HackMD
  • Prime
    Prime  Full-text search on all paid plans
    Search anywhere and reach everything in a Workspace with Prime plan.
    Got it
      • Create new note
      • Create a note from template
    • Prime  Full-text search on all paid plans
      Prime  Full-text search on all paid plans
      Search anywhere and reach everything in a Workspace with Prime plan.
      Got it
      • Sharing Link copied
      • /edit
      • View mode
        • Edit mode
        • View mode
        • Book mode
        • Slide mode
        Edit mode View mode Book mode Slide mode
      • Note Permission
      • Read
        • Only me
        • Signed-in users
        • Everyone
        Only me Signed-in users Everyone
      • Write
        • Only me
        • Signed-in users
        • Everyone
        Only me Signed-in users Everyone
      • More (Comment, Invitee)
      • Publishing
        Everyone on the web can find and read all notes of this public team.
        After the note is published, everyone on the web can find and read this note.
        See all published notes on profile page.
      • Commenting Enable
        Disabled Forbidden Owners Signed-in users Everyone
      • Permission
        • Forbidden
        • Owners
        • Signed-in users
        • Everyone
      • Invitee
      • No invitee
      • Options
      • Versions and GitHub Sync
      • Transfer ownership
      • Delete this note
      • Template
      • Save as template
      • Insert from template
      • Export
      • Dropbox
      • Google Drive
      • Gist
      • Import
      • Dropbox
      • Google Drive
      • Gist
      • Clipboard
      • Download
      • Markdown
      • HTML
      • Raw HTML
    Menu Sharing Create Help
    Create Create new note Create a note from template
    Menu
    Options
    Versions and GitHub Sync Transfer ownership Delete this note
    Export
    Dropbox Google Drive Gist
    Import
    Dropbox Google Drive Gist Clipboard
    Download
    Markdown HTML Raw HTML
    Back
    Sharing
    Sharing Link copied
    /edit
    View mode
    • Edit mode
    • View mode
    • Book mode
    • Slide mode
    Edit mode View mode Book mode Slide mode
    Note Permission
    Read
    Only me
    • Only me
    • Signed-in users
    • Everyone
    Only me Signed-in users Everyone
    Write
    Only me
    • Only me
    • Signed-in users
    • Everyone
    Only me Signed-in users Everyone
    More (Comment, Invitee)
    Publishing
    Everyone on the web can find and read all notes of this public team.
    After the note is published, everyone on the web can find and read this note.
    See all published notes on profile page.
    More (Comment, Invitee)
    Commenting Enable
    Disabled Forbidden Owners Signed-in users Everyone
    Permission
    Owners
    • Forbidden
    • Owners
    • Signed-in users
    • Everyone
    Invitee
    No invitee
       owned this note    owned this note      
    Published Linked with GitHub
    Like4 BookmarkBookmarked
    Subscribed
    • Any changes
      Be notified of any changes
    • Mention me
      Be notified of mention me
    • Unsubscribe
    Subscribe
    # Full verification of the Mina blockchain on EVM ## Introduction The [Ethereum Foundation](https://ethereum.foundation/) (EF) and [Mina Foundation](https://minaprotocol.com/) (MF) would like to announce a Request for Proposals (RfP) for the design and implementation of a mechanism to verify the Pickles SNARK on Ethereum. Direct verification of this SNARK on the EVM appears to be too costly. Thus, we are accepting proposals for systems that may perform some preprocessing on the Pickles SNARK (e.g., by computing a STARK that verifies the Pickles SNARK which itself may be efficiently verified on the EVM). The goal of this is (1) to enable full-verification of the Mina blockchain on Ethereum to enable inter-op between the two chains, and (2) to enable applications more generally to use recursive SNARKs on Ethereum. ## Table of Contents [toc] ## Definitions Let \begin{align*} p &= 2^{254} + 45560315531419706090280762371685220353 \\ q &= 2^{254} + 