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zYWkM?CArz8)$_R-$-+|45M|#rhS$3N;3{I~nfQ>8BtBL=KndAJNnuhsHbGcugB_o( z`SV)$DN2yOaXLBmNU63T-Y62gyaPF=12RC@U71L&V~R%Fd`uS01!hrV)a`Z9cwdnb zC2IzQK&C@{K_jFvw)yr~yGD#gHs;lOFFxOK<4R5SO&$T1TJ^VyD21A6;%^Tm->pG( zdlSm3b<=B4aZ#0U8(8D;XEPFWR`c??&6qK*MgMFc#Hvv7nxYF`XbiGPjMNr?MT=?N znpG|2{)|ZH`)r=Spln||R|CCg5iSswmD8OoYpH_#xxC!4sU(p@U7k%d@2-ThbjhHu z*08ti^rM-4Arjf&s>*ZZdCd*C@x0D#7&_nay9FB@E^4QWnv7~JaEP5v`ip3Lcv)=x zKAw^~oHbC=x_v6+(99Sh)CF=_dihQ3$d!5DcTMru7mtoqI`_%mxO-I+w_!mC`$`Xt zLY-bE76l-vHl|pgiRDAg7Vi*F-e)qIk zylDohCWM{-CuS9k4(3r%Gp7;XFd+9+!_e!qMo(Y+5Up}L9fqzUp~t~QcgbHW#B zhgi->iu@PeJod+$u)9D_juzlO{9O%_`djZRjij=sf#o3{OD{;Cig&T3@+fHBOxsk5 zE~M);#Rt4U6x&;L8ty>P$8*MurnMZUgvioHF@am56xT%Azgj{*?9J3Hp`G8U*>E_4 z{>9${WtXU#&%-TwD|XXH@>5>R$?vGo9w@sW{B-nxJoxcYdi#Yi$sh0E=Wzeb`N>ji znATWbVLfB<^G^alCUz0KUM|h+Kc|^)2~@;55U9SiCrWSS%3hO#W)F=t<_XStarknet STARK Verifier

Short Name: starknet-stark

State of This Document: draft

-

Updated: October 17, 2024

+

Updated: October 18, 2024

View RFC @@ -30,7 +30,7 @@

Starknet FRI Verifier

Short Name: starknet-fri

State of This Document: draft

-

Updated: October 17, 2024

+

Updated: October 18, 2024

View RFC @@ -42,7 +42,7 @@

Starknet Merkle Tree Polynomial Commitmen

Short Name: starknet-commit

State of This Document: draft

-

Updated: October 17, 2024

+

Updated: October 18, 2024

View RFC @@ -54,7 +54,7 @@

Starknet Channels for Fiat-Shamir Instant

Short Name: starknet-channel

State of This Document: draft

-

Updated: October 17, 2024

+

Updated: October 18, 2024

View RFC diff --git a/rfcs/starknet/fri.html b/rfcs/starknet/fri.html index b4c3737..dab58a2 100644 --- a/rfcs/starknet/fri.html +++ b/rfcs/starknet/fri.html @@ -286,14 +286,14 @@

FRI-PCS

Specifically, FRI-PCS proves that they can produce such a (commitment to a) polynomial q.

-

Aggregating multiple FRI proofs

+

Aggregating Multiple FRI Proofs

To prove that two polynomials a and b exist and are of degree at most d, a prove simply prove that a random linear combination of a and b exists and is of degree at most d.

TODO: what if the different polynomials are of different degrees?

TODO: we do not make use of aggregation here, the way the first layer polynomial is created is sort of transparent here, is it still worth having this section?

-

Notable differences with vanilla FRI

+

Notable Differences With Vanilla FRI

Besides obvious missing implementation details from the description above, the protocol is pretty much instantiated as is, except for a few changes to the folding and querying process.

