MpOTR/algorithm dump - learn.equalit.ie

Chatroom setup

Procedure Chatroom Init
Input:  $newRoomName$ ,  $participantNick$ 
  global  $myId:=1$ 
  global  $Nick_{{myId}}:=participantNick$ 
  global  $roomName:=newRoomName$ 
  global  $x_{{myId}},y_{{myId}}:=$  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:  $schnorrRandomPoint_{{other}}$ ,  $Hv_{{other}}$ ,  $v_{{other}}$ ,  $y_{{other}}$ ,  $Nick_{{other}}$ 
  Verify Verifiers()
  global  $sessionKey:=Hash(x_{{myId}}y_{{other}},sessionId)$ 
   $toBeSigned:=Hash(Hash(sessionId||Hash(y_{1},v_{1})||Hash(y_{2},v_{2})))$ 
  Sign Session and Send( $toBeSigned$ )

Join

Procedure Join
Input:  $newRoomName$ ,  $Nickname_{{myId}}$ ,  $participantId$ 
  global  $myId:=participantId$ 
  global  $roomName:=newRoomName$ 
   $x_{{myId}},y_{{myId}}:=$ Generate Initial Paramters( $myId$ )
  global  $signatureKey_{{myId}}:=(x_{{myId}},y_{{myId}})$ 
  Broadcast(":3mpCat:3Join:3",  $myId$ ,  $Nickname_{{myId}}$ ,  $y_{{myId}}$ )
  global  $participantList,ephemeralPublicPointList:=$  Receive()
  global  $sessionId:=$  Compute Session Id( $roomName$ ,  $participantList$ ,  $ephemeralPublicPointList$ )
  Sign and Send Key Confirmation and Shares()
  Wait On Receive(":3mpCat:3KeyConfirmationShare:3")
  global  $keyShareList,keyConfirmationList,signatureList:=$  Receive()
  Verify Key Confirmations and Signatures( $keyConfirmationList$ ,  $signatureList$ )
  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:  $newParticipant$ 
  Broadcast(":3mpCat:3Join:3",  $myId$ ,  $Nickname_{{myId}}$ ,  $y_{{myId}}$ )
  Wait On Receive(":3mpCat:3Join:3")
  global  $nick_{{NewParticipant}}$ ,  $ephemeralPublicPoint_{{NewParticipant}}:=$  Receive()
  Update Lists( $nick_{{NewParticipant}}$ ,  $ephemeralPublicPoint_{{NewParticipant}}$ )
  global  $sessionId:=$  Compute Session Id( $roomName$ ,  $participantList$ ,  $ephemeralPublicPointList$ )
  Sign and Send Key Confirmation and Shares()
  Wait On Receive(":3mpCat:3KeyConfirmationShare:3")
  global  $keyShareList,keyConfirmationList,signatureList:=$  Receive()
  Verify Key Confirmations and Signatures( $keyConfirmationList$ ,  $signatureList$ )
  Update Session Key()
  Send( $sessionDigest$ )

Farewell

Procedure Shrink on Leave
Input:  $leaverId$ 
  remove  $leaverId$  from  $participantIdList$ 
  global  $sessionId:=$  Compute Session Id()
  if  $|participantList|>1$ , then
    Sign and Send Key Shares()
    Wait On Receive(":3mpCat:3KeyShare:3")
     $keyShareList$  := Receive()
    Update Session Key( $keyShareList$ )

Procedure Sign and Send Key Shares
Input: 
  global  $z_{{myId-1,myId}}:=Hash(k_{{myId,myId-1}},sessionId)$ 
  global  $z_{{myId,myId+1}}:=Hash(k_{{myId,myId+1}},sessionId)$ 
   $keyShare_{{myId}}:=z_{{myId-1,myId}}\oplus z_{{myId,myId+1}}$ 
   $originAuthSignature:=$  ED25519Sign( $SignatureKey$ ,  $sessionId$  ||  $z_{{myId}}$ )
  Broadcast(":3mpCat:3KeyShare:3",  $myId$ ,  $keyShare_{{myId}}$ ,  $originAuthSignature$ )  # we can send this encrypted but leaving person can read it, hence theoretically it is the same as sending it unencrypted.

