elliptic.yaml

import:
  dcc: dash.dcc
  html: dash.html
  dbc: dash_bootstrap_components
  daq: dash_daq

external_stylesheets:
  - https://codepen.io/chriddyp/pen/bWLwgP.css
  - https://www.w3schools.com/w3css/4/w3.css
  # - https://stackpath.bootstrapcdn.com/bootstrap/4.5.2/css/bootstrap.min.css
  # - https://cdn.jsdelivr.net/npm/bootstrap@5.1.3/dist/css/bootstrap.min.css
  - https://cdn.jsdelivr.net/npm/bootswatch@5.1.3/dist/slate/bootstrap.min.css

external_scripts:
  - https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_CHTML
  # - https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML
  # - https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.0.0/es5/latest?tex-mml-chtml.js

app:
  jupyter_dash.JupyterDash:
    external_stylesheets: ${external_stylesheets}
    external_scripts: ${external_scripts}
    title: elliptic
    suppress_callback_exceptions: False

run_server:
  host: '0.0.0.0'
  port: 8050
  extra_files:
    - elliptic.yaml
    - problems.yaml
    - ellitic/dashboard.py
  debug: False

input_p:
  dbc.Col:
    width: 5
    children:
      - dbc.Label: p
      - daq.Slider:
          id: user-input-p
          min: 3
          max: 100
          value: 11 # 11th prime=37
          updatemode: drag
          handleLabel: 'me!'

input_a:
  dbc.Col:
    width: 3
    children:
    - dbc.Label: a
    - dbc.Input:
        id: user-input-a
        type: number
        value: 0

input_b:
  dbc.Col:
    width: 3
    children:
    - dbc.Label: b
    - dbc.Input:
        id: user-input-b
        type: number
        value: 7
parameters:
  html.Div:
    children:
      - dbc.Row:
          children:
            - ${input_p}
            - ${input_a}
            - ${input_b}

empty_graph:
  data: []
  layout:
    xaxis:
      showticklabels: False
      ticks: ''
      showgrid: False
      zeroline: False
    yaxis:
      showticklabels: False
      ticks: ''
      showgrid: False
      zeroline: False
    paper_bgcolor: rgba(0,0,0,0)
    plot_bgcolor: rgba(0,0,0,0)
    # margin:
    #   l: 0 #left margin
    #   r: 0 #right margin
    #   b: 0 #bottom margin
    #   t: 0 #top margin
    # width: 500


references_secp256: "### References

* Point implementation from Jimmy Song's [Programming Bitcoin](https://github.com/jimmysong/programmingbitcoin)

* Bitcoin uses [secp256k1](https://en.bitcoin.it/wiki/Secp256k1)

In bitcoin, p is:

$2^{256} - 2^{32} - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1 = 1.15*10^{77}$

or .0012 x number of atoms in the known universe!

"


title: "
## Finite Elliptic Curves
 
An interactive primer on finite elliptic curves. Continuous elliptic curves [here](https://www.geogebra.org/m/baurc6bu).
"

subtitle: "

Asher Pembroke @ BTC++, Dec 9, 2022

"

references: "# References

Further reading:

* Originally presented at [BTC++, June 7, 2022 Austin TX](https://youtu.be/im1-IzaSjXI)

* Ongoing course development for [Timechain Academy](https://timechain.academy/)

* Bitcon's [(Elliptic Curve Digital Signature Algorithm (ECDSA)](https://en.bitcoin.it/wiki/Elliptic_Curve_Digital_Signature_Algorithm)

* [Schnorr Signatures](https://medium.com/coinmonks/on-bitcoins-schnorr-signature-algorithm-and-taproot-script-and-witness-sizes-fe4d1e6591a7) 

* [An illustrated guide to elliptic curve cryptography validation](https://research.nccgroup.com/2021/11/18/an-illustrated-guide-to-elliptic-curve-cryptography-validation/)

* Andrea Corbellini - [Elliptic Curve Cryptography - A gentle introduction](https://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/)

* [Bolt 04 secret sharing](https://github.com/lightning/bolts/blob/master/04-onion-routing.md)

* [PGP](https://en.wikipedia.org/wiki/Pretty_Good_Privacy) [with elliptic curves](https://ieeexplore.ieee.org/abstract/document/7813870)

* [support for secp256 in GPG](https://github.com/openpgpjs/openpgpjs/pull/628)

* [ruben somsen's silent payments!](https://gist.github.com/RubenSomsen/c43b79517e7cb701ebf77eec6dbb46b8?permalink_comment_id=4113680)


