learn.equalit.ie

Revision as of 10:33, 27 July 2014

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  $sessionDigest$ , $lastMessageId$

@@ Line 1: / Line 1: @@
-===Example of an Algorithm in Wiki===
-{{algorithm-begin|name=LargestNumber}}
-   Input: A list of numbers ''L''.
-   Output: The largest number in the list ''L''.
-   ''largest'' ← null
-   '''for each''' ''item'' '''in''' "L"', '''do'''
-     '''if''' ''item'' > ''largest'', '''then'''
-       ''largest'' ← ''item''
-   '''return''' ''largest''
-{{algorithm-end}}
-===mpOTR algorithms===
 ====Chatroom setup====
 <!--alg_chat_setup-->
 {{algorithm-begin|name=Chat Initiator Init}}
-  Input: ''newRoomName'', ''participantNick''
+  Input: <math>newRoomName</math>, <math>participantNick</math>
-    Global ''myId := 1''
+    Global <math>myId := 1</math>
-    Global ''Nick_{myId} := participantNick''
+    Global <math>Nick_{myId} := participantNick</math>
-    Global ''roomName := newRoomName''
+    Global <math>roomName := newRoomName</math>
-    Global ''x_{myId}, y_{myId} :='' '''Call''' '''Generate Initial Paramters'''(''myId'')
+    Global <math>x_{myId}, y_{myId} :=</math> '''Call''' '''Generate Initial Paramters'''(<math>myId</math>)
-    Global ''signatureKey_{myId} := (x_{myId},y_{myId})''
+    Global <math>signatureKey_{myId} := (x_{myId},y_{myId})</math>
-    ''participantList := [Nick_{myId}]''
+    <math>participantList := [Nick_{myId}]</math>
-    ''ephemeralPublicPointList := [y_{myId}, y_{other}]''
+    <math>ephemeralPublicPointList := [y_{myId}, y_{other}]</math>
 {{algorithm-end}}
 {{algorithm-begin|name=Verify Verifier Generate Init Key}}
-  Input: ''schnorrRandomPoint_{other''
+  Input: <math>schnorrRandomPoint_{other</math>
     '''Call''' '''Verify Verifiers'''()
-    Global ''sessionKey := SHA-512(x_{myId}y_{other}, sessionId)''
+    Global <math>sessionKey := SHA-512(x_{myId}y_{other}, sessionId)</math>
-    ''toBeSigned := SHA-512(SHA-512(sessionId||SHA-512(y_1, v_1)||SHA-512(y_2,v_2)))''
+    <math>toBeSigned := SHA-512(SHA-512(sessionId||SHA-512(y_1, v_1)||SHA-512(y_2,v_2)))</math>
-    '''Call''' '''Sign Session and Send'''(''toBeSigned'')
+    '''Call''' '''Sign Session and Send'''(<math>toBeSigned</math>)
 {{algorithm-end}}
@@ Line 40: / Line 27: @@
 <!--alg_join-->
 {{algorithm-begin|name=Join}}
-  Input: ''newRoomName'', ''Nickname_{myId''
+  Input: <math>newRoomName</math>, <math>Nickname_{myId</math>
-    Global ''myId := participantId''
+    Global <math>myId := participantId</math>
-    Global ''roomName := newRoomName''
+    Global <math>roomName := newRoomName</math>
-    ''x_{myId}, y_{myId} := '''''Call''' '''Generate Initial Paramters'''(Participant ID ''myId'')
+    <math>x_{myId}, y_{myId} := </math>'''Call''' '''Generate Initial Paramters'''(Participant ID <math>myId</math>)
-    Global ''signatureKey_{myId} := (x_{myId},y_{myId})''
+    Global <math>signatureKey_{myId} := (x_{myId},y_{myId})</math>
-    '''Call''' '''Broadcast'''(``:3mpCat:3Join:3'', ''myId'', ''Nickname_{myId'')
+    '''Call''' '''Broadcast'''(``:3mpCat:3Join:3'', <math>myId</math>, <math>Nickname_{myId</math>)
-    Global ''participantList, ephemeralPublicPointList :='' '''Call''' '''Receive'''()
+    Global <math>participantList, ephemeralPublicPointList :=</math> '''Call''' '''Receive'''()
-    Global ''sessionId := '' '''Call''' '''Compute Session Id'''(''roomName'', ''participantList'', ''ephemeralPublicPointList'')
