lean Ethereum Part 3: Security of PQ SNARKs and an update about the Proximity Prize

https://youtu.be/v8SGKS3T-3A In this episode, Nico Mohnblatt speaks with Giacomo Fenzi from EPFL and Antonio Sanso from the Ethereum Foundation. For this 3rd instalment of the lean Ethereum miniseries, they talk about the theory and security behind post-quantum SNARKs. They dive into the hash-based proof systems underpinning LeanVM, multilinear approaches like sumcheck, and how these fit into Ethereum's post-quantum upgrades. They cover the $1M Proximity Prize and the recent wave of papers on proximity gaps, correlated agreement, and list decoding. From negative results near the Elias bound to breakthroughs beyond the Johnson bound for certain codes, the discussion explores how new results slightly degrade conjectural security, why the 128-bit threshold still matters, and what it means to move from conjectural to provable security in large-scale systems like Ethereum. Related Links

• lean Ethereum Part 1: Introduction with Justin Drake
• lean Ethereum Part 2: PQ Signatures and Poseidon with Dmitry and Benedikt
• lean Ethereum
• Lean Consensus R&D Progress
• leanSig Implementation
• Poseidon2: A Faster Version of the Poseidon Hash Function
• On Proximity Gaps for Reed–Solomon Codes
• Proximity Gaps in Interleaved Codes
• On Reed–Solomon Proximity Gaps Conjectures
• Optimal Proximity Gaps for Subspace-Design Codes and (Random) Reed-Solomon Codes
• All Polynomial Generators Preserve Distance with Mutual Correlated Agreement

Additional Resources

• Soundcalc GitHub
• Proximity prize
• On the Distribution of the Distances of Random Words
• Small-field hash-based SNARGs are less sound than conjectured by Fenzi and Sanso
• WHIR: Reed–Solomon Proximity Testing with Super-Fast Verification
• STIR: Reed–Solomon Proximity Testing with Fewer Queries
• Linear-Time Accumulation Schemes
• TensorSwitch

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