"

sign_message_ecdsa: "## Signing

To sign a message:

* z = Hash of message (truncated)

* choose $k \\in [1, n]$ for subgroup order $n$

* calculate $P=k \\cdot G$ and $H_A=d_A \\cdot G$

* r = P_x mod n # get x coordinate of P (unless $r=0$)

* $s = k^{-1}(z+rd_A) modn$

"


verify_message_ecdsa: "## Verifying

To verify a signature:

* 𝑢1 = 𝑠−1 𝑧 modn

* 𝑢2 = 𝑠−1 𝑟 modn

* 𝑃 = 𝑢1 𝐺 + 𝑢2 𝐻𝑎

"

sign_message_schnorr: "## Signing

To sign a message:

* choose pub, priv key pair $H_A = d_A \\cdot G_0$

* choose random, unused $k \\in [1, n]$ (for subgroup order $n$)

* calculate $R=k\\cdot G_0$

* concatonate $R||H_A||m$ for a message $m$

* h = $Hash(R||H_A||m) mod_n$

* compute $s = (k + h*(d_A)) mod_n$


Signature: (R, s)

"

verify_message_schnorr: "## Validating

To verify a signature:

* check that $s \\cdot G_0 = R + h \\cdot H_A$

* done!

"

layout:
  dbc.Container:
    children:
    - dcc.Location:
        id: url
    - dbc.Row:
        children:
        - dbc.Col:
            width: 8
            children:
            - dcc.Markdown: ${title}
        - dbc.Col:
            width: 4
            children:
            - html.Br:
            - dcc.Markdown: ${subtitle}
        # - dbc.Col:
        #     width: 4
        #     children:
        #       html.Img:
        #         src: assets/satoshi_energy_logo.png
        #         height: 30px
        #         style:
        #           padding: 10px,10px,10px,10px
        #           background: grey
    - dbc.Row:
        children:
        - dbc.Col:
            width: 8
            children:
            - ${parameters}
    - html.Br:
    - dbc.Tabs:
        id: lesson
        active_tab: point-addition
        children:
        - dbc.Tab:
            tab_id: point-addition
            label: Point Addition
            children:
            - dcc.Store:
                id: add-points
            - dbc.Row:
                children:
                  - dbc.Col:
                      children:
                        - dbc.Card:
                            children:
                            - dbc.CardBody:
                                children:
                                - dcc.Graph:
                                    id: add-graph
                                    mathjax: True
                                    config:
                                      displayModeBar: False
                                    figure: ${empty_graph}
                  - dbc.Col:
                      children:
                      - html.Br:
                      - html.Br:
                      - dcc.Markdown:
                          children: ${references_secp256}
                          mathjax: True
        - dbc.Tab:
            tab_id: point-multiplication
            label: Point Multiplication
            children:
            - dcc.Store:
                id: multiply-points
            - dbc.Card:
                children:
                - dbc.CardBody:
                    children:
                    - dbc.Row:
                        children:
                        - dbc.Col:
                            width: 2
                            children:
                            - dbc.Label: 'n'
                            - dbc.Input:
                                id: user-input-n
                                type: number
                                value: 0
                                min: 0
                        - dbc.Col:
                            width: 2
                            children:
                            - dbc.Checklist:
                                id: multiply-mode
                                switch: True
                                options:
                                - label: 'Multiply'
                                  value: 1
                                - label: 'Inverse'
                                  value: 2
                                value: [1]
                                inline: True
                        - dbc.Col:
                            width: 2
                            children:
                            - dbc.Checklist:
                                id: multiply-subgroup
                                options:
                                - label: 'show subgroup'
                                  value: 1
                                value: []
                                switch: True
                            - html.Div:
                                id: multiply-inverse-message
                    - dbc.Row:
                        children:
                        - dbc.Col:
                            width: 8
                            children:
                            - dcc.Graph:
                                id: multiply-graph
                                mathjax: True
                                config:
                                  displayModeBar: False
                                figure: ${empty_graph}
                        - dbc.Col:
                            width: 4
                            children:
                            - html.Details:
                                children:
                                - html.Summary: Click to reveal clock
                                - dcc.Graph:
                                    id: multiply-clock
                                    mathjax: True
                                    config:
                                      displayModeBar: False
                                    figure: ${empty_graph}
                            - html.Details:
                                children:
                                - html.Summary: Click to expand problem set (Test your might!)
                                - html.Div:
                                    id: multiply-problem-set
        - dbc.Tab:
            tab_id: secret-sharing
            label: Secret Sharing
            children:
            - dcc.Store:
                id: alice-pub
            - dcc.Store:
                id: alice-secret
            - dcc.Store:
                id: bob-pub
            - dcc.Store:
                id: bob-secret
            - dbc.Card:
                children:
                - dbc.CardBody:
                    children:
                    - dbc.Row:
                        justify: left
                        children:
                        - dbc.Col:
                            width: 6
                            children:
                            - dbc.RadioItems:
                                id: sharing-mode
                                options:
                                - label: 'Pub Key'
                                  value: 1
                                - label: 'Shared Secret'
                                  value: 2
                                - label: 'Message'
                                  value: 3
                                value: 1
                                inline: True
                    - dbc.Row:
                        children:
                        - dbc.Col:
                            width: 6
                            children:
                            - dbc.Row:
                                children:
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label:
                                        children: Alice Priv Key
                                    - dbc.Input:
                                        id: alice-priv
                                        type: number
                                        value: 5
                                        min: 1
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label:
                                        children: Alice Pub Key
                                    - dcc.Markdown:
                                        id: alice-pub-key
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label:
                                        children: Shared Secret
                                    - dcc.Markdown:
                                        id: alice-shared-secret
                        - dbc.Col:
                            width: 6
                            children:
                            - dbc.Row:
                                children:
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label:
                                        children: Bob Priv Key
                                    - dbc.Input:
                                        id: bob-priv
                                        type: number
                                        value: 7
                                        min: 1
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label:
                                        children: Bob Pub Key
                                    - dcc.Markdown:
                                        id: bob-pub-key
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label:
                                        children: Shared Secret
                                    - dcc.Markdown:
                                        id: bob-shared-secret
                    - dbc.Row:
                        children:
                          - dbc.Col:
                              width: 6
                              children:
                              - html.Div:
                                  id: pub-graph-alice-outer
                                  children:
                                  - dcc.Graph:
                                      id: pub-graph-alice
                                      mathjax: True
                                      config:
                                        displayModeBar: False
                                      figure: ${empty_graph}
                              - html.Div:
                                  id: secret-graph-alice-outer
                                  children:
                                  - dcc.Graph:
                                      id: secret-graph-alice
                                      mathjax: True
                                      config:
                                        displayModeBar: False
                                      figure: ${empty_graph}
                              - html.Div:
                                  id: encrypt-alice-outer
                                  children:
                                  - html.Br:
                                  - dbc.Textarea:
                                      id: alice-message
                                      value:
                                      placeholder: Enter message to send/encrypt
                                      style:
                                        height: 135
                                  - html.Br:
                                  - dbc.Row:
                                      justify: center
                                      children:
                                        - dbc.Col:
                                            width: 3
                                            children:
                                            - html.Div:
                                                id: alice-error
                                                children:
                                        - dbc.Col:
                                            width: 4
                                            children:
                                            - dbc.ButtonGroup:
                                                children:
                                                - dbc.Button:
                                                    id: alice-encrypt
                                                    children: Encrypt
                                                    color: primary
                                                - dbc.Button:
                                                    id: alice-decrypt
                                                    children: Decrypt
                                                    color: primary
                                                - dbc.Button:
                                                    id: alice-send
                                                    children: Send
                                                    color: success
                          - dbc.Col:
                              width: 6
                              children:
                              - html.Div:
                                  id: pub-graph-bob-outer
                                  children:
                                  - dcc.Graph:
                                      id: pub-graph-bob
                                      mathjax: True
                                      config:
                                        displayModeBar: False
                                      figure: ${empty_graph}
                              - html.Div:
                                  id: secret-graph-bob-outer
                                  children:
                                  - dcc.Graph:
                                      id: secret-graph-bob
                                      mathjax: True
                                      config:
                                        displayModeBar: False
                                      figure: ${empty_graph}
                              - html.Div:
                                  id: encrypt-bob-outer
                                  children:
                                  - html.Br:
                                  - dbc.Textarea:
                                      id: bob-message
                                      value:
                                      placeholder: Enter message to send/encrypt
                                      style:
                                        height: 135
                                  - html.Br:
                                  - dbc.Row:
                                      justify: center
                                      children:
                                        - dbc.Col:
                                            width: 3
                                            children:
                                            - html.Div:
                                                id: bob-error
                                                children:
                                        - dbc.Col:
                                            width: 4
                                            children:
                                            - dbc.ButtonGroup:
                                                children:
                                                - dbc.Button:
                                                    id: bob-encrypt
                                                    children: Encrypt
                                                    color: primary
                                                - dbc.Button:
                                                    id: bob-decrypt
                                                    children: Decrypt
                                                    color: secondary
                                                - dbc.Button:
                                                    id: bob-send
                                                    children: Send
                                                    color: success
        - dbc.Tab:
            tab_id: signatures-ecdsa
            label: Signatures (ECDSA)
            children:
            - dcc.Store:
                id: sign-pub
            - dcc.Store:
                id: sign-secret
            - dcc.Store:
                id: validate-points
            - dbc.Card:
                children:
                - dbc.CardBody:
                    children:
                    - dbc.Row:
                        children:
                        - dbc.Col:
                            width: 6
                            children:
                            - dcc.Markdown:
                                children: ${sign_message_ecdsa}
                                mathjax: True
                            - dbc.Row:
                                children:
                                - dbc.Col:
                                    width: 12
                                    children:
                                    - dbc.RadioItems:
                                        id: sign-sharing-mode
                                        options:
                                        - label: Pub Key
                                          value: 1
                                        - label: k secret
                                          value: 2
                                        - label: Message
                                          value: 3
                                        value: 1
                                        inline: True
                            - dbc.Row:
                                children:
                                - dbc.Col:
                                    width: 2
                                    children:
                                    - dbc.Label: Priv key
                                    - dbc.Input:
                                        id: sign-priv
                                        type: number
                                        value: 7
                                        min: 1
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label: Pub key
                                    - dcc.Markdown:
                                        id: sign-pub-key
                                        children: ''
                                - dbc.Col:
                                    width: 2
                                    children:
                                    - dbc.Label: k
                                    - dbc.Input:
                                        id: sign-k
                                        type: number
                                        value: 10
                                        min: 1
                                - dbc.Col:
                                    width: 2
                                    children:
                                    - dbc.Label: P_k
                                    - dcc.Markdown:
                                        id: sign-p-k
                                        children: ''
                                - dbc.Col:
                                    width: 3
                                    children:
                                    - dbc.Label: (z,r,s)
                                    - dcc.Markdown:
                                        id: sign-z-r-s
                                        children: ''
                            - html.Div:
                                id: pub-graph-sign-outer
                                children:
                                - dcc.Graph:
                                    id: pub-graph-sign
                                    mathjax: True
                                    config:
                                      displayModeBar: False
                                    figure: ${empty_graph}
                            - dcc.Markdown:
                                id: sign-params
                                mathjax: True
                            - html.Div:
                                id: k-graph-sign-outer
                                children:
                                - dcc.Graph:
                                    id: secret-graph-sign
                                    mathjax: True
                                    config:
                                      displayModeBar: False
                                    figure: ${empty_graph}
                            - html.Div:
                                id: sign-message-outer
                                children:
                                - html.Br:
                                - dbc.Textarea:
                                    id: sign-message
                                    value:
                                    placeholder: Enter message to sign
                                    style:
                                      height: 80
                        - dbc.Col:
                            width: 6
                            children:
                            - dcc.Markdown:
                                id: sign-validate
                                children: ${verify_message_ecdsa}
                                mathjax: True
                            # - dcc.Markdown:
                            #     id: sign-validate
                            #     children: 'nothing yet'
                            - dcc.Graph:
                                id: validate-graph
                                mathjax: True
                                config:
                                  displayModeBar: False
                                figure: ${empty_graph}
        - dbc.Tab:
            tab_id: signatures-schnorr
            label: Signatures (Schnorr)
            children:
            - dcc.Store:
                id: schnorr-pub
            - dcc.Store:
                id: secret-schnorr-store
            - dbc.Card:
                body: True
                children:
                - dbc.Row:
                    children:
                    - dbc.Col:
                        children:
                        - dcc.Markdown:
                            children: ${sign_message_schnorr}
                            mathjax: True
                    - dbc.Col:
                        children:
                        - dcc.Markdown:
                            children: ${verify_message_schnorr}
                            mathjax: True
            - dbc.Card:
                body: True
                children:
                - dbc.Row:
                    children:
                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children: 
                            - dcc.Markdown:
                                children: $G_0$
                                mathjax: True
                        - dcc.Markdown:
                            id: generator-point-schnorr
                            mathjax: True
                    - dbc.Col:
                        width: 1
                        children:
                        - dbc.Label:
                            children:
                            - dcc.Markdown:
                                children: $d_A$
                                mathjax: True
                        - dbc.Input:
                            id: alice-priv-schnorr
                            type: number
                            step: 1
                            value: 3
                            min: 1

