learn.equalit.ie

Chatroom setup

Procedure Chat Initiator Init
Input: $newRoomName$, $participantNick$
  Global $myId:=1$
  Global $Nick_{{myId}}:=participantNick$
  Global $roomName:=newRoomName$
  Global $x_{{myId}},y_{{myId}}:=$ Call Generate Initial Paramters($myId$)
  Global $signatureKey_{{myId}}:=(x_{{myId}},y_{{myId}})$
  $participantList:=[Nick_{{myId}}]$
  $ephemeralPublicPointList:=[y_{{myId}},y_{{other}}]$

Procedure Verify Verifier Generate Init Key
Input: Failed to parse (syntax error): schnorrRandomPoint_{other

  Call Verify Verifiers()
  Global $sessionKey:=SHA-512(x_{{myId}}y_{{other}},sessionId)$
  $toBeSigned:=SHA-512(SHA-512(sessionId||SHA-512(y_{1},v_{1})||SHA-512(y_{2},v_{2})))$
  Call Sign Session and Send($toBeSigned$)

Join

Procedure Join
Input: $newRoomName$, Failed to parse (syntax error): Nickname_{myId

  Global $myId:=participantId$
  Global $roomName:=newRoomName$
  $x_{{myId}},y_{{myId}}:=$Call Generate Initial Paramters(Participant ID $myId$)
  Global $signatureKey_{{myId}}:=(x_{{myId}},y_{{myId}})$
  Call Broadcast(``:3mpCat:3Join:3, $myId$, Failed to parse (syntax error): Nickname_{myId

)

  Global $participantList,ephemeralPublicPointList:=$ Call Receive()
  Global $sessionId:=$ Call Compute Session Id($roomName$, $participantList$, $ephemeralPublicPointList$)
  Call Sign and Send Key Confirmation and Shares()
  Call Wait On Receive(``:3mpCat:3KeyConfirmationShare:3)
  Global $keyShareList,keyConfirmationList,signatureList:=$ Call Receive()
  Call Verify Key Confirmations and Signatures($keyConfirmationList$, $signatureList$)
  Call Update Session Key()

Procedure Receive Session Digest
Input: $currentSessionHistoryDigest$
  Global $sessionDigest:=currentSessionHistoryDigest$

Protocol for other participants already in the chat to accept the newcomer

Procedure Accept
Input: newParticipant
  Call Broadcast(``:3mpCat:3Join:3, $myId$, Failed to parse (syntax error): Nickname_{myId

)

  Call Wait On Receive(``:3mpCat:3Join:3)
  Global $nick_{{NewParticipant}}$, $ephemeralPublicPoint_{{NewParticipant}}:=$ Call Receive()
  Call Update Lists(Failed to parse (syntax error): nick_{NewParticipant

)

  Global $sessionId:=$ Call Compute Session Id($roomName$, $participantList$, $ephemeralPublicPointList$)
  Call Sign and Send Key Confirmation and Shares()
  Call Wait On Receive(``:3mpCat:3KeyConfirmationShare:3)
  Global $keyShareList,keyConfirmationList,signatureList:=$ Call Receive()
  Call Verify Key Confirmations and Signatures($keyConfirmationList$, $signatureList$)
  Call Update Session Key()
  Call Send($sessionDigest$)

Farewell

Procedure Shrink on Leave
Input: $leaverId$
  Remove $leaverId$ from $participantIdList$
  Global $sessionId:=$ Call Compute Session Id()
 \If{$|participantList|>1$}
  Call Sign and Send Key Shares()
  Call Wait On Receive(``:3mpCat:3KeyShare:3)
  $keyShareList$ := Receive{}
  Call Update Session Key($keyShareList$)

Procedure Sign and Send Key Shares
Input: 
  Global $z_{{myId-1,myId}}:=SHA-512(k_{{myId,myId-1}},sessionId)$
  Global $z_{{myId,myId+1}}:=SHA-512(k_{{myId,myId+1}},sessionId)$
  $keyShare_{{myId}}:=z_{{myId-1,myId}}\oplus z_{{myId,myId+1}}$
  $originAuthSignature:=$ Call ED25519Sign($SignatureKey$, $sessionId$ || Failed to parse (syntax error): z_{myId

)

  Call Broadcast(``:3mpCat:3KeyShare:3, $myId$, Failed to parse (syntax error): keyShare_{myId

)

