From bd05a5a6f4211de0da60ef33547bc8c364be841f Mon Sep 17 00:00:00 2001 From: Balazs Komuves Date: Sun, 9 Feb 2025 12:20:06 +0100 Subject: [PATCH] add an FRI verifier summary in the commentary --- commentary/FRI.md | 14 ++++++++++++++ commentary/Lookups.md | 2 +- commentary/commentary.pdf | Bin 480569 -> 482705 bytes 3 files changed, 15 insertions(+), 1 deletion(-) diff --git a/commentary/FRI.md b/commentary/FRI.md index f483c6f..b303656 100644 --- a/commentary/FRI.md +++ b/commentary/FRI.md @@ -230,6 +230,20 @@ As what we really want to compute is $\sum_k \beta^k P_k(x_0^8)$, we can see tha This can be reinterpreted as interpolating a degree `arity-1` polynomial from these values, and evaluating it at $\beta$, and indeed this is how Plonky2 implements it. +### FRI verifier summary + +So what does the verifier needs to check at the end? + +- check if the public parameters match the proof "shape" (arities, number of query rounds, Merkle cap sizes, etc) +- check the proof-of-work response +- then for each query round: + - check the initial tree Merkle proofs against the 4 commitments (constants, witness, partial products and quotient) + - compute the evaluation of the combined polynomial from these values (a single row) at the query location + - for each folding step: + - check the coset opening proof against the corresponding commit phase Merkle cap + - check if the right element in the coset values matches the evaluation coming from the previous step (in the very first step, against the above compute value) + - calculate the folded value, and pass it to the next step + - check the final folded value against the evaluation of the final polynomial ### FRI verification cost diff --git a/commentary/Lookups.md b/commentary/Lookups.md index f1ea1fc..b734b5c 100644 --- a/commentary/Lookups.md +++ b/commentary/Lookups.md @@ -132,7 +132,7 @@ Lookup tables are encoded in several `LookupTable` gates, which are just below e +---------------+ | .... | -Both type of gates are padded if necessary to get full rows. The `Lookup` gates are padded with the first entry in the corresponding table, while the `LookupTable` gates are padded with zeros (which is actually a soundness bug, as now you can prove that `(0,0)` is an element of any table whose length is not divisible by 26). +Both type of gates are padded if necessary to get full rows. The `Lookup` gates are padded with the first entry in the corresponding table, while the `LookupTable` gates used to be padded with zeros (which was actually a soundness bug, as you could prove that `(0,0)` is an element of any table whose length is not divisible by 26), but this was fixed in [commit 091047f](https://github.com/0xPolygonZero/plonky2/commit/091047f7f10cae082716f3738ad59a583835f7b6), and now that's also padded by the first entry. ### Lookup selectors diff --git a/commentary/commentary.pdf b/commentary/commentary.pdf index 46b55e32960755890bcdf6dd1e1af3810d45f2f7..9159922d889d1e572a4556c66f6d595c4ae52319 100644 GIT binary patch delta 71378 zcmZs?Q+S|Vux=aMwr$%^$F^;=lYFtwj&0kv*-6Lh*k&jDU;A9G=j^+>ns@com~V~h ztRhV6CTzH#183)9OSzk)1#}b={IO z9bKi5CHs0&_X|m4RhDsFp5<-F9f~t8ztbd-R=pTva#D29%RIl}9{}H;KOaukqRlN- z=*pTlyJP88tdnS&;1v}-yJrJ*{oB9Zp7k1vGwFWJ#g==V#=(4$9|Be3yMDl)i7Hjd&V5;17;IW*X!8kEEr{Sb8P)ABnw5*l+%!}T*$T&OAvj$2Z_iw}Iju1lyfO36U~7KVB1v2kk$@2Y%J1tj zELkW@%VaBzyariGUZq*2oIR32RuV&#ieD6gnA8`c)zv(7{WQ{}8U&bY&g%NZDtB)L z8W}uQiN&Uqz+xDeYVCeK7V4d2UuW;z)0i#Yr1coZK(Li+TB2~K0}{9JKlvuco)0c^ zWh;f}K^-E2ec878fQ~n8F5BkOA$c^SMW4c0a*I+y|AP0hX{aFn;nlwO6~~$ZC+CPn{T50vD9F7?J@yC~Va27

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