+    Global <math>sessionId := </math> '''Call''' '''Compute Session Id'''(<math>roomName</math>, <math>participantList</math>, <math>ephemeralPublicPointList</math>)
     '''Call''' '''Sign and Send Key Confirmation and Shares'''()
     '''Call''' '''Wait On Receive'''(``:3mpCat:3KeyConfirmationShare:3'')
-    Global ''keyShareList, keyConfirmationList, signatureList :='' '''Call''' '''Receive'''()
+    Global <math>keyShareList, keyConfirmationList, signatureList :=</math> '''Call''' '''Receive'''()
-    '''Call''' '''Verify Key Confirmations and Signatures'''(''keyConfirmationList'', ''signatureList'')
+    '''Call''' '''Verify Key Confirmations and Signatures'''(<math>keyConfirmationList</math>, <math>signatureList</math>)
     '''Call''' '''Update Session Key'''()
 {{algorithm-end}}
@@ Line 57: / Line 44: @@
 {{algorithm-begin|name=Receive Session Digest}}
-  Input: ''currentSessionHistoryDigest''
+  Input: <math>currentSessionHistoryDigest</math>
-    Global ''sessionDigest := currentSessionHistoryDigest''
+    Global <math>sessionDigest := currentSessionHistoryDigest</math>
 {{algorithm-end}}
@@ Line 68: / Line 55: @@
 {{algorithm-begin|name=Accept}}
   Input: newParticipant
-    '''Call''' '''Broadcast'''(``:3mpCat:3Join:3'', ''myId'', ''Nickname_{myId'')
+    '''Call''' '''Broadcast'''(``:3mpCat:3Join:3'', <math>myId</math>, <math>Nickname_{myId</math>)
     '''Call''' '''Wait On Receive'''(``:3mpCat:3Join:3'')
-    Global ''nick_{NewParticipant}'', ''ephemeralPublicPoint_{NewParticipant} := '' '''Call''' '''Receive'''()
+    Global <math>nick_{NewParticipant}</math>, <math>ephemeralPublicPoint_{NewParticipant} := </math> '''Call''' '''Receive'''()
-    '''Call''' '''Update Lists'''(''nick_{NewParticipant'')
+    '''Call''' '''Update Lists'''(<math>nick_{NewParticipant</math>)
-    Global ''sessionId := '' '''Call''' '''Compute Session Id'''(''roomName'', ''participantList'', ''ephemeralPublicPointList'')
+    Global <math>sessionId := </math> '''Call''' '''Compute Session Id'''(<math>roomName</math>, <math>participantList</math>, <math>ephemeralPublicPointList</math>)
     '''Call''' '''Sign and Send Key Confirmation and Shares'''()
     '''Call''' '''Wait On Receive'''(``:3mpCat:3KeyConfirmationShare:3'')
-    Global ''keyShareList, keyConfirmationList, signatureList :='' '''Call''' '''Receive'''()
+    Global <math>keyShareList, keyConfirmationList, signatureList :=</math> '''Call''' '''Receive'''()
-    '''Call''' '''Verify Key Confirmations and Signatures'''(''keyConfirmationList'', ''signatureList'')
+    '''Call''' '''Verify Key Confirmations and Signatures'''(<math>keyConfirmationList</math>, <math>signatureList</math>)
     '''Call''' '''Update Session Key'''()
-    '''Call''' '''Send'''(''sessionDigest'')
+    '''Call''' '''Send'''(<math>sessionDigest</math>)
 {{algorithm-end}}
@@ Line 85: / Line 72: @@
 <!--alg_farewell-->
 {{algorithm-begin|name=Shrink on Leave}}
-  Input: ''leaverId''
+  Input: <math>leaverId</math>
-    Remove ''leaverId'' from ''participantIdList''
+    Remove <math>leaverId</math> from <math>participantIdList</math>
-    Global ''sessionId :='' '''Call''' '''Compute Session Id'''()
+    Global <math>sessionId :=</math> '''Call''' '''Compute Session Id'''()
-   \If{''|participantList| > 1''}
+   \If{<math>|participantList| > 1</math>}
     '''Call''' '''Sign and Send Key Shares'''()
     '''Call''' '''Wait On Receive'''(``:3mpCat:3KeyShare:3'')
