Ulrich Haböck, an applied cryptographer at Polygon Labs, talks about his journey into applied zero-knowledge cryptography, his breakthrough research on Multivariate lookups with logUp, and his innovative approaches to STARKs over finite fields. They discuss FRI low degree test, logarithmic derivative lookups using GKR, and the advantages of the Mer Senn 31 Prime. A deep dive into the complexities and breakthroughs in applied cryptography.
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Quick takeaways
Ulrich Habak's journey into applied ZK cryptography and his contributions to the field.
Ulrich Habak's work on log-up as an improvement to lookup arguments using logarithmic derivatives.
The use of Mersenne 31 Prime and its complex extension for FFT-friendly fields in cryptographic protocols.
Deep dives
Exploring Applied ZK Cryptography and the Decentralized Web
Ulrich Habak, an applied cryptographer at Polygon Labs, discusses his journey into applied ZK cryptography. He highlights the contributions he has made to the field, including write-ups and manuscripts on topics like fry, breakdown, multivariate look-ups, and logarithmic derivative look-ups. The discussion also touches on his work at Polygon Labs on Starks over finite fields. Additionally, Ulrich mentions the upcoming ZKHAC 4 virtual event, which focuses on showcasing the state-of-the-art in tooling for ZK builders.
Learning Cryptography Through Teaching and Exploration
Ulrich Habak shares his journey into cryptography, which began through teaching positions he held at a university. He explains how he shifted his focus to cryptography by teaching math and cryptography-related topics and later discovered his passion for the field. Through his work at Horizon Labs and Polygon Labs, he further expanded his expertise in cryptographic protocols, including the use of SNARKs and logarithmic derivatives. Ulrich emphasizes the versatility and immediate usefulness of cryptography in practice, which drove his interest in industry.
Improving Lookups with Logarithmic Derivatives
Ulrich Habak discusses his work on log-up, an improvement to lookup arguments using logarithmic derivatives. He explains the benefits of using logarithmic derivatives in lookup arguments and the advantages they offer in terms of efficiency and scalability. Ulrich also mentions the ongoing collaboration with Stockware on further advancements in this area.
Exploring Mersenne 31 Prime and FFT-Friendly Fields
Ulrich Habak explores the use of Mersenne 31 Prime and its complex extension for FFT-friendly fields. He highlights the advantages of using this field in polynomial IOPs and the efficiency it offers in terms of FFT computations. Ulrich also discusses ongoing work on Planck E3, which incorporates Mersenne 31 and FFT-friendly fields.
Ongoing Research and Collaborations
Ulrich Habak mentions ongoing work on Planck E3 and collaborations with Stockware. He hints at upcoming developments in the field of CKs and FFT-friendly fields, while emphasizing the challenges of benchmarking and advertisement in the cryptography research community.
In this week’s episode, host Anna Rose and cohost Nico Mohnblatt catch up with Ulrich Haböck, an applied cryptographer at Polygon Labs. This episode revolves around Ulrich’s journey into applied zero-knowledge cryptography, transitioning from an academic environment to being a full-time practitioner. They discuss his contributions to the field, including his many write-ups and manuscripts as well as his breakthrough research on Multivariate lookups with his work logUp. They also cover his work on logarithmic derivative lookups using GKR with Shahar Papini, as well as his innovative approaches to STARKs over finite fields that are not ‘NTT-friendly’. This episode offers a deep dive into the complexities and breakthroughs in applied cryptography.
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