SEASON 3 MODULE 5
The Ligero Proof System, w/ Muthu Venkitasubramaniam
In this module, Guillermo Angeris and Muthu Venkitasubramaniam, Co-founder at Ligero Inc, professor at Georgetown University and co-author of the original Ligero paper, deliver a comprehensive technical walkthrough of the Ligero proof system. After situating Ligero within the broader landscape of zero-knowledge proof constructions, Muthu introduces the MPC-in-the-head approach. Using this framework, he explains the Ligero proof system in detail, walking through its use of packed secret sharing, its constraint system, and the three core tests—proximity, multiplication, and linear—that ensure its correctness. Finally, he discusses practical considerations, including how Ligero achieves zero-knowledge, succinct verification, and memory efficiency, making it suitable for client-side proving on resource-constrained devices
What you’ll learn:
- 00:00 Introduction, Session Outline, and the OGs of Cryptography
- 04:36 Introducing Knowledge Act
- 07:33 Defining Zero Knowledge
- 18:55 Defining MPC (Multi-Party Computation)
- 25:46 The “MPC in the Head” Paradigm
- 33:39 Ligero Preliminaries: Secret Sharing
- 40:05 Ligero Proof System: System of Equations
- 47:08 The Three Core Tests of Ligero: Proximity, Multiplication, and Linear Tests
- 55:48 Soundness Argument for Ligero
- 1:02:44 Fixing the Linear Test
- 1:09:22 Achieving Zero Knowledge with Masking Rows
- 1:14:08 Making Ligero into a Pre-Processing SNARK
- 1:18:16 On Memory Efficiency and Client-Side Proving
- 1:25:15 Summary and Conclusion
Below is an accompanying reading list:
- Silvio Micali: Proofs, Knowledge, and Computation (Berkeley ACM A.M. Turing Laureate Lecture): https://www.youtube.com/watch?v=WSuUTLqqLIU
- Goldwasser defines zero knowledge proofs: https://www.youtube.com/watch?v=DfJ8W49R0rI
- Probabilistic encryption (Shafi Goldwasser and Silvio Micali, 1984): https://www.sciencedirect.com/science/article/pii/0022000084900709
- The Knowledge Complexity of Interactive Proof Systems (Shafi Goldwasser, Silvio Micali and Charles Rackoff, 1986): https://epubs.siam.org/doi/10.1137/0218012
- Zero-Knowledge from Secure Multiparty Computation (Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky and Amit Sahai, 2007): https://web.cs.ucla.edu/~rafail/PUBLIC/77.pdf
- Introduction to Secure Multi Party Computation (Yuval Ishai, The 10th BIU Winter School on Cryptography, 2020): https://www.youtube.com/watch?v=xwxkp4fMWsk
- Actively Secure Garbled Circuits with Constant Communication Overhead in the Plain Model (Carmit Hazay, Yuval Ishai, and Muthuramakrishnan Venkitasubramaniam, 2017): https://eprint.iacr.org/2017/947
- Ligero: Lightweight Sublinear Arguments Without a Trusted Setup (Scott Ames, Carmit Hazay, Yuval Ishai, Technion, Muthuramakrishnan Venkitasubramaniam, 2022): https://eprint.iacr.org/2022/1608
- Communication complexity of secure computation (Matthew Franklin and Moti Yung, 1992): https://dl.acm.org/doi/10.1145/129712.129780
- Ligerito: A Small and Concretely Fast Polynomial Commitment Scheme (Andrija Novakovic and Guillermo Angeris, 2025): https://eprint.iacr.org/2025/1187
ZK Whiteboard Sessions is an educational series on all things zero knowledge. Presented by ZK Hack.
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