As explained above, in the "vanilla FRI" protocol the verifier gets evaluations of p0(v) and p0(v) and computes the next layer's evaluation at v2 as

pi+1(v2)=pi(v)+pi(v)2+ζipi(v)pi(v)2v diff --git a/rfcs/starknet/stark.html b/rfcs/starknet/stark.html index 8bf4002..70f37cd 100644 --- a/rfcs/starknet/stark.html +++ b/rfcs/starknet/stark.html @@ -79,7 +79,6 @@

Overview

-

In this section we give an overview of the STARK protocol.

+

In this section we give a brief overview of the Starknet STARK protocol.

+

The protocol is divided in three main parts, which we will explain in more detail below:

STARK overview

AIR Arithmetization

-

TKTK

+

But first, we quickly remind the reader that the Starknet STARK protocol allows a prover to convince a verifier that an AIR (Algebraic Intermediate Representation) arithmetization is satisfied by their witness. This is generally augmented to also include a public input, usually via a public memory extension.

+

AIR is essentially an indexed table of runtime values, on which a number of fixed constraints are agreed on:

+

air

Interactive Arithmetization

TKTK

+

Composition Polynomial

+

TKTK

+
+

Constraints To Prove

+

TKTK

+
+
+

Composition Polynomial and Schwartz-Zippel

+

TKTK

+
+
+

Evaluations And Evaluation Proofs

+ +
+
+
+

Aggregation and FRI Proof

+ +
+

STARK

TKTK

diff --git a/source/starknet/fri.md b/source/starknet/fri.md index 6209640..3b78dc4 100644 --- a/source/starknet/fri.md +++ b/source/starknet/fri.md @@ -255,7 +255,7 @@ $$ Specifically, FRI-PCS proves that they can produce such a (commitment to a) polynomial $q$. -### Aggregating multiple FRI proofs +### Aggregating Multiple FRI Proofs To prove that two polynomials $a$ and $b$ exist and are of degree at most $d$, a prove simply prove that a random linear combination of $a$ and $b$ exists and is of degree at most $d$. @@ -263,7 +263,7 @@ TODO: what if the different polynomials are of different degrees? TODO: we do not make use of aggregation here, the way the first layer polynomial is created is sort of transparent here, is it still worth having this section? -## Notable differences with vanilla FRI +## Notable Differences With Vanilla FRI Besides obvious missing implementation details from the description above, the protocol is pretty much instantiated as is, except for a few changes to the folding and querying process. diff --git a/source/starknet/stark.md b/source/starknet/stark.md index 3732002..ea41ddc 100644 --- a/source/starknet/stark.md +++ b/source/starknet/stark.md @@ -11,8 +11,6 @@ tags: ["starknet", "stark", "ethSTARK"] -In this section we give an overview of the STARK protocol. - +In this section we give a brief overview of the Starknet STARK protocol. + +The protocol is divided in three main parts, which we will explain in more detail below: + ![STARK overview](/img/starknet/stark_overview.png) ### AIR Arithmetization -TKTK +But first, we quickly remind the reader that the Starknet STARK protocol allows a prover to convince a verifier that an AIR (Algebraic Intermediate Representation) arithmetization is satisfied by their witness. This is generally augmented to also include a public input, usually via a [public memory](https://zksecurity.github.io/stark-book/cairo/memory.html) extension. + +AIR is essentially an indexed table of runtime values, on which a number of fixed constraints are agreed on: + +![air](/img/starknet/air.png) ### Interactive Arithmetization TKTK +### Composition Polynomial + +TKTK + +#### Constraints To Prove + +TKTK + +#### Composition Polynomial and Schwartz-Zippel + +TKTK + +#### Evaluations And Evaluation Proofs + +* we use FRI-PCS as described in [the FRI-PCS section of the Starknet FRI Verifier Specification](fri.html#fri-pcs). + +### Aggregation and FRI Proof + +* we use FRI Aggregation as described in [the Aggregating Multiple FRI Proofs section of the Starknet FRI Verifier Specification](fri.html#aggregating-multiple-fri-proofs). +* we use FRI as described in [the Starknet FRI Verifier Specification](fri.html). + ### STARK TKTK