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MpOTR/algorithm dump

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Input: <math>newRoomName</math>, <math>participantNick</math>

~~Global~~ '''global''' <math>myId := 1</math> ~~Global~~ '''global''' <math>Nick_{myId} := participantNick</math> ~~Global~~ '''global''' <math>roomName := newRoomName</math> ~~Global~~ '''global''' <math>x_{myId}, y_{myId} :=</math> '''Generate Initial Paramters'''(<math>myId</math>) ~~Global~~ '''global''' <math>signatureKey_{myId} := (x_{myId},y_{myId})</math>

<math>participantList := [Nick_{myId}]</math>

<math>ephemeralPublicPointList := [y_{myId}, y_{other}]</math>

Input: <math>schnorrRandomPoint_{other}</math>, <math>Hv_{other}</math>, <math>v_{other}</math>, <math>y_{other}</math>, <math>Nick_{other}</math>

'''Verify Verifiers'''() ~~Global~~ '''global''' <math>sessionKey := Hash(x_{myId}y_{other}, sessionId)</math>

<math>toBeSigned := Hash(Hash(sessionId||Hash(y_1, v_1)||Hash(y_2,v_2)))</math>

'''Sign Session and Send'''(<math>toBeSigned</math>)

====Join====

Input: <math>newRoomName</math>, <math>Nickname_{myId}</math>, <math>participantId</math>

~~Global~~ '''global''' <math>myId := participantId</math> ~~Global~~ '''global''' <math>roomName := newRoomName</math> <math>x_{myId}, y_{myId} := </math> '''Generate Initial Paramters'''(~~Participant ID~~ <math>myId</math>) ~~Global~~ '''global''' <math>signatureKey_{myId} := (x_{myId},y_{myId})</math> '''Broadcast'''(":3mpCat:3Join:3", <math>myId</math>, <math>Nickname_{myId}</math>, <math>y_{myId}</math>) ~~Global~~ '''global''' <math>participantList, ephemeralPublicPointList :=</math> '''Receive'''() ~~Global~~ '''global''' <math>sessionId := </math> '''Compute Session Id'''(<math>roomName</math>, <math>participantList</math>, <math>ephemeralPublicPointList</math>) '''Sign and Send Key Confirmation and Shares'''() '''Wait On Receive'''(":3mpCat:3KeyConfirmationShare:3") ~~Global~~ '''global''' <math>keyShareList, keyConfirmationList, signatureList :=</math> '''Receive'''() '''Verify Key Confirmations and Signatures'''(<math>keyConfirmationList</math>, <math>signatureList</math>) '''Update Session Key'''()

Input: <math>currentSessionHistoryDigest</math>

~~Global~~ '''global''' <math>sessionDigest := currentSessionHistoryDigest</math>

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

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

Input: <math>newParticipant</math> '''Broadcast'''(":3mpCat:3Join:3", <math>myId</math>, <math>Nickname_{myId}</math>, <math>y_{myId}</math>) '''Wait On Receive'''(":3mpCat:3Join:3") ~~Global~~ '''global''' <math>nick_{NewParticipant}</math>, <math>ephemeralPublicPoint_{NewParticipant} := </math> '''Receive'''() '''Update Lists'''(<math>nick_{NewParticipant}</math>, <math>ephemeralPublicPoint_{NewParticipant}</math>) ~~Global~~ '''global''' <math>sessionId := </math> '''Compute Session Id'''(<math>roomName</math>, <math>participantList</math>, <math>ephemeralPublicPointList</math>) '''Sign and Send Key Confirmation and Shares'''() '''Wait On Receive'''(":3mpCat:3KeyConfirmationShare:3") ~~Global~~ '''global''' <math>keyShareList, keyConfirmationList, signatureList :=</math> '''Receive'''() '''Verify Key Confirmations and Signatures'''(<math>keyConfirmationList</math>, <math>signatureList</math>) '''Update Session Key'''() '''Send'''(<math>sessionDigest</math>)

Input: <math>leaverId</math>

~~Remove~~ '''remove''' <math>leaverId</math> from <math>participantIdList</math> ~~Global~~ '''global''' <math>sessionId :=</math> '''Compute Session Id'''() '''Ifif'''<math>|participantList| > 1</math>''', then''' '''Sign and Send Key Shares'''() '''Wait On Receive'''(":3mpCat:3KeyShare:3") <math>keyShareList</math> := '''Receive{}'''() '''Update Session Key'''(<math>keyShareList</math>)

Input:

~~Global~~ '''global''' <math>z_{myId -1, myId} := Hash(k_{myId,myId-1}, sessionId)</math> ~~Global~~ '''global''' <math>z_{myId, myId+1} := Hash(k_{myId,myId+1}, sessionId)</math>

<math>keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}</math>

<math>originAuthSignature :=</math> '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>z_{myId}</math>) '''Broadcast'''(":3mpCat:3KeyShare:3", <math>myId</math>, <math>keyShare_{myId}</math>, <math>originAuthSignature</math>) # we can send this encrypted but leaving person can read it, hence theoretically it is the same as sending it unencrypted.

