Np1sec/algebraic - Revision history

Dmitri: Dmitri moved page MpOTR/algebraic to Np1sec/algebraic

2014-12-02T18:46:53Z

Dmitri moved page MpOTR/algebraic to Np1sec/algebraic

Vmon: /* Receive */

2014-09-11T07:19:06Z

‎Receive

Vmon at 07:00, 11 September 2014

2014-09-11T07:00:52Z

Vmon: /* Receive */

2014-09-11T06:59:09Z

‎Receive

Vmon: /* Send */

2014-09-11T06:47:31Z

‎Send

Vmon: /* Accept */

2014-09-11T06:45:10Z

‎Accept

Vmon: /* Join */

2014-09-11T06:44:00Z

‎Join

Vmon: /* Leave */

2014-09-11T06:42:41Z

‎Leave

Vmon: /* Join */

2014-09-11T06:34:23Z

‎Join

Vmon: /* Accept */

2014-09-11T06:29:10Z

‎Accept

@@ Line 201: / Line 201: @@
 |align="right"| check signature
 |align="center"|<math> verify(m,\sigma) </math>
 |-
 |align="right"| decrypt messagen

← Older revision		Revision as of 07:00, 11 September 2014
Line 217:		Line 217:
	\|align="center"\|<math>m</math>		\|align="center"\|<math>m</math>
	\|}		\|}
		+
		+	[[Category: mpOTR]]

@@ Line 200: / Line 200: @@
 |-
 |align="right"| check signature
-|align="center"|<math> verify(m) == (m, \sigma) </math>
+|align="center"|<math> verify(m,\sigma) </math>
 |-
 |align="right"| decrypt messagen
@@ Line 206: / Line 206: @@
 |-
 |align="right"| Verify session id and hash
-|align="center"|<math>\sigma \leftarrow sid_i == sid_{rec} & h == Digest(parent\_id)</math>
+|align="center"|<math> sid_i == sid_{rec} \;  \textrm{and}  \; h == Digest(parent\_id)</math>
 |-
-|align="right"| Update key share or session key
+|align="right"| Update sender key or share key
-|align="center"|<math>(y_j,z_{ji})</math>
+|align="center"|<math>y_j \leftarrow s \; \textrm {  or  } \; z_{j} \leftarrow s</math>
 |-
 |align="right"| return m
 |align="center"|<math>m</math>
 |}

@@ Line 182: / Line 182: @@
 |-
 |align="right"| Append the hash of the session digest up to parent of current message
-|align="center"|<math> m \leftarrow (m, Digest(parnet(m)), parent\_id) </math>
+|align="center"|<math> m \leftarrow (m, Digest(parent(m)), parent\_id) </math>
 |-
 |align="right"| Sign the message
@@ Line 188: / Line 188: @@
 |-
 |align="right"|Encrypt
-|align="center"|<math>e \leftarrow Enc_k_{sid}(m)</math>
+|align="center"|<math>e \leftarrow Enc_{k_{sid}}(m)</math>
 |-
 |align="right"| Broadcast the message

@@ Line 128: / Line 128: @@
 |-
 |align="right"|Broadcast session key confirmation
-|align="center"|<math>k_i \leftarrow H(k_i, sid_i, U_i)</math>
+|align="center"|<math>skc_i \leftarrow H(k_i, sid_i, U_i)</math>
 |}

← Older revision	Revision as of 18:46, 2 December 2014
(No difference)

@@ Line 137: / Line 137: @@
 |-
 |align="right"| Remove leaving user's id/key and update participant list
-|align="center"|<math>plist_i|klist_i \textrm{remove} (U_j|y_j)</math>
+|align="center"|<math>(plist_i|klist_i) \backslash (U_j|y_j)</math>
 |-
 |align="right"|Compute Session Id
 |align="center"|<math>sid_i \leftarrow H(U_1|y_1|\dots|U_n|y_n)</math>
 |-
 |align="right"|Generate secret shares
@@ Line 155: / Line 152: @@
 |-
 |align="right"|Broadcast key shares
-|align="center"|<math>(U_i, z_i, \sigma_i,>kc_i</math>}}<math>)</math>
+|align="center"|<math>(U_i, z_i, \sigma_i)</math>
 |-
 |align="right"| Receive other users' key shares
-|align="center"|<math>(U_1|z_1,\sigma_1,\dots U_n|z_n,\sigma_n)
+|align="center"|<math>(U_1|z_1,\sigma_1,\dots U_n|z_n,\sigma_n)</math>
-|-
-|align="right"|Check validity of key confirmation
-|align="center"|<math>kc_i[j] == kc_j[i]</math>
 |-
 |align="right"|Check public shares
@@ Line 178: / Line 172: @@
 |align="center"|<math>skc_i \leftarrow H(k_i, sid_i, U_i)</math>
 |}
 ==Send==

