learn.equalit.ie

MpOTR/algorithm dump

6,246 bytes added, 9 years ago

/* Common functions used by other procedures in different stages */

~~===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====

{{algorithm-begin|name=~~Chat Initiator~~ Chatroom Init}} Input: ''<math>newRoomName''</math>, <math>participantNick</math> ''~~participantNick~~'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} :=~~'' '''Call'''~~ </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> ~~'''Call'''~~ '''Verify Verifiers'''() ~~Global~~ '''global''' <math>sessionKey := ~~SHA-512~~Hash(x_{myId}y_{other}, sessionId)''</math> ''<math>toBeSigned := ~~SHA-512~~Hash(~~SHA-512~~Hash(sessionId||~~SHA-512~~Hash(y_1, v_1)||~~SHA-512~~Hash(y_2,v_2)))''</math> ~~'''Call'''~~ '''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} := ~~'''''Call'''~~ </math>'''Generate Initial Paramters'''(~~Participant ID~~ <math>myId</math>) ''~~myId~~'global') ~~Global~~ ''<math>signatureKey_{myId} := (x_{myId},y_{myId})''</math> ~~'''Call'''~~ '''Broadcast'''(``":3mpCat:3Join:3''", ''<math>myId''</math>, ''<math>Nickname_{myId''}</math>, <math>y_{myId}</math>) ~~Global~~ '''global''' <math>participantList, ephemeralPublicPointList :=~~'' '''Call'''~~ </math> '''Receive'''() ~~Global~~ ''~~sessionId :=~~ 'global' ''~~'Call'''~~ <math>sessionId := </math> '''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~~ '''global''' <math>keyShareList, keyConfirmationList, signatureList :=~~'' '''Call'''~~ </math> '''Receive'''() ~~'''Call'''~~ '''Verify Key Confirmations and Signatures'''(''<math>keyConfirmationList''</math>, ''<math>signatureList''</math>) ~~'''Call'''~~ '''Update Session Key'''()

Input: <math>currentSessionHistoryDigest</math> ''~~currentSessionHistoryDigest~~'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> ~~'''Call'''~~ '''Broadcast'''(``":3mpCat:3Join:3''", ''<math>myId''</math>, ''<math>Nickname_{myId''}</math>, <math>y_{myId}</math>) ~~'''Call'''~~ '''Wait On Receive'''(``":3mpCat:3Join:3''") ~~Global~~ '''global''' <math>nick_{NewParticipant}''</math>, ''<math>ephemeralPublicPoint_{NewParticipant} := ~~'' '''Call'''~~ </math> '''Receive'''() ~~'''Call'''~~ '''Update Lists'''(''<math>nick_{NewParticipant''}</math>, <math>ephemeralPublicPoint_{NewParticipant}</math>) ~~Global~~ ''~~sessionId :=~~ 'global' ''~~'Call'''~~ <math>sessionId := </math> '''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~~ '''global''' <math>keyShareList, keyConfirmationList, signatureList :=~~'' '''Call'''~~ </math> '''Receive'''() ~~'''Call'''~~ '''Verify Key Confirmations and Signatures'''(''<math>keyConfirmationList''</math>, ''<math>signatureList''</math>) ~~'''Call'''~~ '''Update Session Key'''() ~~'''Call'''~~ '''Send'''(''<math>sessionDigest''</math>)

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

Input:

~~Global~~ '''global''' <math>z_{myId -1, myId} := ~~SHA-512~~Hash(k_{myId,myId-1}, sessionId)''</math> ~~Global~~ '''global''' <math>z_{myId, myId+1} := ~~SHA-512~~Hash(k_{myId,myId+1}, sessionId)''</math> ''<math>keyShare_{myId} := z_{myId -1, myId} \oplus z_{myId, myId+1}''</math> ''<math>originAuthSignature :=~~'' '''Call'''~~ </math> '''ED25519Sign'''(''<math>SignatureKey''</math>, ''<math>sessionId'' </math> || ''<math>z_{myId''}</math>) ~~'''Call'''~~ '''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~~<math>metaMessage</math>, <math>message</math> '' <math>keyShareMessage'' </math> = ~~'''Call'''~~ '''NewKeyShareMessage'''(~~MetaMessage~~<math>metaMessage</math>) '' <math>cryptMessage'' </math> := ~~'''Call'''~~ '''AES CTR Encrypt'''(''<math>sessionKey''</math>,''<math>message | keyShareMessage''</math>) '' <math>originAuthSignature'' </math> := ~~'''Call'''~~ '''ED25519Sign'''(''<math>SignatureKey''</math>, ''<math>sessionId'' </math> || ''<math>cryptMetatMessage''</math>) '' <math>sessionDigest'' </math> := ~~'''Call'''~~ '''Compute Session Digest'''(''<math>lastMessage''</math>) ~~'''Call'''~~ '''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 := ~~'' '''Call'''~~ </math> '''ED25519VerifySignature'''(''<math>ephemeralPublicKeyList[Sender]''</math>, ''<math>sessionId || encryptedMessage''</math>, ''<math>originAuthSignature''</math>) ~~'''Call'''~~ '''Assert'''(<math>v</math>) or ''v'return') ''Reject <math>message, keyShareMessage :=~~'' '''Call'''~~ </math> '''AES CTR Decrypt'''(''<math>sessionKey''</math>, ''<math>encryptedMessage''</math>){} '' <math>isMetaMessage = ~~'''''Call'''~~ </math>'''UpdateNewKeyStatus'''(''<math>keyShareMessage''</math>) ~~'''Call'''~~ '''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 := ~~'' '''Call'''~~ </math> '''RandomBits'''(256) ''<math>x_{myId} :=~~'' '''Call'''~~ </math> '''Ed25519 Scalar'''(''<math>signaturePrivateKey''</math>))#{This is both Diffie-Hellman secret and ephemeral signature private key} ''<math>y_{myId} := x_{myId}P''</math> '''~~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 ~~SHA-512~~Hash(k_{myId,participant}, U_{myId})</math>''} '~~''Call~~, then''' '''Halt'''() ' ~~\If{~~''else'~~Call~~''' ''if''' '''ED25519VerifySignature'''(''<math>ephemeralPublicKeyList[particicpant]''</math>, ''<math>sessionId ||keyShares[myId]''</math>, ''<math>originAuthSignature''</math>)= Fail ' ''~~'Call~~, then''' '''Halt'''()

