Very excited to introduce Khatam (eprint 2024/1843): a new Proximity Gaps result for Multilinear Polynomial Commitment Schemes. Not only does it reduce the size of Basefold (including over Random Foldable Codes), but it also improves Blaze, WHIR, Ligero, and others. 🧵(1/x).

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RT @zeroknowledgefm: @idocryptography presents Blaze at zkSummit - a new multilinear polynomial commitment scheme (MLPCS) for binary fields….

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This exactly matches the proof size of FRI for small fields, is ~25% improvement over the previous Khatam results and a ~50% improvement over the original BaseFold result. If using large fields or proof-of-work, BaseFold over RS codes matches FRI using (2024/1571) cc @UHaboeck.

- When you are using codes that are not Reed-Solomon.- If you don't want to use proof-of-work but you still want to use small fields (e.g. 128-bit field). Alternatives only allow ~190bit fields or proof-of-work, which lengthens prover time.

Presenting a new improved Khatam result showing BaseFold secure within one-and-a-half Johnson bound! ( with very small error probability < 2/eps^{2}|\FF}, which significantly improves recent work (2024/1810). Concretely, when to use these results? 🧵.

RT @Charles_Chen533: Excited by LatticeFold+(, a joint work with @danboneh for constructing post-quantum secure and….

RT @benafisch: Blaze will be in Eurocrypt 2025 🇪🇸. Blaze is a multilinear polynomial commitment with ultra-efficient proving over binary fi….

RT @Dan_Jeffries1: As we are learning DeepSeek is one of the most sophisticated psyops of all time. Here's how it went down:. 1) Release….

RT @TheBealDeal: Excited to share Mira, a new folding scheme for pairing-based arguments. Mira enables efficient proof aggregation for Grot….

Jokes aside - I feel lucky to be apart of such a talented community of researchers, and this experience has taught me a valuable lesson in trusting the process of research. (end).

This thread is dedicated to the SBC reviewer who rejected Basefold because they were "skeptical this technique will ever be useful due to its proof size" :) (6/x).

Now Basefold matches FRI proof size in nearly all settings. One is still missing - the 1.5 Johnson Bound, but at this point, I think it's a matter of weeks, and other concurrent work (2024/1810) has potentially already made a lot of progress towards that. (5/x).

that Basefold over RS codes matches the best results of FRI.2) @YanpeiGuo et. al. publishes a paper showing that Deep-FRI can be applied to Basefold over RS codes, another setting where Basefold matches FRI. Nov '24: Khatam published (4/x).

Nov '23: Basefold published, a field-agnostic Multilinear PCS with identical performance to univariate PCS (enabling more efficient SNARKs) with one caveat: It's proof size was still a few times larger than FRI.Oct '24: 1) @UHaboeck publishes a result showing (3/x).

Currently, the write-up presents the new proof - Soon, it will also contain the concrete improvements to various multilinear PCS. There has been a flurry of activity surrounding Basefold + Proximity Gaps lately so here's a timeline to summarize: (2/x).

RT @fermatslibrary: 2¹³⁶²⁷⁹⁸⁴¹−1, discovered today, is the largest known prime. It's a Mersenne prime (2ᵖ-1), which are easier to find. It….