                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children: 
                            - dcc.Markdown:
                                children: $H_A$
                                mathjax: True
                        - dcc.Markdown:
                            id: alice-pub-schnorr
                            mathjax: True

                    - dbc.Col:
                        width: 1
                        children:
                        - dbc.Label:
                            children:
                            - dcc.Markdown:
                                children: $k$
                                mathjax: True
                        - dbc.Input:
                            id: secret-schnorr
                            type: number
                            step: 1
                            value: 5
                            min: 1

                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children:
                            - dcc.Markdown:
                                children: $R$
                                mathjax: True
                        - dcc.Markdown:
                            id: secret-schnorr-render
                            mathjax: True

                    - dbc.Col:
                        width: 3
                        children:
                        - dbc.Label:
                            children: 
                            - dcc.Markdown: message
                        - dbc.Input:
                            id: schnorr-message
                            type: text
                            value: btc++ is the best!
                - html.Br:
                - dbc.Row:
                    children:
                    - dbc.Col:
                        width: 3
                        children:
                        - dbc.Label:
                            children:
                                dcc.Markdown:
                                    children: concat $R||H_A||m$
                                    mathjax: True
                        - dcc.Markdown:
                            id: concat
                            mathjax: True
                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children:
                                dcc.Markdown:
                                    children: $Hash(R||H_A||m)_n$
                                    mathjax: True
                        - dbc.Input:
                            id: hash-concat
                            type: number
                            step: 1
                            min: 1
                            disabled: True
                            style:
                                width: 75
                                height: 40
                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children:
                                dcc.Markdown:
                                    children: $s = (k + h*(d_A))_n$
                                    mathjax: True
                        - dbc.Input:
                            id: schnorr-s
                            type: number
                            step: 1
                            min: 1
                            disabled: True
                            style:
                                width: 75
                                height: 40

                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children:
                                dcc.Markdown:
                                    children: "signature:"
                                    mathjax: True
                        - dcc.Markdown:
                            id: signatures-schnorr-render
                            mathjax: True
            - dbc.Card:
                body: True
                children:
                - dbc.Row:
                    justify: center
                    children:
                    - dbc.Col:
                        width: 6
                        children:
                        - dcc.Graph:
                            id: schnorr-graph
                            mathjax: True
                            config:
                              displayModeBar: False
                            figure: ${empty_graph}
                    - dbc.Col:
                        width: 2
                        children:
                        - dbc.Label:
                            children:
                                dcc.Markdown:
                                    children: "validation: $s \\cdot G_0 = R + h \\cdot H_A$"
                                    mathjax: True
                        - dcc.Markdown:
                            id: signatures-schnorr-validate
                            mathjax: True

        - dbc.Tab:
            tab_id: references
            label: References
            children:
            - dcc.Markdown:
                children: ${references}


callbacks:
  # update_validate_points:
  #   input:
  #     - id: user-input-p
  #       attr: value
  #     - id: user-input-a
  #       attr: value
  #     - id: user-input-b
  #       attr: value
  #     - id: validate-graph
  #       attr: clickData
  #   state:
  #     - id: validate-points
  #       attr: data
  #   output:
  #     - id: validate-points
  #       attr: data
  #   callback: elliptic.dashboard.update_add_points


  show_hide_sign_pub:
    input:
      - id: sign-sharing-mode
        attr: value
    output:
      - id:  pub-graph-sign-outer
        attr: style
    callback: elliptic.dashboard.show_hide_pub

  show_hide_sign_k:
    input:
      - id: sign-sharing-mode
        attr: value
    output:
      - id:  k-graph-sign-outer
        attr: style
    callback: elliptic.dashboard.show_hide_secret

  show_hide_alice_message:
    input:
      - id: sign-sharing-mode
        attr: value
    output:
      - id:  sign-message-outer
        attr: style
    callback: elliptic.dashboard.show_hide_message

  update_sign_priv_bounds:
    input:
    - id: user-input-p
      attr: value
    - id: user-input-a
      attr: value
    - id: user-input-b
      attr: value
    - id: pub-graph-sign
      attr: clickData
    state:
    - id: sign-priv
      attr: value
    output:
    - id: sign-priv
      attr: max
    - id: sign-priv
      attr: value
    callback: elliptic.dashboard.priv_in_bounds



  update_sign_pub:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-priv
        attr: value
      - id: pub-graph-sign
        attr: clickData
    state:
      - id: sign-pub
        attr: data
    output:
      - id: sign-pub
        attr: data
    callback: elliptic.dashboard.update_multiply_points