-    ''keyShareList'' := Receive{}
+    <math>keyShareList</math> := Receive{}
-    '''Call''' '''Update Session Key'''(''keyShareList'')
+    '''Call''' '''Update Session Key'''(<math>keyShareList</math>)
 {{algorithm-end}}
@@ Line 98: / Line 85: @@
 {{algorithm-begin|name=Sign and Send Key Shares}}
   Input:
-    Global ''z_{myId -1, myId} := SHA-512(k_{myId,myId-1}, sessionId)''
+    Global <math>z_{myId -1, myId} := SHA-512(k_{myId,myId-1}, sessionId)</math>
-    Global ''z_{myId, myId+1} := SHA-512(k_{myId,myId+1}, sessionId)''
+    Global <math>z_{myId, myId+1} := SHA-512(k_{myId,myId+1}, sessionId)</math>
-    ''keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}''
+    <math>keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}</math>
-    ''originAuthSignature :='' '''Call''' '''ED25519Sign'''(''SignatureKey'', ''sessionId'' || ''z_{myId'')
+    <math>originAuthSignature :=</math> '''Call''' '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>z_{myId</math>)
-    '''Call''' '''Broadcast'''(``:3mpCat:3KeyShare:3'', ''myId'', ''keyShare_{myId'')
+    '''Call''' '''Broadcast'''(``:3mpCat:3KeyShare:3'', <math>myId</math>, <math>keyShare_{myId</math>)
 {{algorithm-end}}
@@ Line 110: / Line 97: @@
 {{algorithm-begin|name=Send}}
   Input: Message
-  ''keyShareMessage'' = '''Call''' '''NewKeyShareMessage'''(MetaMessage)
+  <math>keyShareMessage</math> = '''Call''' '''NewKeyShareMessage'''(MetaMessage)
-  ''cryptMessage'' := '''Call''' '''AES CTR Encrypt'''(''sessionKey'',''message | keyShareMessage'')
+  <math>cryptMessage</math> := '''Call''' '''AES CTR Encrypt'''(<math>sessionKey</math>,<math>message | keyShareMessage</math>)
-  ''originAuthSignature'' := '''Call''' '''ED25519Sign'''(''SignatureKey'', ''sessionId'' || ''cryptMetatMessage'')
+  <math>originAuthSignature</math> := '''Call''' '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>cryptMetatMessage</math>)
-  ''sessionDigest'' := '''Call''' '''Compute Session Digest'''(''lastMessage'')
+  <math>sessionDigest</math> := '''Call''' '''Compute Session Digest'''(<math>lastMessage</math>)
-  '''Call''' '''Broadcast'''(``:3mpCat:3'', ''sessionId'', ''cryptMessage'', ''sessionDigest'', ''originAuthSignature'',``:3'')
+  '''Call''' '''Broadcast'''(``:3mpCat:3'', <math>sessionId</math>, <math>cryptMessage</math>, <math>sessionDigest</math>, <math>originAuthSignature</math>,``:3'')
 {{algorithm-end}}
@@ Line 121: / Line 108: @@
 <!--alg_recv-->
 {{algorithm-begin|name=Receive}}
-  Input: ''sender'', ''encryptedMessage'', ''originAuthSignature'', ''sessionDigest''
+  Input: <math>sender</math>, <math>encryptedMessage</math>, <math>originAuthSignature</math>, <math>sessionDigest</math>
-  ''v := '' '''Call''' '''ED25519VerifySignature'''(''ephemeralPublicKeyList[Sender]'', ''sessionId || encryptedMessage'', ''originAuthSignature'')
+  <math>v := </math> '''Call''' '''ED25519VerifySignature'''(<math>ephemeralPublicKeyList[Sender]</math>, <math>sessionId || encryptedMessage</math>, <math>originAuthSignature</math>)
-  '''Call''' '''Assert'''(''v'')
+  '''Call''' '''Assert'''(<math>v</math>)
-  ''message, keyShareMessage :='' '''Call''' '''AES CTR Decrypt'''(''sessionKey'', ''encryptedMessage'')
+  <math>message, keyShareMessage :=</math> '''Call''' '''AES CTR Decrypt'''(<math>sessionKey</math>, <math>encryptedMessage</math>)
-  ''isMetaMessage = '''''Call''' '''UpdateNewKeyStatus'''(''keyShareMessage'')