45560315531506369815346746415080538113 \\ \mathbb{G}_1 &= \left\{ (x, y) \in \mathbb{F}_p \mid y^2 = x^3 + 5 \right\} \\ \mathbb{G}_2 &= \left\{ (x, y) \in \mathbb{F}_q \mid y^2 = x^3 + 5 \right\} \\ n_1 = 17 \\ n_2 = 16 \end{align*} Note that $|\mathbb{G}_1| = q$ and $|\mathbb{G}_2| = p$. The Pickles SNARK verifier as used in Mina has several components 1. Computing several hash values from the data of the proof. This involves using the Poseidon hash function with 63 full rounds both over $\mathbb{F}_p$ and $\mathbb{F}_q$ with round constants and MDS matrix specified [here for $\mathbb{F}_p$](https://github.com/o1-labs/marlin/blob/master/oracle/src/pasta/fp.rs) and [here for $\mathbb{F}_q$](https://github.com/o1-labs/marlin/blob/master/oracle/src/pasta/fq.rs). This step is fairly cheap and could likely be implemented with reasonable gas cost on EVM. 2. Checking several arithmetic equations. Again, this step is fairly cheap and could be implemented directly on EVM. 3. Performing one multi-scalar multiplication (MSM) of size $2 n_2 + 4 + (2 + 25) = 63$, for which some of the bases are fixed and some are variable. The step could likely be implemented directly on EVM with reasonable efficiency, although it is likely to be more expensive than steps 1 and 2. 4. For each $i$, performing a multi-scalar multiplication over $\mathbb{G}_i$ of size $2^{n_i}$ with a fixed array of bases, and with scalars that can be very efficiently computed from the proof. Step 4 is very unlikely to be efficiently computed directly on EVM, unless the computation is split over several blocks. As an alternative, we suggest grant recipients produce an additional proof (e.g., a AIR-based STARK or a BN128-based SNARK) which verifies the computation of that step. ## Reference implementation A Rust implementation of the Pickles verifier can be found [here](https://github.com/o1-labs/marlin/blob/master/dlog/plonk/src/verifier.rs#L207). It makes a procedure call to verify the underlying polynomial commitment opening, which code is located [here](https://github.com/o1-labs/marlin/blob/master/dlog/commitment/src/commitment.rs#L612). ## Extended discussion As mentioned above, the most expensive part of the verifier, and the part which would likely have to be verified in an auxiliary proof-system outside of EVM, is two MSMs. In this section, we describe these MSMs in more detail. Let $\mathbb{G}_k$ be one of the two curves defined above and let $\mathbb{F}$ be its scalar field. Let $\phi \colon \{ 0, 1 \}^{128} \to \mathbb{F}$ be the algorithm defined by `to_field` [here](https://github.com/o1-labs/marlin/blob/49f81edc9c86e5907d26ea791fa083640ad0ef3e/oracle/src/sponge.rs#L33). Given an integer $i < 2^{n_k}$, define $\mathsf{bits}(i)$ to be the little-endian bit array of length $n$ representing the binary expansion of $i$. From a given Pickles SNARK, one will derive a sequence of challenges $c_0, \dots, c_{n_k - 1} \in \{ 0, 1 \}^{128}$. The associated MSM is $$ \sum_{i = 0}^{2^{n_k} - 1} s_i G_i = H $$ where $$ s_i := \prod_{\substack{0 \leq j < n_k \\ \mathsf{bits}(i)[j] = 1}} \phi(c_j) $$ and where $G_0, \dots, G_{2^{n_k} - 1} \in \mathbb{G}$ is a fixed sequence of group elements as generated by [this algorithm](https://github.com/o1-labs/marlin/blob/master/dlog/commitment/src/srs.rs#L70). ### Observations The sequence of scalars $\left\{ s_i \right\}_{0 \leq i < 2^{n - 1}}$ can be reordered in such a way that each term can be obtained by the previous by at most one multiplication and one division. If one also reorders the fixed sequence of bases $\left\{ {G}_i \right\}_{0 \leq i < 2^{n - 1}}$ accordingly, this makes the MSM $\sum_i s_i {G}_i$ well suited to verifying with an AIR-based STARK, since the computation can be expressed as a loop in which each iteration is very efficiently expressed as an arithmetic computation (modulo lookups in a fixed lookup table). ## Version of code The github commit of the code which will serve as the spec will be determined at the beginning of the project. The code is developed in the open at https://github.com/o1-labs/marlin and https://github.com/minaprotocol/mina/. ## Process summary The entire process can be summarised as follows: 1. **Request:** Release of RfP (this post) 2. **Gather:** Vendors submit proposals 3. **Deliberate:** EF and MF decide which proposal to accept, and comes up with a plan based on the resources and needs of the accepted proposal. 