====Send====

Input: ~~Message}{MetaMessage~~<math>metaMessage</math>, <math>message</math> <math>keyShareMessage</math> = '''NewKeyShareMessage'''(~~MetaMessage~~<math>metaMessage</math>) <math>cryptMessage</math> := '''AES CTR Encrypt'''(<math>sessionKey</math>,<math>message | keyShareMessage</math>) <math>originAuthSignature</math> := '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>cryptMetatMessage</math>) <math>sessionDigest</math> := '''Compute Session Digest'''(<math>lastMessage</math>) '''Broadcast'''(":3mpCat:3", <math>sessionId</math>, <math>cryptMessage</math>, <math>sessionDigest</math>, <math>originAuthSignature</math>,":3")

====Recieve====

Input: <math>sender</math>, <math>encryptedMessage</math>, <math>originAuthSignature</math>, <math>sessionDigest</math>

<math>v := </math> '''ED25519VerifySignature'''(<math>ephemeralPublicKeyList[Sender]</math>, <math>sessionId || encryptedMessage</math>, <math>originAuthSignature</math>) '''Assert'''(<math>v</math>)or '''return''' Reject <math>message, keyShareMessage :=</math> '''AES CTR Decrypt'''(<math>sessionKey</math>, <math>encryptedMessage</math>){} <math>isMetaMessage = </math> '''UpdateNewKeyStatus'''(<math>keyShareMessage</math>) '''Verify Digests'''(<math>sessionDiges</math>) '''~~Return~~return'''{<math>isMetaMessage, message</math>} # isMetaMessage is true if the message is purely meta message and there is nothing to display

~~\subsection{Common functions}~~

====Common functions used by other procedures in different stages====

Input: <math>myId</math>

<math>signaturePrivateKey := </math> '''RandomBits'''(256) <math>x_{myId} :=</math> '''Ed25519 Scalar'''(<math>signaturePrivateKey</math>))#{This is both Diffie-Hellman secret and ephemeral signature private key}

'''~~Return~~return''' <math>x,y</math>

Input: <math>signatureList</math>, <math>keyConfirmationList</math>

'''~~For~~ for each''' <math>participant \in participantList</math>}, '''do''' ~~\If{~~'''if''' <math>keyConfirmationList[participant][myId] \neq Hash(k_{myId,participant}, U_{myId})</math>}''', then''' '''Halt'''() ' '''if''' ~~\If{~~ '''ED25519VerifySignature'''(''', then'''{<math>ephemeralPublicKeyList[particicpant]</math>, <math>sessionId ||keyShares[myId]</math>, <math>originAuthSignature</math>)} = Fail}' '''Halt'''()

Input: <math>participantList</math>, <math>ephemeralPublicPointList</math>

'''~~Return~~return''' <math>Hash(roomeName, zip(participantList, ephemeralPublicPointList))</math> # <math>zip([a,b],[c,d]):=[(a,c),(b,d)]</math>

Input: <math>longPublicList</math>,<math>schnorrRandomPointList</math>,

# standard signature verification

{{algorithm-begin|name=Sign and Send Key Confirmation and Share}}

Input: <math>schnorrRandomPointList</math>

'''~~For~~ for each''' <math>participant \in participantList</math>, '''do''' <math>k_{myId, participant} := HHash(~~g^{lp_~~x_{myId}}LP_{participant} |lp_{myId}y_{participant}^{| x_{myId}y_{participant})</math> # Triple DH <math>kc_{myId} := kc_{myId} | HHash(k_{myId,participant}, U_{participant})</math> ~~Global~~ '''global''' <math>z_{myId -1, myId} := Hash(k_{myId,myId-1}, sessionId)</math> ~~Global~~ '''global''' <math>z_{myId, myId+1} := Hash(k_{myId,myId+1}, sessionId)</math>

<math>keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}</math>

<math>originAuthSignature :=</math> '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>z_{myId}</math>) '''Broadcast'''(":3mpCat:3KeyConfirmationAndShare:3", <math>myId</math>, <math>keyShare_{myId}</math>, <math>originAuthSignature</math>, <math>kc_{myId}</math>)

Input: <math>keyShareList</math>

'''~~For~~ for each''' <math>{j \in [i,...,i+n-1]}</math>}, '''do'''

<math>z_{j,j+1} := z_{j-1,j} \oplus keyShareListe[j+1]</math>

# recovered <math>z_{i-1,i}</math> should be equal to its original value ~~Global~~ '''global''' <math>sessionKey := Hash(z_{j,j+1} | j \in [1...n])</math>

Input: <math>toBeSigned</math>, <math>signatureList</math>, <math>keyShareList</math>

'''Update Session Key'''()

<math>toBeSigned := Hash(sessionId, ||Hash(verifierList, ephemeralPublicPointList, keyShareList)))</math>

<math>signature_{myId} := </math> '''Sign Session and Send'''(<math>toBeSigned</math>) '''Broadcast'''(":3mpCat:3SignedSessionParameters:3",<math>signature_{myId}</math>)

Input: <math>lastMessage</math>

'''~~For~~ for each''' <math>message</math> in Messages Received from <math>lastDigestedMessage</math>+1 till <math>lastMessage</math>}, '''do''' <math>sesionDigest :=Hass(sessionDigest, message)</math> '''~~Hash~~LRU Cache Store Digest'''(<math>sessionDigest</math>, <math>message</math>) '''return''' <math>sessionDigest</math>,<math>lastMessageId</math>{{algorithm-end}} {{algorithm-begin|name=NewKeyShareMessage}} Input: <math>metaMessage</math> # Based on metaMessage Determines what type of keyshare needs to be send (Ephemeral point or Group key share) and returen it.{{algorithm-end}} {{algorithm-begin|name=UpdateNewKeyStatus}} Input: <math>keyShareMessage</math> # Update the table of which participant has sent its new ephemeral point or its new group key share{{algorithm-end}} {{algorithm-begin|name=Hash}} Input: <math>message</math> '''return''' '''~~LRU Cache Store Digest~~SHA-512'''(~~<math>sessionDigest</math>,~~ <math>message</math>) ~~'''Return''' <math>sessionDigest</math>,<math>lastMessageId</math>~~

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