+  <math>isMetaMessage = </math>'''Call''' '''UpdateNewKeyStatus'''(<math>keyShareMessage</math>)
-  '''Call''' '''Verify Digests'''(''sessionDiges'')
+  '''Call''' '''Verify Digests'''(<math>sessionDiges</math>)
-  '''Return'''{''isMetaMessage, message''}
+  '''Return'''{<math>isMetaMessage, message</math>}
 {{algorithm-end}}
@@ Line 140: / Line 127: @@
 {{algorithm-begin|name=Generate Initial Paramters}}
-  Input: ''myId''
+  Input: <math>myId</math>
-    ''signaturePrivateKey := '' '''Call''' '''RandomBits'''(256)
+    <math>signaturePrivateKey := </math> '''Call''' '''RandomBits'''(256)
-    ''x_{myId} :='' '''Call''' '''Ed25519 Scalar'''(''signaturePrivateKey''))
+    <math>x_{myId} :=</math> '''Call''' '''Ed25519 Scalar'''(<math>signaturePrivateKey</math>))
-    ''y_{myId} := x_{myId}P''
+    <math>y_{myId} := x_{myId}P</math>
-   '''Return''' ''x,y''
+   '''Return''' <math>x,y</math>
 {{algorithm-end}}
 {{algorithm-begin|name=Verify Key Confirmation and Signatures}}
-  Input: ''signatureList'', ''keyConfirmationList''
+  Input: <math>signatureList</math>, <math>keyConfirmationList</math>
-    '''For each''' ''participant \in participantList''}, '''do'''
+    '''For each''' <math>participant \in participantList</math>}, '''do'''
-      \If{''keyConfirmationList[participant][myId] \neq SHA-512(k_{myId,participant}, U_{myId})''}
+      \If{<math>keyConfirmationList[participant][myId] \neq SHA-512(k_{myId,participant}, U_{myId})</math>}
         '''Call''' '''Halt'''()
-       ' \If{'''Call''' '''ED25519VerifySignature'''(''ephemeralPublicKeyList[particicpant]'', ''sessionId ||keyShares[myId]'', ''originAuthSignature'')'
+       ' \If{'''Call''' '''ED25519VerifySignature'''(<math>ephemeralPublicKeyList[particicpant]</math>, <math>sessionId ||keyShares[myId]</math>, <math>originAuthSignature</math>)'
         '''Call''' '''Halt'''()
 {{algorithm-end}}
@@ Line 159: / Line 146: @@
 {{algorithm-begin|name=Compute Session Id}}
-  Input: ''participantList'', ''ephemeralPublicPointList''
+  Input: <math>participantList</math>, <math>ephemeralPublicPointList</math>
-    '''Return''' ''SHA-512(roomeName, zip(participantList, ephemeralPublicPointList))'' # ''zip([a,b],[c,d]):=[(a,c),(b,d)]''
+    '''Return''' <math>SHA-512(roomeName, zip(participantList, ephemeralPublicPointList))</math> # <math>zip([a,b],[c,d]):=[(a,c),(b,d)]</math>
 {{algorithm-end}}
 {{algorithm-begin|name=Verify Signatures}}
-  Input: ''longPublicList'',''schnorrRandomPointList'',
+  Input: <math>longPublicList</math>,<math>schnorrRandomPointList</math>,
 {{algorithm-end}}
 {{algorithm-begin|name=Sign and Send Key Confirmation and Share}}
-  Input: ''schnorrRandomPointList''
+  Input: <math>schnorrRandomPointList</math>
-  '''For each''' ''participant \in participantList'', '''do'''
+  '''For each''' <math>participant \in participantList</math>, '''do'''
-      ''k_{myId, participant} := H(g^{lp_{myId}}LP_{participant}y_{participant}^{x_{myId}})'' # Triple DH
+      <math>k_{myId, participant} := H(g^{lp_{myId}}LP_{participant}y_{participant}^{x_{myId}})</math> # Triple DH
-      ''kc_{myId} := kc_{myId} | H(k_{myId,participant}, U_{participant})''
+      <math>kc_{myId} := kc_{myId} | H(k_{myId,participant}, U_{participant})</math>
-    Global ''z_{myId -1, myId} := SHA-512(k_{myId,myId-1}, sessionId)''
+    Global <math>z_{myId -1, myId} := SHA-512(k_{myId,myId-1}, sessionId)</math>
-    Global ''z_{myId, myId+1} := SHA-512(k_{myId,myId+1}, sessionId)''
