From f4f8d6a02ceab40a166269ccf2fb418aed45fd1e Mon Sep 17 00:00:00 2001 From: Balazs Komuves Date: Tue, 25 Feb 2025 15:01:10 +0100 Subject: [PATCH] add a description of the duplex algorithm in the commentary --- commentary/Challenges.md | 78 ++++++++++++++++++++++++++++++++++++-- commentary/commentary.pdf | Bin 482705 -> 488340 bytes 2 files changed, 75 insertions(+), 3 deletions(-) diff --git a/commentary/Challenges.md b/commentary/Challenges.md index b46b8aa..0e5dd13 100644 --- a/commentary/Challenges.md +++ b/commentary/Challenges.md @@ -7,7 +7,7 @@ This uses the hash permutation in a duplex construction, alternatively absorbing All the challenges in the proof are summarized in the following data structure -``` +```rs struct ProofChallenges, const D: usize> { plonk_betas: Vec, // Random values used in Plonk's permutation argument. plonk_gammas: Vec, // Random values used in Plonk's permutation argument. @@ -20,7 +20,7 @@ struct ProofChallenges, const D: usize> { And the FRI-specific challenges are: -``` +```rs struct FriChallenges, const D: usize> { fri_alpha: F::Extension, // Scaling factor to combine polynomials. fri_betas: Vec, // Betas used in the FRI commit phase reductions. @@ -31,7 +31,79 @@ struct FriChallenges, const D: usize> { ### Duplex construction -TODO +The duplex construction is similar the sponge construction, but it interleaves absorbing and squeezing. This is a very natural fit for Fiat-Shamir, as these are exactlty the operations we do: + +- absorb the prover's message (transcript so far); +- then generate some challenges; +- then the prover replies with more messsages; +- based on which we generate more challenges; +- and so on... + +We have to be careful with the details though. + +To have a nice API, we want an API which can absorb and generate various data types (Goldilocks elements, field extension elements, hash digests, etc). + +The duplex can be modelled as a state machine: + +- We are either in absorbing or squeezing mode. +- In absorbing mode, we just collect inputs in a buffer +- In squeezing mode, we have a buffer initialized by `rate` elements of the state, from which we can produce outputs, until it becomes empty; then we do a permutation which refills the buffer +- When switching from absorbing mode to squeezing mode, we absorb the collected buffer exactly like a sponge. + +#### Duplex algorithm pseudo code + +```hs +type State = [F] + +permute :: State -> State +permute = ... + +rate = 8 + +data DuplexState + = Absorbing State [F] + | Squeezing State [F] + +initialDuplexState = Absorbing zeroState [] + +-- Absorb an element +absorb :: F -> DuplexState -> DuplexState +absorb what duplex = case duplex of + Absorbing state list -> Absorbing state (list ++ [what]) + Squeezing state _ -> Absorbing state [what] + +-- Squeeze an element +squeeze :: DuplexState -> (F, DuplexState) +squeeze duplex = case duplex of + Absorbing state list -> squeezing (sponge list state) + Squeezing state buf -> case buf of + [] -> squeezing (permute state) + (y:ys) -> (y, Squeezing state ys) + +-- Helper function +squeezing :: State -> (F, DuplexState) +squeezing state = squeeze $ Squeezing state (extract state) + +-- Classic sponge in overwrite mode +sponge :: [F] -> State -> State +sponge = go where + go [] state = state + go list state = case splitAt rate list of + (this,rest) -> go rest (permute $ overwrite this state) + +-- Plonky2 uses "overwrite mode" +overwrite :: [F] -> State -> State +overwrite input state + | k > rate = error "overwrite: expecting at most `rate` elements" + | otherwise = input ++ drop k state + where + k = length input + +-- The reverse is because Plonky2 uses `pop` (from the end of) the buffer +extract :: State -> [F] +extract = reverse . take rate + +``` ### Transcript diff --git a/commentary/commentary.pdf b/commentary/commentary.pdf index 9159922d889d1e572a4556c66f6d595c4ae52319..6a50dd3738339bf63ea61a2c36d18ea8d486ddc7 100644 GIT binary patch delta 122841 zcmV)IK)k<^yB(D09k40m135Q1lkv_ee;R9V8#nU1f5m<~8Hs3exzC^|khXD=Hn^sV z(JyTgP%FwJvJYh+v6Vybx8IO6D{EJ_V@q+<0}Ke_lFJzm=S|LX@7&|wk4K!^@6L`+ zPJ_@(SsM9~cee0^lq`-CFA8Jk%g{TUd%sWKR$VzSb<-UGdG^!EsSLIO8214efA_={ ztV~!Ez}sQ~JC$KNF}98PWM*0%Xls)l`|;%c8vC>3sh>>rv6y74Yc$TT7BqQD15Kgw z9LN6PGSK;)9Zy3UOkU?z`F`!=D}blv6b=;TvhC_Cq_CZ9H{eGsNd<18QN=1Z<+;Tm zCyTl&@JV4q%VS4hwz_OgRnnA_f5vOOpB3&*wVFm@-^pYN8`0&tBNWEkia;GxmPUU( 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