Zero Knowledge lean Ethereum Part 3: Security of PQ SNARKs and an update about the Proximity Prize
Mar 4, 2026
Antonio Sanso, cryptography researcher at the Ethereum Foundation, and Giacomo Fenzi, EPFL PhD in coding theory, discuss post-quantum SNARK security. They cover hash-based proof systems, LeanVM’s multilinear sumcheck design, and the $1M Proximity Prize spurring work on proximity gaps, correlated agreement, and list-decoding. They also talk about recent papers shifting some guarantees from conjectural to computational security.
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LeanVM Chooses Multilinear SNARKs
- LeanVM and post-quantum signature aggregation use a multilinear, sumcheck-oriented SNARK stack rather than classic univariate quotient SNARKs.
- Giacomo explains LeanVM layers Super Spartan with LogUp/LogUp Star and multilinear optimizations to suit hash-based proof systems.
Proximity Prize Sparked Rapid Research
- The $1M Proximity Prize aimed to formalize and spur research on proximity gap conjectures underlying hash-based SNARK security.
- Antonio and Giacomo served as judges and saw rapid paper influx addressing distance-preservation and batching properties.
Johnson Bound Left A Critical Unknown Region
- Before the recent papers, security was provable below the Johnson bound and hopeless past capacity; the middle region was unknown.
- This unknown “middle” is where new results either reduce or extend provable guarantees for SNARK batching.