Input: ''<math>participantList''</math>, ''<math>ephemeralPublicPointList''</math> '''~~Return~~return''' ~~''SHA-512~~<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''' <math>z_{myId -1, myId} := Hash(k_{myId,myId-1}, sessionId)</math> '''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>){{algorithm-end}}

~~Global ''z_~~{~~myId~~ {algorithm-~~1, myId~~begin|name=Update Session Key} } Input: <math>keyShareList</math> <math>i := ~~SHA-512(k_{~~myId</math> '''for each''' <math>{j \in [i,~~myId~~...,i+n-1]}</math>, ~~sessionId)~~'' ~~Global~~ 'do''' <math>z_{~~myId~~j, ~~myId~~j+1} := ~~SHA-512(k_~~z_{~~myId~~j-1,~~myId~~j} \oplus keyShareListe[j+1}]</math> # recovered <math>z_{i-1, ~~sessionId)~~i}</math> should be equal to its original value '' 'global'~~keyShare_{myId}~~ '' <math>sessionKey := Hash(z_{~~myId -~~j,j+1~~, myId~~} | j \~~oplus z_~~in [1...n])</math>{~~myId, myId+1~~{algorithm-end}}''

~~''originAuthSignature~~ {{algorithm-begin|name=Sign Params Update Session Key}} Input:<math>toBeSigned</math>, <math>signatureList</math>,<math>keyShareList</math> '' '~~''Call''' '''ED25519Sign~~Update Session Key'''(~~''SignatureKey'', ''~~) <math>toBeSigned := Hash(sessionId'' , || ~~''z_{myId''~~Hash(verifierList, ephemeralPublicPointList, keyShareList)))</math> <math>signature_{myId} := </math>'''~~Call~~Sign Session and Send''' (<math>toBeSigned</math>) '''Broadcast'''(``":3mpCat:~~3KeyConfirmationAndShare~~3SignedSessionParameters:3''", ~~''myId'', ''keyShare_~~<math>signature_{myId''}</math>)

{{algorithm-begin|name=~~Update Session Key~~ComputeSessionDigest}} Input: ~~''keyShareList''~~ ~~''i := myId''~~<math>lastMessage</math> '''~~For~~ for each''' ~~''{j \~~<math>message</math> in ~~[i,...,i~~Messages Received from <math>lastDigestedMessage</math>+n-1~~]}''}~~till <math>lastMessage</math>, '''do''' ~~''z_{j,j+1}~~ <math>sesionDigest := ~~z_{j-1~~Hass(sessionDigest,~~j} \oplus keyShareListe[j+1]''~~message)</math> ~~# recovered~~ ''~~z_{i-1,i}~~'LRU Cache Store Digest' ~~should be equal to its original value~~ ~~Global~~ ''~~sessionKey := SHA-512~~(~~z_{j~~<math>sessionDigest</math>,~~j+1} | j \in [1...n]~~<math>message</math>) '''return''' <math>sessionDigest</math>,<math>lastMessageId</math>

{{algorithm-begin|name=~~Sign Params Update Session Key~~NewKeyShareMessage}} Input: ~~''toBeSigned'', ''signatureList'', ''keyShareList''~~<math>metaMessage</math> ~~'''Call''' '''Update Session Key'''~~# Based on metaMessage Determines what type of keyshare needs to be send (Ephemeral point or Group key share) ~~''toBeSigned := SHA-512(sessionId, ||SHA-512(verifierList, ephemeralPublicPointList, keyShareList)))''~~ ~~''signature_{myId} := '''''Call''' '''Sign Session~~ and ~~Send'''(''toBeSigned'')~~ ~~'''Call''' '''Broadcast'''(``:3mpCat:3SignedSessionParameters:3'',''signature_{myId'')~~returen it.

{{algorithm-begin|name=~~ComputeSessionDigest~~UpdateNewKeyStatus}} Input: ~~''lastMessage''~~<math>keyShareMessage</math>~~'''For each''' ''message'' in Messages Received from ''lastDigestedMessage''+1 till ''lastMessage''~~ # Update the table of which participant has sent its new ephemeral point or its new group key share{{algorithm-end}} {{algorithm-begin|name=Hash}}~~, '''do'''~~ ~~''sesionDigest~~ Input:=<math>message</math> '' '~~''Call~~return''' '''SHA-512'''(~~''sessionDigest'', ''~~<math>message''</math>) ~~'''Call''' '''LRU Cache Store Digest'''(''sessionDigest'', ''message'')~~ ~~'''Return''' ''sessionDigest'',''lastMessageId''~~

Vmon

Administrator

148

edits

learn.equalit.ie

Changes

MpOTR/algorithm dump

Search

Personal tools

Tools