revisit the quantum threat to cryptography, looking at recent advances in quantum attacks on RSA and elliptic-curve cryptography, and discuss why JP remains cautious about predictions of an imminent “Q-day.” They then explore how AI is changing cryptanalysis, from recent RSA factoring records to the growing divide between symmetric and asymmetric cryptography. The conversation then turns to Poseidon and recent attacks that have challenged confidence in ZK-friendly hash functions, as well as China’s new NGCC competition, where AI is already being used to find weaknesses in candidate designs. JP shares his experiments using AI for cryptanalysis, why it could accelerate both the building and breaking of cryptographic systems, and a introduces a project exploring AI-driven attacks on hash functions.   Related Links   Too Much Crypto by Jean-Philippe AumassonSecuring Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations Flock: Fast Proving for Batch Boolean ComputationsFlock ChallengePOSEIDON: A New Hash Function for Zero-Knowledge Proof Systems (Updated Version) Ngcc.devChinese NGCC Algorithms: The First Week of AI CryptanalysisJP Aumasson PapersYukon.orgZK Podcast Episode: The Quantum Question Panel – Live from zkSummit14!ZK Podcast Episode: Quantum Advances, Hybrid Signatures and SNARKs to the Rescue with Dan Boneh     Sovright builds the critical infrastructure that preserves your right to choose. Discover more at sovright.com.     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address Read transcript

This week, Anna is joined by Soubhik Deb, Head of Research at EigenLabs, to explore Yukon, a platform for collaborative AI-powered research. Soubhik traces the project’s origins to ECDSA.fail, a competition launched in response to Google’s work on more resource-efficient quantum circuits for breaking secp256k1. They discuss how researchers and their AI agents build on one another’s submissions, turning traditional research into a multiplayer process that can iterate at machine speed. The conversation then explores Yukon’s expansion into ZK proving, inference optimisation, coding theory and mathematics through challenges like SNARK.fast, better.codes, mlx.fast and lighter.fast. Soubhik explains the importance of well-defined problems and verifiers for AI-driven research, and shares Yukon’s vision for an “AI-native scientific institution” where humans and agents collaborate to accelerate discovery.   Related Links Yukon.orgECDSA.fail Flock ChallengeThe Proximity Prize (better.codes)Mlx.fastDarkbloomLighter Prover ChallengeECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor’s AlgorithmOptimized Point Addition Circuits for Elliptic Curve Discrete LogarithmsSecuring Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations ZK Podcast Episode: The Quantum Question Panel – Live from zkSummit14!ZK Podcast Episode: Quantum Advances, Hybrid Signatures and SNARKs to the Rescue with Dan Boneh     Sovright builds the critical infrastructure that preserves your right to choose. Discover more at sovright.com.     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address   Read transcript

This week, Anna and Kobi are joined by Ron Rothblum, Professor of Computer Science at Technion and researcher at Succinct. They catch up on Ron’s move from theory into practice, including his work on the SP1 zkVM, Jagged Polynomial Commitments, and a recent Fiat-Shamir attack that exposed vulnerabilities in practical uses of GKR. Ron explains what the attack revealed about Fiat-Shamir’s security assumptions and why it prompted changes to deployed systems.   The conversation then explores Ron’s recent work on faster and more efficient proof systems, from Blaze, TensorSwitch, BOLT and Veil to Flock, a proof system for batch proving Boolean computations. They discuss how new approaches to polynomial commitments and error-correcting codes can improve prover performance, before turning to snark.fast and zkGolf, experiments using AI agents to optimise provers and circuits. Ron shares what these efforts reveal about AI-assisted research and engineering, and how pushing proving closer to the speed of ordinary computation could unlock entirely new applications for verifiable computation.   Related Links Jagged Polynomial Commitments (or: How to Stack Multilinears)The Random Oracle Methodology, RevisitedBlaze: Fast SNARKs from Interleaved RAA Codes TensorSwitch: Nearly Optimal Polynomial Commitments from Tensor Codes Flock: Fast Proving for Batch Boolean Computations VEIL: Lightweight Zero-Knowledge for Hash-Based Multilinear Proof SystemsBolt: Faster SNARKs from Sketched CodeszkGolf WebsiteProving as Fast as Computing: Succinct Arguments with Constant Prover Overhead SNARK.fast WebsiteZK Podcast Episode: Error Correcting Codes & Information Theory with Ron RothblumFiat-Shamir via List-Recoverable Codes (or: Parallel Repetition of GMW is not Zero-Knowledge) Delegating Computation: Interactive Proofs for MugglesHow to Prove False Statements: Practical Attacks on Fiat-Shamir         **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address Read transcript

