learn.equalit.ie

MpOTR/algorithm dump

4,117 bytes added, 9 years ago

====Chatroom setup====

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

Global <math>myId := 1</math>

Global <math>Nick_{myId} := participantNick</math>

Global <math>roomName := newRoomName</math>

Global <math>x_{myId}, y_{myId} :=</math> ~~'''Call'''~~ '''Generate Initial Paramters'''(<math>myId</math>)

Global <math>signatureKey_{myId} := (x_{myId},y_{myId})</math>

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

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

Global <math>myId := participantId</math>

Global <math>roomName := newRoomName</math>

<math>x_{myId}, y_{myId} := </math>~~'''Call'''~~ '''Generate Initial Paramters'''(Participant ID <math>myId</math>)

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 <math>participantList, ephemeralPublicPointList :=</math> ~~'''Call'''~~ '''Receive'''() 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 <math>keyShareList, keyConfirmationList, signatureList :=</math> ~~'''Call'''~~ '''Receive'''() ~~'''Call'''~~ '''Verify Key Confirmations and Signatures'''(<math>keyConfirmationList</math>, <math>signatureList</math>) ~~'''Call'''~~ '''Update Session Key'''()

Input: newParticipant

~~'''Call'''~~ '''Broadcast'''(``":3mpCat:3Join:3''", <math>myId</math>, <math>Nickname_{myId}</math>, <math>y_{myId}</math>) ~~'''Call'''~~ '''Wait On Receive'''(``":3mpCat:3Join:3''") Global <math>nick_{NewParticipant}</math>, <math>ephemeralPublicPoint_{NewParticipant} := </math> ~~'''Call'''~~ '''Receive'''() ~~'''Call'''~~ '''Update Lists'''(<math>nick_{NewParticipant}</math>, <math>ephemeralPublicPoint_{NewParticipant}</math>) 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 <math>keyShareList, keyConfirmationList, signatureList :=</math> ~~'''Call'''~~ '''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 <math>leaverId</math> from <math>participantIdList</math>

Global <math>sessionId :=</math> ~~'''Call'''~~ '''Compute Session Id'''() \'''If{'''<math>|participantList| > 1</math>} '''~~Call~~, then''' '''Sign and Send Key Shares'''() ~~'''Call'''~~ '''Wait On Receive'''(``":3mpCat:3KeyShare:3''")

<math>keyShareList</math> := Receive{}

~~'''Call'''~~ '''Update Session Key'''(<math>keyShareList</math>)

Input:

Global <math>z_{myId -1, myId} := ~~SHA-512~~Hash(k_{myId,myId-1}, sessionId)</math> 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 :=</math> ~~'''Call'''~~ '''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>)

Input: Message}{MetaMessage, message <math>keyShareMessage</math> = ~~'''Call'''~~ '''NewKeyShareMessage'''(MetaMessage) <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''")

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

<math>v := </math> ~~'''Call'''~~ '''ED25519VerifySignature'''(<math>ephemeralPublicKeyList[Sender]</math>, <math>sessionId || encryptedMessage</math>, <math>originAuthSignature</math>) ~~'''Call'''~~ '''Assert'''(<math>v</math>) <math>message, keyShareMessage :=</math> ~~'''Call'''~~ '''AES CTR Decrypt'''(<math>sessionKey</math>, <math>encryptedMessage</math>) <math>isMetaMessage = </math>~~'''Call'''~~ '''UpdateNewKeyStatus'''(<math>keyShareMessage</math>) ~~'''Call'''~~ '''Verify Digests'''(<math>sessionDiges</math>)

'''Return'''{<math>isMetaMessage, message</math>}

Input: <math>myId</math>

<math>signaturePrivateKey := </math> ~~'''Call'''~~ '''RandomBits'''(256) <math>x_{myId} :=</math> ~~'''Call'''~~ '''Ed25519 Scalar'''(<math>signaturePrivateKey</math>))

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

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

'''For each''' <math>participant \in participantList</math>}, '''do'''

\If{<math>keyConfirmationList[participant][myId] \neq ~~SHA-512~~Hash(k_{myId,participant}, U_{myId})</math>} ~~'''Call'''~~ '''Halt'''() ' \If{~~'''Call'''~~ '''ED25519VerifySignature'''(<math>ephemeralPublicKeyList[particicpant]</math>, <math>sessionId ||keyShares[myId]</math>, <math>originAuthSignature</math>)' ~~'''Call'''~~ '''Halt'''()

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

'''Return''' <math>~~SHA-512~~Hash(roomeName, zip(participantList, ephemeralPublicPointList))</math> # <math>zip([a,b],[c,d]):=[(a,c),(b,d)]</math>

Global <math>z_{myId -1, myId} := ~~SHA-512~~Hash(k_{myId,myId-1}, sessionId)</math> 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 :=</math> ~~'''Call'''~~ '''ED25519Sign'''(<math>SignatureKey</math>, <math>sessionId</math> || <math>z_{myId}</math>) ~~'''Call'''~~ '''Broadcast'''(``":3mpCat:3KeyConfirmationAndShare:3''", <math>myId</math>, <math>keyShare_{myId}</math>, <math>originAuthSignature</math>, <math>kc_{myId}</math>)

<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 <math>sessionKey := ~~SHA-512~~Hash(z_{j,j+1} | j \in [1...n])</math>

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

~~'''Call'''~~ '''Update Session Key'''() <math>toBeSigned := ~~SHA-512~~Hash(sessionId, ||~~SHA-512~~Hash(verifierList, ephemeralPublicPointList, keyShareList)))</math> <math>signature_{myId} := </math>~~'''Call'''~~ '''Sign Session and Send'''(<math>toBeSigned</math>) ~~'''Call'''~~ '''Broadcast'''(``":3mpCat:3SignedSessionParameters:3''",<math>signature_{myId}</math>)

Input: <math>lastMessage</math>

'''For each''' <math>message</math> in Messages Received from <math>lastDigestedMessage</math>+1 till <math>lastMessage</math>}, '''do'''

<math>sesionDigest :=</math> '''~~Call''' '''SHA-512~~Hash'''(<math>sessionDigest</math>, <math>message</math>) ~~'''Call'''~~ '''LRU Cache Store Digest'''(<math>sessionDigest</math>, <math>message</math>)

'''Return''' <math>sessionDigest</math>,<math>lastMessageId</math>

Vmon

Administrator

148

edits

learn.equalit.ie

Changes

MpOTR/algorithm dump

Search

Personal tools

Tools