SIGMA-R negotiates both isPKA and isPKB fields

Moved requirements, approach and scope to new XEP-0210

Incorporated whole forms into SAS calculation

Added PKI Independence and Robustness requirements; added optional public key independence, hash commitment, SAS authentication, retained secrets and other secrets to SIGMA-R key exchange

Removed public key IDs from Offline options

Initial version (extracted from XEP-0116 version 0.9).

*Note: The protocols developed according to the cryptographic design described in this document are described in Encrypted Session Negotiation (XEP-0116) XEP-0116: Encrypted Session Negotiation <https://xmpp.org/extensions/xep-0116.html>., Simplified Encrypted Session Negotiation (XEP-0217) XEP-0217: Simplified Encrypted Session Negotiation <https://xmpp.org/extensions/xep-0217.html>., Offline Encrypted Sessions (XEP-0187) XEP-0187: Offline Encrypted Sessions <https://xmpp.org/extensions/xep-0187.html>. and Stanza Encryption (XEP-0200) XEP-0200: Stanza Encryption <https://xmpp.org/extensions/xep-0200.html>.. The information in those documents should be sufficient for implementors. This purely informative document is primarily for people interested in the design and analysis of those protocols.*

As specified in RFC 3920

XMPP is a session-oriented communication technology: normally, a client authenticates with a server and maintains a long-lived connection that defines the client's XMPP session. Such stream-level sessions may be secured via channel encryption using Transport Level Security (RFC 2246

This document specifies a method for encrypted sessions ("ESessions") that takes advantage of the inherent possibilities and strengths of session encryption as opposed to object encryption. The detailed requirements for encrypted sessions are defined in Requirements for Encrypted Sessions (XEP-0210)

The conceptual model for the approach specified in this document was inspired by "off-the-record" (OTR) communication, as implemented in the Gaim encryption plugin and described in Off-the-Record Communication

Note: In order to gain a thorough understanding of this document, it is recommended that the Off-the-Record Communication paper and RFC 6189

This document introduces two characters to help the reader follow the necessary exchanges:

- "Alice" is the name of the initiator of the ESession.
- "Bob" is the name of the other participant in the ESession started by Alice.

While Alice and Bob are introduced as "end users", they are simply meant to be examples of XMPP entities. Any directly addressable XMPP entity may participate in an ESession.

Authenticated key-exchange is the most challenging part of the design of any secure communication protocol. The ESessions key exchange essentially translates the SIGMA *variant (ii)*, as described in Secion 5.4 of the SIGMA paper.

Note: Although this section provides an overview of SIGMA, it is strongly recommended that the SIGMA paper is read first in order to gain a thorough understanding of this document.

The 3-message SIGMA-I-based key exchange protects the identity of the *initiator* against active attacks. This SHOULD NOT be used to establish client to client sessions since the *responder's* identity is not protected against active attacks. However, it SHOULD be used to establish client to service (server) sessions, especially where the identity of the service is well known to third parties.

The two 4-message SIGMA-R-based key exchanges with hash commitment defend the *responder's* identity against active attacks and facilitate detection of a Man in the Middle attack. They SHOULD be used to establish client to client sessions.

Note: The block cipher function, *cipher*, uses CTR mode.

Parameter | Description |
---|---|

g | Diffie-Hellman generator |

x, y | Alice and Bob's private Diffie-Hellman keys |

gx, gy | Alice and Bob's public Diffie-Hellman keys |

Hgx | Hash of Alice's public Diffie-Hellman key |

KSA, KSB | The MAC keys (derived from K) that Alice and Bob use to calculate macA and macB |

pubKeyA, pubKeyB | The public keys that represent the identity of Alice and Bob, and are used to verify their signatures |

macA, macB | The MAC values that associate the shared secret with the identity of Alice or Bob |

signKeyA, signKeyB | The private keys that Alice and Bob use to sign |

signA, signB | Alice's and Bob's signatures of the shared secret |

KCA, KCB | The cipher keys (derived from K) that Alice and Bob use to encrypt |

IDA, IDB | The encrypted parameters that identify Alice and Bob to each other |

SAS | Short Authentication String |

Parameter | Description |
---|---|

p | Diffie-Hellman prime |

e, d | Alice and Bob's public Diffie-Hellman keys (the same as gx, gy) |

He | Hash of Alice's public Diffie-Hellman key |

K | Shared secret (derived by Alice from gy and x, or by Bob from gx and y) |

HASH | Selected hash algorithm |

NA, NB | Alice and Bob's session freshness nonces (ESession IDs) |

CA, CB | Block cipher initial counter value for blocks sent by Alice and Bob |

n | Block size of selected cipher algorithm in bits |

KMA, KMB | The MAC keys (derived from K) that Alice and Bob use to protect the integrity of encrypted data |