+    Global <math>z_{myId, myId+1} := SHA-512(k_{myId,myId+1}, sessionId)</math>
-    ''keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}''
+    <math>keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}</math>
-      ''originAuthSignature :='' '''Call''' '''ED25519Sign'''(''SignatureKey'', ''sessionId'' || ''z_{myId'')
+      <math>originAuthSignature :=</math> '''Call''' '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>z_{myId</math>)
-    '''Call''' '''Broadcast'''(``:3mpCat:3KeyConfirmationAndShare:3'', ''myId'', ''keyShare_{myId'')
+    '''Call''' '''Broadcast'''(``:3mpCat:3KeyConfirmationAndShare:3'', <math>myId</math>, <math>keyShare_{myId</math>)
 {{algorithm-end}}
 {{algorithm-begin|name=Update Session Key}}
-  Input: ''keyShareList''
+  Input: <math>keyShareList</math>
-  ''i := myId''
+  <math>i := myId</math>
-'''For each''' ''{j \in [i,...,i+n-1]}''}, '''do'''
+'''For each''' <math>{j \in [i,...,i+n-1]}</math>}, '''do'''
-    ''z_{j,j+1} := z_{j-1,j} \oplus keyShareListe[j+1]''
+    <math>z_{j,j+1} := z_{j-1,j} \oplus keyShareListe[j+1]</math>
-  # recovered ''z_{i-1,i}'' should be equal to its original value
+  # recovered <math>z_{i-1,i}</math> should be equal to its original value
-  Global ''sessionKey := SHA-512(z_{j,j+1} | j \in [1...n])''
+  Global <math>sessionKey := SHA-512(z_{j,j+1} | j \in [1...n])</math>
 {{algorithm-end}}
 {{algorithm-begin|name=Sign Params Update Session Key}}
-  Input: ''toBeSigned'', ''signatureList'', ''keyShareList''
+  Input: <math>toBeSigned</math>, <math>signatureList</math>, <math>keyShareList</math>
   '''Call''' '''Update Session Key'''()
-  ''toBeSigned := SHA-512(sessionId, ||SHA-512(verifierList, ephemeralPublicPointList, keyShareList)))''
+  <math>toBeSigned := SHA-512(sessionId, ||SHA-512(verifierList, ephemeralPublicPointList, keyShareList)))</math>
-  ''signature_{myId} := '''''Call''' '''Sign Session and Send'''(''toBeSigned'')
+  <math>signature_{myId} := </math>'''Call''' '''Sign Session and Send'''(<math>toBeSigned</math>)
-  '''Call''' '''Broadcast'''(``:3mpCat:3SignedSessionParameters:3'',''signature_{myId'')
+  '''Call''' '''Broadcast'''(``:3mpCat:3SignedSessionParameters:3'',<math>signature_{myId</math>)
 {{algorithm-end}}
 {{algorithm-begin|name=ComputeSessionDigest}}
-  Input: ''lastMessage''
+  Input: <math>lastMessage</math>
-'''For each''' ''message'' in Messages Received from ''lastDigestedMessage''+1 till ''lastMessage''}, '''do'''
+'''For each''' <math>message</math> in Messages Received from <math>lastDigestedMessage</math>+1 till <math>lastMessage</math>}, '''do'''
-  ''sesionDigest :='' '''Call''' '''SHA-512'''(''sessionDigest'', ''message'')
+  <math>sesionDigest :=</math> '''Call''' '''SHA-512'''(<math>sessionDigest</math>, <math>message</math>)
-  '''Call''' '''LRU Cache Store Digest'''(''sessionDigest'', ''message'')
+  '''Call''' '''LRU Cache Store Digest'''(<math>sessionDigest</math>, <math>message</math>)
-  '''Return''' ''sessionDigest'',''lastMessageId''
+  '''Return''' <math>sessionDigest</math>,<math>lastMessageId</math>
 {{algorithm-end}}

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Difference between revisions of "MpOTR/algorithm dump"

Revision as of 10:33, 27 July 2014

Contents

Chatroom setup

Join

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

Farewell

Send

Recieve

Common functions used by other procedures in different stages

Search

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