Send

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

Recieve

Procedure Receive
Input:  $sender$ ,  $encryptedMessage$ ,  $originAuthSignature$ ,  $sessionDigest$ 
   $v:=$  ED25519VerifySignature( $ephemeralPublicKeyList[Sender]$ ,  $sessionId||encryptedMessage$ ,  $originAuthSignature$ )
  Assert( $v$ ) or return Reject
   $message,keyShareMessage:=$  AES CTR Decrypt( $sessionKey$ ,  $encryptedMessage$ ){}
   $isMetaMessage=$ UpdateNewKeyStatus( $keyShareMessage$ )
  Verify Digests( $sessionDiges$ )
  return{ $isMetaMessage,message$ }  # isMetaMessage is true if the message is purely meta message and there is nothing to display

Common functions used by other procedures in different stages

Procedure Generate Initial Paramters
Input:  $myId$ 
   $signaturePrivateKey:=$  RandomBits(256)
   $x_{{myId}}:=$  Ed25519 Scalar( $signaturePrivateKey$ )) #{This is both Diffie-Hellman secret and ephemeral signature private key}
   $y_{{myId}}:=x_{{myId}}P$ 
  return  $x,y$

Procedure Verify Key Confirmation and Signatures
Input:  $signatureList$ ,  $keyConfirmationList$ 
  for each  $participant\in participantList$ , do
    if  $keyConfirmationList[participant][myId]\neq Hash(k_{{myId,participant}},U_{{myId}})$ , then
      Halt()
    else if ED25519VerifySignature( $ephemeralPublicKeyList[particicpant]$ ,  $sessionId|keyShares[myId]$ ,  $originAuthSignature$ ) = Fail , then
      Halt()

Procedure Compute Session Id
Input:  $participantList$ ,  $ephemeralPublicPointList$ 
  return  $Hash(roomeName,zip(participantList,ephemeralPublicPointList))$   #  $zip([a,b],[c,d]):=[(a,c),(b,d)]$

Procedure Verify Signatures
Input:  $longPublicList$ , $schnorrRandomPointList$ , 
# standard signature verification

Procedure Sign and Send Key Confirmation and Share
Input:  $schnorrRandomPointList$ 
  for each  $participant\in participantList$ , do
     $k_{{myId,participant}}:=Hash(x_{{myId}}LP_{{participant}}|lp_{{myId}}y_{{participant}}|x_{{myId}}y_{{participant}})$   # Triple DH
     $kc_{{myId}}:=kc_{{myId}}|Hash(k_{{myId,participant}},U_{{participant}})$ 
  global  $z_{{myId-1,myId}}:=Hash(k_{{myId,myId-1}},sessionId)$ 
  global  $z_{{myId,myId+1}}:=Hash(k_{{myId,myId+1}},sessionId)$ 
   $keyShare_{{myId}}:=z_{{myId-1,myId}}\oplus z_{{myId,myId+1}}$ 
   $originAuthSignature:=$  ED25519Sign( $SignatureKey$ ,  $sessionId$  ||  $z_{{myId}}$ )
  Broadcast(":3mpCat:3KeyConfirmationAndShare:3",  $myId$ ,  $keyShare_{{myId}}$ ,  $originAuthSignature$ ,  $kc_{{myId}}$ )

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  $sessionKey:=Hash(z_{{j,j+1}}|j\in [1...n])$

Procedure Sign Params Update Session Key
Input:  $toBeSigned$ ,  $signatureList$ , $keyShareList$ 
  Update Session Key()
   $toBeSigned:=Hash(sessionId,||Hash(verifierList,ephemeralPublicPointList,keyShareList)))$ 
   $signature_{{myId}}:=$ Sign Session and Send( $toBeSigned$ )
  Broadcast(":3mpCat:3SignedSessionParameters:3", $signature_{{myId}}$ )

Procedure ComputeSessionDigest
Input:  $lastMessage$ 
  for each  $message$  in Messages Received from  $lastDigestedMessage$ +1 till  $lastMessage$ , do
      $sesionDigest:=Hass(sessionDigest,message)$  
     LRU Cache Store Digest( $sessionDigest$ ,  $message$ )
  return  $sessionDigest$ , $lastMessageId$

Procedure NewKeyShareMessage
Input:  $metaMessage$ 
# Based on metaMessage Determines what type of keyshare needs to be send (Ephemeral point or Group key share) and returen it.

Procedure UpdateNewKeyStatus
Input:  $keyShareMessage$ 
# Update the table of which participant has sent its new ephemeral point or its new group key share

Procedure Hash
Input:  $message$ 
   return SHA-512( $message$ )

Last modified 11 years ago