learn.equalit.ie

===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''
   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}]''
{{algorithm-end}}


{{algorithm-begin|name=Verify Verifier Generate Init Key}}
 Input: ''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'')
{{algorithm-end}}




====Join====
<!--alg_join-->
{{algorithm-begin|name=Join}}
 Input: ''newRoomName'', ''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'', ''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'''()
{{algorithm-end}}


{{algorithm-begin|name=Receive Session Digest}}
 Input: ''currentSessionHistoryDigest''
   Global ''sessionDigest := currentSessionHistoryDigest''
{{algorithm-end}}




====Protocol for other participants already in the chat to accept the newcomer====
<!--alg_accept-->
{{algorithm-begin|name=Accept}}
 Input: newParticipant
   '''Call''' '''Broadcast'''(``:3mpCat:3Join:3'', ''myId'', ''Nickname_{myId'')
   '''Call''' '''Wait On Receive'''(``:3mpCat:3Join:3'')
   Global ''nick_{NewParticipant}'', ''ephemeralPublicPoint_{NewParticipant} := '' '''Call''' '''Receive'''()
   '''Call''' '''Update Lists'''(''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'')
{{algorithm-end}}


====Farewell====
<!--alg_farewell-->
{{algorithm-begin|name=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'')
{{algorithm-end}}


{{algorithm-begin|name=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'' || ''z_{myId'')
   '''Call''' '''Broadcast'''(``:3mpCat:3KeyShare:3'', ''myId'', ''keyShare_{myId'')
{{algorithm-end}}


====Send====
<!--alg_send-->
{{algorithm-begin|name=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'')
{{algorithm-end}}


====Recieve====
<!--alg_recv-->
{{algorithm-begin|name=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''}
{{algorithm-end}}


\subsection{Common functions}



====Common functions used by other procedures in different stages====
<!--alg_comm-->


{{algorithm-begin|name=Generate Initial Paramters}}
 Input: ''myId''
   ''signaturePrivateKey := '' '''Call''' '''RandomBits'''(256)
   ''x_{myId} :='' '''Call''' '''Ed25519 Scalar'''(''signaturePrivateKey''))
   ''y_{myId} := x_{myId}P''
  '''Return''' ''x,y''
{{algorithm-end}}


{{algorithm-begin|name=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'''()
{{algorithm-end}}


{{algorithm-begin|name=Compute Session Id}}
 Input: ''participantList'', ''ephemeralPublicPointList''
   '''Return''' ''SHA-512(roomeName, zip(participantList, ephemeralPublicPointList))'' # ''zip([a,b],[c,d]):=[(a,c),(b,d)]''
{{algorithm-end}}


{{algorithm-begin|name=Verify Signatures}}
 Input: ''longPublicList'',''schnorrRandomPointList'', 
{{algorithm-end}}


{{algorithm-begin|name=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'' || ''z_{myId'')
   '''Call''' '''Broadcast'''(``:3mpCat:3KeyConfirmationAndShare:3'', ''myId'', ''keyShare_{myId'')
{{algorithm-end}}


{{algorithm-begin|name=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])''
{{algorithm-end}}


{{algorithm-begin|name=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'',''signature_{myId'')
{{algorithm-end}}


{{algorithm-begin|name=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''
{{algorithm-end}}