  update_sign_secret_bounds:
    input:
    - id: user-input-p
      attr: value
    - id: user-input-a
      attr: value
    - id: user-input-b
      attr: value
    - id: secret-graph-sign
      attr: clickData
    state:
    - id: sign-k
      attr: value
    output:
    - id: sign-k
      attr: max
    - id: sign-k
      attr: value
    callback: elliptic.dashboard.priv_in_bounds


  update_sign_secret:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-k
        attr: value
      - id: secret-graph-sign
        attr: clickData
    state:
      - id: sign-secret
        attr: data
    output:
      - id: sign-secret
        attr: data
    callback: elliptic.dashboard.update_multiply_points


  pub_graph_sign:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-priv
        attr: value
      - id: sign-pub
        attr: data
    output:
      - id: pub-graph-sign
        attr: figure
    callback: elliptic.dashboard.multiply_graph

  secret_graph_sign:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-k
        attr: value
      - id: sign-secret
        attr: data
    output:
      - id: secret-graph-sign
        attr: figure
    callback: elliptic.dashboard.multiply_graph


  render_sign_pub:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-pub
        attr: data
    output:
      - id: sign-pub-key
        attr: children
    callback: elliptic.dashboard.render_pub_key


  render_sign_secret:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-secret
        attr: data
    output:
      - id: sign-p-k
        attr: children
    callback: elliptic.dashboard.render_pub_key

# p_i, a, b, priv_key, k, pub_points, secret_points, message
  render_sign_params:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-priv
        attr: value
      - id: sign-k
        attr: value
      - id: sign-pub
        attr: data
      - id: sign-secret
        attr: data
      - id: sign-message
        attr: value
    output:
      - id: sign-params
        attr: children
      - id: sign-z-r-s
        attr: children
    callback: elliptic.dashboard.render_sign_params

  validate_signature:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: sign-z-r-s
        attr: children
      - id: sign-pub
        attr: data
      - id: sign-pub-key
        attr: children
    output:
      - id: sign-validate
        attr: children
    callback: elliptic.dashboard.validate_signature



  add_graph:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: add-points
        attr: data
    output:
      - id: add-graph
        attr: figure

    callback: elliptic.dashboard.add_graph

  multiply_graph:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: user-input-n
        attr: value
      - id: multiply-points
        attr: data
      - id: multiply-mode
        attr: value
      - id: multiply-subgroup
        attr: value
    output:
      - id: multiply-graph
        attr: figure
      - id: multiply-inverse-message
        attr: children
    callback: elliptic.dashboard.multiply_inverse_graph

  multiply_inverse_clock:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: user-input-n
        attr: value
      - id: multiply-points
        attr: data
      - id: multiply-mode
        attr: value
      # - id: multiply-subgroup
      #   attr: value
    output:
      - id: multiply-clock
        attr: figure
    callback: elliptic.dashboard.multiply_inverse_clock

  load_multiply_problems:
    input:
      - id: url
        attr: pathname
    output:
      - id: multiply-problem-set
        attr: children
    callback: elliptic.dashboard.load_multiply_problems

  validate_user_answer:
    input:
      - id:
          kind: point-multiplication
          index: MATCH
        attr: value
    output:
      - id:
          kind: point-multiplication
          index: MATCH
        attr: valid
      - id:
          kind: point-multiplication
          index: MATCH
        attr: invalid
      - id:
          kind: point-multiplication-render
          index: MATCH
        attr: children
    callback: elliptic.dashboard.validate_user_answer  

  update_slider_label:
    input:
      - id: user-input-p
        attr: value
    output:
      - id: user-input-p
        attr: handleLabel
    callback: elliptic.dashboard.update_p_slider_label


  update_bob_secret:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: bob-priv
        attr: value
      - id: secret-graph-bob
        attr: clickData
    state:
      - id: bob-secret
        attr: data
    output:
      - id: bob-secret
        attr: data
    callback: elliptic.dashboard.update_multiply_points


  update_alice_secret:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-priv
        attr: value
      - id: secret-graph-alice
        attr: clickData
    state:
      - id: alice-secret
        attr: data
    output:
      - id: alice-secret
        attr: data
    callback: elliptic.dashboard.update_multiply_points

  render_alice_pub:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-pub
        attr: data
    output:
      - id: alice-pub-key
        attr: children
    callback: elliptic.dashboard.render_pub_key

