The chapter delves into the concept of logarithmic derivative lookups and their potential applications in CKVM protocols. The speakers discuss the advantages of encoding witness data elements as poles instead of zeros, and the use of fractional decomposition and logarithmic derivatives in cryptography. They also explore the connection between Fast Reed-Solomon Interactive Oracle Proofs (FRI) and recursion to lookups, as well as the improvements made in log up commitment schemes and the reduction of lookup arguments.
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.
Here’s some additional links for this episode:
- A summary on the FRI low degree test by Ulrich Haböck
- Brakedown's expander code by Ulrich Haböck
- Improving LogUp with GKR - By Ulrich from Polygon
- Improving logarithmic derivative lookups using GKR by Papini and Haböck
- flookup: Fractional decomposition-based lookups in quasi-linear time independent of table size by Gabizon and Khovratovich
- Bulletproofs++: Next Generation Confidential Transactions via Reciprocal Set Membership Arguments by Eagen Kanjalkar, Ruffing and Nick
- Nearly Linear-Time Zero-Knowledge Proofs for Correct Program Execution by Bootle, Cerulli, Groth, Jakobsen and Maller
- Understanding Lasso and Jolt, from theory to code
- ZK8: Hyperplonk: PLONK without FFTs and with high degree gates - Benedikt Bünz
- ZK9: logUp - Lookup arguments based on the logarithmic derivative - Ulrich Haböck
- ZK10: Degree tricks in DEEP STARKs - Shahar Papini
- Orion: Zero Knowledge Proof with Linear Prover Time by Xie, Zhang and Song
- Reed-Solomon Codes over the Circle Group by Haböck, Lubarov and Nabaglo
- Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS by Chiesa, Hu, Maller, Mishra, Vesely and Ward
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