This week, Anna catches up with Richard Liang from Peer, formerly ZKP2P. They trace the project’s evolution over the past two years, from their initial ZKP2P product that used ZK email proofs to connect Venmo payments with on-chain USDC, to their use of ZK TLS, and most recently, their move to using TEEs (trusted execution environments) and the rebrand to Peer. Richard breaks down what motivated each shift and how the team has navigated the trade-offs around privacy, speed, and UX. The conversation then explores Peer’s current approach to connecting traditional payment platforms and stablecoins, including why “ephemeral privacy” makes TEEs a compelling fit for their use case and what the move away from ZK has unlocked. Richard and Anna also reflect on the broader evolution of ZK from an experimental technology into infrastructure that increasingly underpins real world applications. Finally, they discuss Peer’s expansion into payments, its ambitions to support more currencies and fintech platforms around the world, and how AI is changing both the team’s development process and the possibilities for agentic payments.   Related Links Peer X Profile Peer Pay X ProfilePeer WebsiteAnnouncement of ZKP2P becoming PeerPeer Docs RepoZK Podcast: ZKP2P with Brian and RichardZK Hack Lisbon 2023ZK EmailZK Podcast: Is ZK dead? Or has it just begun? With the ZK Pod co-hosts     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address Read transcript

This week, Anna and Guillermo are joined by Patrick O'Grady, founder of Commonware. They discuss his journey from Coinbase and Avalanche to building Commonware, a Rust library of composable primitives for blockchain development. They explore Commonware's "anti-framework" philosophy, why it gives developers control over every layer of the stack, and how its modular approach differs from traditional blockchain SDKs.   The conversation then turns to consensus research, examining how changing assumptions around Byzantine fault tolerance have unlocked faster consensus designs. Patrick explains the motivation behind Commonware's new protocols, Minimmit and Multimmit, discusses the influence of Simplex and Solana's Alpenglow, and shares how Commonware combines engineering, research, and cryptography to build the next generation of blockchain infrastructure.   Related Links CommonwareMinimmit: Fast Finality with Even Faster BlocksCommonware blog post announcing MinimmitSimplex Consensus: A Simple and Fast Consensus Protocol Commonware docs - Simplex ConsensusPatrick O’Grady’s X Post on Multimmit (July 2026)Multimmit: Extending Blocks for Faster Finality (draft)Alpenglow GitHub Progress UpdatesGolden: Lightweight Non-Interactive Distributed Key Generation     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address Read transcript

In this episode, Anna and Kobi are joined by Alex Hoover, cryptographer and Assistant Professor at Stevens Institute of Technology. They explore Private Information Retrieval (PIR)—a cryptographic primitive that lets users query public databases without revealing what they're looking for.   They trace PIR's evolution from its early theoretical foundations to modern, practical constructions, unpack key variants like batch and keyword PIR, and discuss emerging blockchain applications, from private state queries to Merkle proof generation. They also examine the latest research making PIR increasingly practical, and why it could become a core building block for privacy-preserving systems.   A quick note: Alex mentioned during the interview that preprocessing in SimplePIR is independent of the database. But it is in fact independent of the queried index, and does depend on the database. He asked us to highlight this correction   Related Links One Server for the Price of Two: Simple and Fast Single-Server Private Information RetrievalDon’t be Dense: Efficient Keyword PIR for Sparse DatabasesThe two papers that introduced client-side preprocessing:PPY18CK20 Piano: Extremely Simple, Single-Server PIR with Sublinear Server Computation  Simple and Practical Amortized Sublinear Private Information Retrieval using Dummy Subsets  Plinko: Single-Server PIR with Efficient Updates via Invertible PRFs (builds on Piano and RMS)  Doubly Efficient Private Information Retrieval and Fully Homomorphic RAM Computation from Ring LWE (LMW23)  Lower Bounds for PIR with Preprocessing from Blackbox Cryptography     **If you like what we do:** * Find all our links here! @ZeroKnowledge | Linktree * Subscribe to our podcast newsletter * Follow us on Twitter @zeroknowledgefm * Join us on Telegram * Catch us on YouTube   **Support the show:** * Patreon * ETH - Donation address * BTC - Donation address   Read transcript