MA, MB | The MAC values that Alice and Bob use to confirm the integrity of encrypted data |

SRS | Shared retained secret (derived from K in previous session between the clients) |

RS1A...RSZA | Retained secrets Alice shares with Bob (one for each client he uses) |

RS1B...RSZB | Retained secrets Bob shares with Alice (one for each client she uses) |

RSH1A...RSHZA | HMACs of retained secrets Alice shares with Bob |

SRSH | Bob's HMAC of SRS |

OSS | Other shared secret of Alice and Bob (e.g. a shared password) defaults to "secret" |

isPKA, isPKB | Whether or not Alice and Bob prefer to receive a public key (booleans) |

The diagram below demonstrates the barest cryptographic skeleton of the SIGMA-I key exchange protocol. Here Bob allows Alice to protect her identity from active attacks, by allowing her to authenticate him before she communicates her identity. Note: The cipher keys (KCA and KCB) are different in each direction, making this exchange slightly more conservative than SIGMA.

```
```**ALICE** **BOB**
gx
------------>
macB = *HMAC*(KSB, {gx, gy, pubKeyB})
signB = *sign*(signKeyB, macB)
IDB = *cipher*(KCB, {pubKeyB, signB})
gy, IDB
<------------
*authenticate*(IDB)
macA = *HMAC*(KSA, {gy, gx, pubKeyA})
signA = *sign*(signKeyA, macA)
IDA = *cipher*(KCA, {pubKeyA, signA})
IDA
------------>
*authenticate*(IDA)

The diagram below demonstrates the skeleton of the Diffie-Hellman key exchange that employs out-of-band Short Authentication String (SAS) verification. If Alice and Bob's public keys are not yet trusted, or if their private keys have been compromised, then the hash commitment sent in the first step enables Alice and Bob to verify their copies of each other's Diffie-Hellman (and public) keys and detect a Man in the Middle more easily.

If a Man in the Middle changes the public Diffie-Hellman keys that Alice and Bob receive, then he could potentially use his knowledge of the SAS that Bob will eventually calculate when choosing the key he will send to Alice in the second step. However, the fact that the value he received in the first step is only a hash means the Man in the Middle must choose the key he sends to Alice before he can predict the SAS that she will calculate with it. Therefore, even if the SAS is very short, he is unable to use his resources to choose a key that will (have a better than random chance to) result in a SAS that matches Bob's. So only a truncated version of the HASH of Alice and Bob's keys needs to be verified out-of-band in the final step.

```
```**ALICE** **BOB**
Hgx
------------>
gy
<------------
SAS = *truncate*(HASH(gx | gy))
gx
------------>
*assert* Hgx = HASH(gx)
SAS = *truncate*(HASH(gx | gy))
SAS
<===========>

The logic of the four-step SIGMA-R protocol is similar to the three-step SIGMA-I protocol. The difference being that Bob protects his identity from active attacks by by delaying communicating his identity to Alice until he has authenticated her. The diagram below demonstrates the skeleton of the key exchange. Note that it also takes advantage of the extra step required for SIGMA-R to incorporate a hash commitment, thus enabling *optional* out-of-band SAS authentication.

```
```**ALICE** **BOB**
Hgx
------------>
gy
<------------
macA = *HMAC*(KSA, {gy, gx, pubKeyA})
signA = *sign*(signKeyA, macA)
IDA = *cipher*(KCA, {pubKeyA, signA})
SAS = *truncate*(HASH(gx | gy))
gx, IDA
------------>
*assert* Hgx = HASH(gx)
SAS = *truncate*(HASH(gx | gy))
SAS
<===========>
*authenticate*(IDA)
macB = *HMAC*(KSB, {gx, gy, pubKeyB})
signB = *sign*(signKeyB, macB)
IDB = *cipher*(KCB, {pubKeyB, signB})
IDB
<------------
*authenticate*(IDB)