4. **Propose:** EF and MF propose the plan to vendor, and makes adjustments based on vendor's feedback 5. **Begin:** Vendor accepts and work begins ## Engagement timeline The proposed timeline of the engagement is approximately 6 months. Members of the EF and the MF will be available at all times to answer questions and comments during planning and implementation in order to make life as easy as possible for the vendor. ## Deliverables Deliverable will take the form of - A program `aux-proof-gen` that takes as input a Mina blockchain-state and associated Pickles SNARK and produces an auxiliary proof. It must be possible to run this program in less than 15 minutes on a cloud instance with at most 16 cores and 32 GB of memory. - An Ethereum smart contract `aux-proof-verify` that has an internal state corresponding to the Mina blockchain state, and which can be set to a new state only if one provides an auxiliary proof that verifies. The contract should use at most 5M gas. - For a given Mina blockchain state $s$, it should be possible to produce an auxiliary proof using `aux-proof-gen` that verifies on `aux-proof-verify` with state $s$ if and only if one posseses a Pickles SNARK associated to state $s$. - A high-level description of the implemented auxiliary proof system. - Two blog posts describing the progress of the work; one halfway through the engagement and one at the end. - All code delivered under this RfP will be released under Apache License, Version 2.0. ## Fee Structure ### Invoices Based on the timeline of this RfP, the chosen vendor will be expected to submit 2 invoices: - a first invoice of 50% of the total engagement fee at the start of the engagement - a second invoice of 50% of the total engagement fee at the end of the engagement, following the delivery of all Deliverables, including the code and the final blog post, and a 5 day review period. ### Payment method The vendor will be given the option to be paid in Fiat money (via bank transfer), ETH, or MINA. If the vendor chooses to be paid in ETH, the value of ETH described under the agreement will be the value in USD at NYSE closing time (4 PM EST) on the day prior to the due date (as described at https://www.coingecko.com). If the vendor chooses to be paid in MINA, the value of MINA described under the agreement will be either: - the value in USD at NYSE closing time (4 PM EST) on the day prior to the due date (as described at https://www.coingecko.com), if there exists a reputable exchange with a publicly accessible market for the MINA tokens; - or the implied value in USD from Mina Tokens' latest private funding round, if there does not exist a reputable exchange with a publicly accessible market for the MINA tokens. ## Selection criteria The selected vendor will have significant expertise in the areas necessary to meet the needs and requirements set forth in this RfP. Particularly: - Expertise in applied cryptography and cryptographic systems, specifically STARKs and SNARKs - Expertise in low level, optimised code - Experience with EVM ## Bidding instructions Upon reception of this request, interested vendors are expected to confirm receipt and intention to bid on the engagement. In this confirmation, they should explain what they need from us in order to get started. As well as bring attention to areas in which they feel they do not have significant expertise. We will use this information to try to provide appropriate entrance material for the engagement. Proposals must be submitted before *March 31st, 2021 at 5pm PST*. We expect to take 1 week to deliberate and respond. Please send initial confirmations, and proposals (in PDF format) to the following address: rfp@ethereum.org _Feel free to send us any questions you may have: rfp@ethereum.org_