Send

Procedure Send
Input: Message
$keyShareMessage$ = Call NewKeyShareMessage(MetaMessage)
$cryptMessage$ := Call AES CTR Encrypt($sessionKey$,$message|keyShareMessage$)
$originAuthSignature$ := Call ED25519Sign($SignatureKey$, $sessionId$ || $cryptMetatMessage$)
$sessionDigest$ := Call Compute Session Digest($lastMessage$)
Call Broadcast(``:3mpCat:3, $sessionId$, $cryptMessage$, $sessionDigest$, $originAuthSignature$,``:3)

Recieve

Procedure Receive
Input: $sender$, $encryptedMessage$, $originAuthSignature$, $sessionDigest$
$v:=$ Call ED25519VerifySignature($ephemeralPublicKeyList[Sender]$, $sessionId||encryptedMessage$, $originAuthSignature$)
Call Assert($v$)
$message,keyShareMessage:=$ Call AES CTR Decrypt($sessionKey$, $encryptedMessage$)
$isMetaMessage=$Call UpdateNewKeyStatus($keyShareMessage$)
Call Verify Digests($sessionDiges$)
Return{$isMetaMessage,message$}

\subsection{Common functions}

Common functions used by other procedures in different stages

Procedure Generate Initial Paramters
Input: $myId$
  $signaturePrivateKey:=$ Call RandomBits(256)
  $x_{{myId}}:=$ Call Ed25519 Scalar($signaturePrivateKey$))
  $y_{{myId}}:=x_{{myId}}P$
 Return $x,y$

Procedure Verify Key Confirmation and Signatures
Input: $signatureList$, $keyConfirmationList$
  For each $participant\in participantList$}, do
    \If{$keyConfirmationList[participant][myId]\neq SHA-512(k_{{myId,participant}},U_{{myId}})$}
      Call Halt()
     ' \If{Call ED25519VerifySignature($ephemeralPublicKeyList[particicpant]$, $sessionId||keyShares[myId]$, $originAuthSignature$)'
      Call Halt()

Procedure Compute Session Id
Input: $participantList$, $ephemeralPublicPointList$
  Return $SHA-512(roomeName,zip(participantList,ephemeralPublicPointList))$ # $zip([a,b],[c,d]):=[(a,c),(b,d)]$

Procedure Verify Signatures
Input: $longPublicList$,$schnorrRandomPointList$, 

Procedure Sign and Send Key Confirmation and Share
Input: $schnorrRandomPointList$
For each $participant\in participantList$, do
    $k_{{myId,participant}}:=H(g^{{lp_{{myId}}}}LP_{{participant}}y_{{participant}}^{{x_{{myId}}}})$ # Triple DH
    $kc_{{myId}}:=kc_{{myId}}|H(k_{{myId,participant}},U_{{participant}})$

  Global $z_{{myId-1,myId}}:=SHA-512(k_{{myId,myId-1}},sessionId)$
  Global $z_{{myId,myId+1}}:=SHA-512(k_{{myId,myId+1}},sessionId)$
  $keyShare_{{myId}}:=z_{{myId-1,myId}}\oplus z_{{myId,myId+1}}$

    $originAuthSignature:=$ Call ED25519Sign($SignatureKey$, $sessionId$ || Failed to parse (syntax error): z_{myId

)

  Call Broadcast(``:3mpCat:3KeyConfirmationAndShare:3, $myId$, Failed to parse (syntax error): keyShare_{myId

)

Procedure Update Session Key
Input: $keyShareList$
$i:=myId$

For each ${j\in [i,...,i+n-1]}$}, do

  $z_{{j,j+1}}:=z_{{j-1,j}}\oplus keyShareListe[j+1]$
# recovered $z_{{i-1,i}}$ should be equal to its original value
Global $sessionKey:=SHA-512(z_{{j,j+1}}|j\in [1...n])$

Procedure Sign Params Update Session Key
Input: $toBeSigned$, $signatureList$, $keyShareList$
Call Update Session Key()
$toBeSigned:=SHA-512(sessionId,||SHA-512(verifierList,ephemeralPublicPointList,keyShareList)))$
$signature_{{myId}}:=$Call Sign Session and Send($toBeSigned$)
Call Broadcast(``:3mpCat:3SignedSessionParameters:3,Failed to parse (syntax error): signature_{myId

)

Procedure ComputeSessionDigest
Input: $lastMessage$

For each $message$ in Messages Received from $lastDigestedMessage$+1 till $lastMessage$}, do

$sesionDigest:=$ Call SHA-512($sessionDigest$, $message$)
Call LRU Cache Store Digest($sessionDigest$, $message$)
Return $sessionDigest$,$lastMessageId$