The diagram below describes exactly the same SIGMA-I key exchange protocol as the SIGMA-I Overview above. It provides much more detail, without specifying any ESession-specific details. The differences between it and the SIGMA-R with SAS Key Exchange are highlighted.

```
```**ALICE** **BOB**
NA = *random*()
x = *random*()
e = gx mod p
e, NA
------------>
NB = *random*()
CA = *random*()
CB = CA XOR 2n-1
y = *random*()
d = gy mod p
*assert* 1 < e < p-1
K = HASH(ey mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, CA})
signB = *sign*(signKeyB, macB)
IDB = *cipher*(KCB, CB, {pubKeyB, signB})
MB = *HMAC*(HASH, KMB, CB, IDB)
d, CA, NB
<------------
IDB, MB
CB = CA XOR 2n-1
*assert* 1 < d < p-1
K = HASH(dx mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
*assert* MB = *HMAC*(HASH, KMB, CB, IDB)
{pubKeyB, signB} = *decipher*(KCB, CB, IDB)
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, CA})
*verify*(signB, pubKeyB, macB)
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA})
signA = *sign*(signKeyA, macA)
IDA = *cipher*(KCA, CA, {pubKeyA, signA})
MA = *HMAC*(HASH, KMA, CA, IDA)
IDA
------------>
MA
*assert* MA = *HMAC*(HASH, KMA, CA, IDA)
{pubKeyA, signA} = *decipher*(KCA, CA, IDA)
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA})
*verify*(signA, pubKeyA, macA)

The Short Authentication String technique enables protection against a Man in the Middle without the need to generate, distribute or authenticate any public keys. As long as a hash commitment is used at the start of the key exchange then only a short human-friendly string needs to be verified out-of-band (e.g. by recognizable voice communication).

Furthermore, if retained secrets associated with a client/user combination are employed *consistently* during key exchanges, then the Man in the Middle would need to be present for every session, including the first, and the out-of-band verification would only need to be performed once to verify the absence of a Man in the Middle for all sessions between the parties (past, present and future).

Public keys are optional in the diagram below. It describes the same SIGMA-R with SAS key exchange protocol as the SIGMA-R Overview. It provides much more detail including the use of retained secrets and other secrets. The use of public keys is negotiated in the first two messages. Note: These *optional* security enhancements are especially important when the protocol is being used without public keys.

The diagram does not specify any ESession-specific details. The differences between it and the SIGMA-I Key Exchange are highlighted.

```
```**ALICE** **BOB**
NA = *random*()
x = *random*()
e = gx mod p
He = SHA256(e)
He, isPKA
------------>
isPKB, NA
NB = *random*()
CA = *random*()
CB = CA XOR 2n-1
y = *random*()
d = gy mod p
d, CA, NB
<------------
isPKA, isPKB
CB = CA XOR 2n-1
*assert* 1 < d < p-1
K = HASH(dx mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
RSH1A...RSHZA = *HMAC*(HASH, NA, RS1A...RSZA)
*if* isPKB *equals false then:*
macA = *HMAC*(HASH, KSA, {NB, NA, e, RSH1A...RSHZA})
IDA = *cipher*(KCA, CA, macA)
*else:*
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA, RSH1A...RSHZA})
signA = *sign*(signKeyA, macA)
IDA = *cipher*(KCA, CA, {pubKeyA, signA})
MA = *HMAC*(HASH, KMA, CA, IDA)
SAS = *truncate*(HASH(MA | d | "Short Authentication String"))
IDA, MA
------------>
e, RSH1A...RSHZA
*assert* He = SHA256(e)
SAS = *truncate*(HASH(MA | d | "Short Authentication String"))
SAS
<===========>
*assert* 1 < e < p-1
K = HASH(ey mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
*assert* MA = *HMAC*(HASH, KMA, CA, IDA)
*if* isPKB *equals false then:*
macA = *decipher*(KCA, CA, IDA)
*assert* macA = *HMAC*(HASH, KSA, {NB, NA, e, RSH1A...RSHZA})
*else:*
{pubKeyA, signA} = *decipher*(KCA, CA, IDA)
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA, RSH1A...RSHZA})
*verify*(signA, pubKeyA, macA)
SRS = *choose*(RS1B...RSZB, RSH1A...RSHZA, NA)
K = HASH(K | SRS | OSS)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
SRSH = *HMAC*(HASH, SRS, "Shared Retained Secret")
*retain*(*HMAC*(HASH, K, "New Retained Secret"))
*if* isPKA *equals false then:*
macB = *HMAC*(HASH, KSB, {NA, NB, d, CA})
IDB = *cipher*(KCB, CB, macB)
*else:*
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, CA})
signB = *sign*(signKeyB, macB)
IDB = *cipher*(KCB, CB, {pubKeyB, signB})
MB = *HMAC*(HASH, KMB, CB, IDB)
IDB
<------------
MB, SRSH
SRS = *choose*(RS1A...RSZA, SRSH)
K = HASH(K | SRS | OSS)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
*retain*(*HMAC*(HASH, K, "New Retained Secret"))
*assert* MB = *HMAC*(HASH, KMB, CB, IDB)
*if* isPKA *equals false then:*
macB = *decipher*(KCB, CB, IDB)
*assert* macB = *HMAC*(HASH, KSB, {NA, NB, d, CA})
*else:*
{pubKeyB, signB} = *decipher*(KCB, CB, IDB)
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, CA})
*verify*(signB, pubKeyB, macB)