@@ Line 31: / Line 31: @@
 |-
 |align="right"| Receive other users' id/key
-|align="center"|<math>plist_i|klist_i \leftarrow (U_1|y_1|\dots|U_n|y_n)</math>
+|align="center"|<math>plist_i|klist_i \leftarrow (U_1|y_1|\dots|U_n|y_n)\cup(U_i,y_i)</math>
 |-
 |align="right"|Compute Session Id
@@ Line 52: / Line 52: @@
 |-
 |align="right"|Broadcast key shares and confirmation
-|align="center"|<math>(U_i, z_i, \sigma_i kc_i)</math>
+|align="center"|<math>(U_i, z_i, \sigma_i, kc_i)</math>
 |-
 |align="right"| Receive other users' key shares and confirmation
@@ Line 58: / Line 58: @@
 |-
 |align="right"|Check validity of key confirmation
-|align="center"|<math>kc_i[j] == kc_j[i] \textrm{ for } j \in \{1,\dots,n\}</math>
+|align="center"|<math>kc_i[j] == H(k_{j,i}, U_j) \textrm{ for } j \in \{1,\dots,n\}</math>
 |-
 |align="right"|Check public shares

@@ Line 82: / Line 82: @@
 !align="center"|Pseudo-code
 |-
-|align="right"| broadcast all user's identities (U_1|y_1|\dots|U_n|y_n)
+|align="right"| broadcast all user's identities
-|align="center"|<math> x_i \leftarrow [0, order(g)]</math>
+|align="center"|<math> (U_1|y_1|\dots|U_n|y_n) </math>
 |-
 |align="right"| Receive other users' id/key and update participant list
-|align="center"|<math>plist_i|klist_i \textrm{append} (U_j|y_j)</math>
+|align="center"|<math>(plist_i|klist_i) \cup (U_j|y_j)</math>
-|-
-|align="right"|Broadcast User identity and the DH key
-|align="center"|<math>(U_i, y_i)</math>
-|-
-|align="right"| Receive other users' id/key
-|align="center"|<math>plist_i|klist_i \leftarrow (U_j|y_j|\dots|U_j|y_j)</math>
 |-
 |align="right"|Compute Session Id
@@ Line 98: / Line 92: @@
 |-
 |align="right"|Generate Triple Diffie-Hellman P2P key for the new participant
-|align="center"|<math>k_{i,j} \leftarrow H({y_j}^{lp_i},LP_j^{x_i},y_j^{x_i})</math>}}
+|align="center"|<math>k_{i,j} \leftarrow H({y_j}^{lp_i},LP_j^{x_i},y_j^{x_i})</math>
 |-
 |align="right"|Generate key confirmations
-|align="center"|<math>kc_i \leftarrow (H(k_{i,j}, U_j)</math>
+|align="center"|<math>kc_{i,j}\leftarrow H(k_{i,j}, U_i) </math>
 |-
 |align="right"|Generate secret shares
@@ Line 116: / Line 110: @@
 |-
 |align="right"| Receive other users' key shares and new users confirmation
-|align="center"|<math>(U_1|z_1,\sigma_1,\dots U_n|z_n,\sigma_n), kc_{ij}</math>
+|align="center"|<math>(U_1|z_1,\sigma_1,\dots U_n|z_n,\sigma_n), kc_{i,j}</math>
 |-
 |align="right"|Check validity of key confirmation
-|align="center"|<math>kc_i[j] == kc_j[i]</math>
+|align="center"|<math>kc_{j,i} == H(k_{i,j},U_j)</math>
 |-
 |align="right"|Check public shares