  render_alice_secret:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-secret
        attr: data
    output:
      - id: alice-shared-secret
        attr: children
    callback: elliptic.dashboard.render_pub_key


  render_bob_pub:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: bob-pub
        attr: data
    output:
      - id: bob-pub-key
        attr: children
    callback: elliptic.dashboard.render_pub_key

  render_bob_secret:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: bob-secret
        attr: data
    output:
      - id: bob-shared-secret
        attr: children
    callback: elliptic.dashboard.render_pub_key

  update_alice_pub:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-priv
        attr: value
      - id: pub-graph-alice
        attr: clickData
    state:
      - id: alice-pub
        attr: data
    output:
      - id: alice-pub
        attr: data
    callback: elliptic.dashboard.update_multiply_points

  update_alice_priv_bounds:
    input:
    - id: user-input-p
      attr: value
    - id: user-input-a
      attr: value
    - id: user-input-b
      attr: value
    - id: pub-graph-alice
      attr: clickData
    state:
    - id: alice-priv
      attr: value
    output:
    - id: alice-priv
      attr: max
    - id: alice-priv
      attr: value
    callback: elliptic.dashboard.priv_in_bounds

  update_bob_priv_bounds:
    input:
    - id: user-input-p
      attr: value
    - id: user-input-a
      attr: value
    - id: user-input-b
      attr: value
    - id: pub-graph-bob
      attr: clickData
    state:
    - id: bob-priv
      attr: value
    output:
    - id: bob-priv
      attr: max
    - id: bob-priv
      attr: value
    callback: elliptic.dashboard.priv_in_bounds

  pub_graph_alice:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-priv
        attr: value
      - id: alice-pub
        attr: data
      - id: sharing-mode
        attr: value
    output:
      - id: pub-graph-alice
        attr: figure
    callback: elliptic.dashboard.multiply_graph

  secret_graph_alice:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-priv
        attr: value
      - id: alice-secret
        attr: data
      - id: sharing-mode
        attr: value
    output:
      - id: secret-graph-alice
        attr: figure
    callback: elliptic.dashboard.multiply_graph

  secret_graph_bob:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: bob-priv
        attr: value
      - id: bob-secret
        attr: data
      - id: sharing-mode
        attr: value
    output:
      - id: secret-graph-bob
        attr: figure
    callback: elliptic.dashboard.multiply_graph

  show_hide_alice_pub:
    input:
      - id: sharing-mode
        attr: value
    output:
      - id:  pub-graph-alice-outer
        attr: style
    callback: elliptic.dashboard.show_hide_pub

  show_hide_alice_secret:
    input:
      - id: sharing-mode
        attr: value
    output:
      - id:  secret-graph-alice-outer
        attr: style
    callback: elliptic.dashboard.show_hide_secret


  show_hide_alice_message:
    input:
      - id: sharing-mode
        attr: value
    output:
      - id:  encrypt-alice-outer
        attr: style
    callback: elliptic.dashboard.show_hide_message


  show_hide_bob_pub:
    input:
      - id: sharing-mode
        attr: value
    output:
      - id:  pub-graph-bob-outer
        attr: style
    callback: elliptic.dashboard.show_hide_pub

  show_hide_bob_secret:
    input:
      - id: sharing-mode
        attr: value
    output:
      - id:  secret-graph-bob-outer
        attr: style
    callback: elliptic.dashboard.show_hide_secret

  show_hide_bob_message:
    input:
      - id: sharing-mode
        attr: value
    output:
      - id:  encrypt-bob-outer
        attr: style
    callback: elliptic.dashboard.show_hide_message

  update_bob_pub:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: bob-priv
        attr: value
      - id: pub-graph-bob
        attr: clickData
    state:
      - id: bob-pub
        attr: data
    output:
      - id: bob-pub
        attr: data
    callback: elliptic.dashboard.update_multiply_points


  pub_graph_bob:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: bob-priv
        attr: value
      - id: bob-pub
        attr: data
      - id: sharing-mode
        attr: value
    output:
      - id: pub-graph-bob
        attr: figure
    callback: elliptic.dashboard.multiply_graph

  update_multiply_inverse_points:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: user-input-n
        attr: value
      - id: multiply-graph
        attr: clickData
      - id: multiply-mode
        attr: value
    state:
      - id: multiply-points
        attr: data
    output:
      - id: multiply-points
        attr: data
    callback: elliptic.dashboard.update_multiply_inverse_points

  update_add_points:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: add-graph
        attr: clickData
    state:
      - id: add-points
        attr: data
    output:
      - id: add-points
        attr: data
    callback: elliptic.dashboard.update_add_points