    Import from clipboard

    Advanced permission required

    Your current role can only read. Ask the system administrator to acquire write and comment permission.

    This team is disabled

    Sorry, this team is disabled. You can't edit this note.

    This note is locked

    Sorry, only owner can edit this note.

    Reach the limit

    Sorry, you've reached the max length this note can be.
    Please reduce the content or divide it to more notes, thank you!

    Import from Gist

    Import from Snippet

    or

    Export to Snippet

    Are you sure?

    Do you really want to delete this note?
    All users will lost their connection.

    Create a note from template

    Create a note from template

    Oops...
    This template is not available.


    Upgrade

    All
    • All
    • Team
    No template found.

    Create custom template


    Upgrade

    Delete template

    Do you really want to delete this template?

    This page need refresh

    You have an incompatible client version.
    Refresh to update.
    New version available!
    See releases notes here
    Refresh to enjoy new features.
    Your user state has changed.
    Refresh to load new user state.

    Sign in

    Forgot password

    or

    By clicking below, you agree to our terms of service.

    Sign in via Facebook Sign in via Twitter Sign in via GitHub Sign in via Dropbox

    New to HackMD? Sign up

    Help

    • English
    • 中文
    • Français
    • Deutsch
    • 日本語
    • Español
    • Català
    • Ελληνικά
    • Português
    • italiano
    • Türkçe
    • Русский
    • Nederlands
    • hrvatski jezik
    • język polski
    • Українська
    • हिन्दी
    • svenska
    • Esperanto
    • dansk

    Documents

    Tutorials

    Book Mode Tutorial

    Slide Mode Tutorial

    YAML Metadata

    Contacts

    Facebook

    Twitter

    Feedback

    Send us email

    Resources

    Releases

    Pricing

    Blog

    Policy

    Terms

    Privacy

    Cheatsheet

    Syntax Example Reference
    # Header Header 基本排版
    - Unordered List
    • Unordered List
    1. Ordered List
    1. Ordered List
    - [ ] Todo List
    • Todo List
    > Blockquote
    Blockquote
    **Bold font** Bold font
    *Italics font* Italics font
    ~~Strikethrough~~ Strikethrough
    19^th^ 19th
    H~2~O H2O
    ++Inserted text++ Inserted text
    ==Marked text== Marked text
    [link text](https:// "title") Link
    ![image alt](https:// "title") Image
    `Code` Code 在筆記中貼入程式碼
    ```javascript
    var i = 0;
    ```
    var i = 0;
    :smile: :smile: Emoji list
    {%youtube youtube_id %} Externals
    $L^aT_eX$ LaTeX
    :::info
    This is a alert area.
    :::

    This is a alert area.

    Versions

    Versions and GitHub Sync

    Sign in to link this note to GitHub Learn more
    This note is not linked with GitHub Learn more
     
    Add badge Pull Push GitHub Link Settings
    Upgrade now

    Version named by    

    More Less
    • Edit
    • Delete

    Note content is identical to the latest version.
    Compare with
      Choose a version
      No search result
      Version not found

    Feedback

    Submission failed, please try again

    Thanks for your support.

    On a scale of 0-10, how likely is it that you would recommend HackMD to your friends, family or business associates?

    Please give us some advice and help us improve HackMD.

     

    Thanks for your feedback

    Remove version name

    Do you want to remove this version name and description?

    Transfer ownership

    Transfer to
      Warning: is a public team. If you transfer note to this team, everyone on the web can find and read this note.

        Link with GitHub

        Please authorize HackMD on GitHub

        Please sign in to GitHub and install the HackMD app on your GitHub repo. Learn more

         Sign in to GitHub

        HackMD links with GitHub through a GitHub App. You can choose which repo to install our App.

        Push the note to GitHub Push to GitHub Pull a file from GitHub

          Authorize again
         

        Choose which file to push to

        Select repo
        Refresh Authorize more repos
        Select branch
        Select file
        Select branch
        Choose version(s) to push
        • Save a new version and push
        • Choose from existing versions
        Available push count

        Upgrade

        Pull from GitHub

         
        File from GitHub
        File from HackMD

        GitHub Link Settings

        File linked

        Linked by
        File path
        Last synced branch
        Available push count

        Upgrade

        Danger Zone

        Unlink
        You will no longer receive notification when GitHub file changes after unlink.

        Syncing

        Push failed

        Push successfully