  update_message_alice:
    input:
      - id: alice-shared-secret
        attr: children
      - id: alice-encrypt
        attr: n_clicks
      - id: alice-decrypt
        attr: n_clicks
      - id: bob-send
        attr: n_clicks
    state:
      - id: bob-message
        attr: value
      - id: alice-message
        attr: value
    output:
      - id: alice-message
        attr: value
      - id: alice-error
        attr: children
    callback: elliptic.dashboard.update_message


  update_message_bob:
    input:
      - id: bob-shared-secret
        attr: children
      - id: bob-encrypt
        attr: n_clicks
      - id: bob-decrypt
        attr: n_clicks
      - id: alice-send
        attr: n_clicks
    state:
      - id: alice-message
        attr: value
      - id: bob-message
        attr: value
    output:
      - id: bob-message
        attr: value
      - id: bob-error
        attr: children
    callback: elliptic.dashboard.update_message

  update_alice_buttons:
    input:
      - id: alice-shared-secret
        attr: children
    output:
      - id: alice-encrypt
        attr: color
      - id: alice-decrypt
        attr: color
    callback: elliptic.dashboard.update_crypto_buttons


  update_bob_buttons:
    input:
      - id: bob-shared-secret
        attr: children
    output:
      - id: bob-encrypt
        attr: color
      - id: bob-decrypt
        attr: color
    callback: elliptic.dashboard.update_crypto_buttons

### schnorr
  schnorr_graph_sign:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-priv-schnorr
        attr: value
      - id: schnorr-pub
        attr: data
      - id: secret-schnorr
        attr: value
    output:
      - id: schnorr-graph
        attr: figure
    callback: elliptic.dashboard.schnorr_graph_sign


  update_alice_pub_schnorr:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: alice-priv-schnorr
        attr: value
      - id: secret-schnorr
        attr: value
      - id: schnorr-graph
        attr: clickData
    state:
      - id: schnorr-pub
        attr: data
    output:
      - id: schnorr-pub
        attr: data
    callback: elliptic.dashboard.update_schnorr_points


  render_alice_pub_schnorr:
    input:
      - id: user-input-p
        attr: value
      - id: user-input-a
        attr: value
      - id: user-input-b
        attr: value
      - id: schnorr-pub
        attr: data
    output:
      - id: generator-point-schnorr
        attr: children
      - id: alice-pub-schnorr
        attr: children
      - id: secret-schnorr-render
        attr: children
    callback: elliptic.dashboard.render_schnorr_keys


  # render_alice_secret_schnorr:
  #   input:
  #     - id: user-input-p
  #       attr: value
  #     - id: user-input-a
  #       attr: value
  #     - id: user-input-b
  #       attr: value
  #     - id: secret-schnorr-store
  #       attr: data
  #   output:
  #     - id: secret-schnorr-render
  #       attr: children
  #   callback: elliptic.dashboard.render_pub_key

  concatonate:
    input:
      - id: alice-pub-schnorr
        attr: children
      - id: secret-schnorr-render
        attr: children
      - id: schnorr-message
        attr: value
    output:
      - id: concat
        attr: children
    callback: elliptic.dashboard.cat


# hash_concat(p_i, a, b, pub_points, message)
  hash_concat:
    input:
    - id: user-input-p
      attr: value
    - id: user-input-a
      attr: value
    - id: user-input-b
      attr: value
    - id: schnorr-pub
      attr: data
    # - id: secret-schnorr-store
    #   attr: data
    - id: concat
      attr: children
    - id: alice-priv-schnorr
      attr: value
    - id: secret-schnorr
      attr: value
    output:
    - id: hash-concat
      attr: value
    - id: schnorr-s
      attr: value
    callback: elliptic.dashboard.hash_concat



  render_signature_schnorr:
    input:
    - id: schnorr-s
      attr: value
    - id: secret-schnorr-render
      attr: children
    output:
    - id: signatures-schnorr-render
      attr: children

    callback: elliptic.dashboard.render_signature_schnorr
  

  validate_schnorr_signature: #(p_i, a, b, h, s, points):
    input:
    - id: user-input-p
      attr: value
    - id: user-input-a
      attr: value
    - id: user-input-b
      attr: value
    - id: hash-concat
      attr: value
    - id: schnorr-s
      attr: value
    - id: schnorr-pub
      attr: data
    output:
    - id: signatures-schnorr-validate
      attr: children
    callback: elliptic.dashboard.validate_schnorr_signature