This section provides an overview of the full ESession key-exchange protocol from a cryptographic point of view. This protocol is based on the *full fledge* protocol, as described in Appendix B of the SIGMA paper. It also uses *variant (ii)*, as described in Secion 5.4 of the same paper.

The table below describes the parameters that are not found in the Parameter Descriptions tables above.

Parameter | Description |
---|---|

options | Includes a set of possible values for each and every ESession parameter (see the ESession Request sub-section in Encrypted Session Negotiation), including sets of possible values for p, g, HASH, CIPHER, SIGN |

chosen | Includes a chosen value for each ESession parameter |

CIPHER | Selected CTR-mode block cipher algorithm |

DECIPHER | Selected CTR-mode block decipher algorithm (corresponds to CIPHER) |

SIGN | Selected signature algorithm |

VERIFY | The selected signature verification algorithm (corresponds to SIGN) |

SASGEN | The selected SAS generation algorithm |

x1...xZ | Alice's private Diffie-Hellman keys - each value corresponds to one of Z different DH groups |

e1...eZ | The choice of public Diffie-Hellman keys that Alice offers Bob - each value corresponds to one of Z different DH groups (and a different value of x) |

He1...HeZ | The list of hash commitments that Alice sends to Bob (hashes of e1...eZ) |

*signKeysA | All the private keys that Alice is able to use to create signatures |

*signsB | The set of signatures of formB (one for each of Bob's private keys) |

*pubKeysA | All of Alice's public keys that Bob has access to |

* Offline negotiation only

Alice uses this protocol when Bob is Online. In addition to the key exchange described in the SIGMA-I Key Exchange protocol above, she offers Bob a choice of Diffie-Hellman groups with her corresponding values of e, various algorithms and other parameters. The differences between this protocol and Online ESession-R Negotiation are highlighted.

```
```**ALICE** **BOB**
NA = *random*()
*for* g,p ∈ options
x = *random*()
e = gx mod p
formA = {e1...eZ, options, NA}
formA
--------->
chosen = {p,g,HASH,CIPHER,SIGN...} = *choose*(options)
e = *choose*(e1...eZ, p)
NB = *random*()
CA = *random*()
CB = CA XOR 2n-1
y = *random*()
d = gy mod p
formB = {CA, chosen, d, NA, NB}
*assert* 1 < e < p-1
K = HASH(ey mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, formB})
signB = SIGN(signKeyB, macB)
IDB = CIPHER(KCB, CB, {pubKeyB, signB})
MB = *HMAC*(HASH, KMB, CB, IDB)
formB
<---------
IDB, MB
*assert* chosen ∈ options
x = *choose*(x1...xZ, p)
e = gx mod p
CB = CA XOR 2n-1
*assert* 1 < d < p-1
K = HASH(dx mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
*assert* MB = *HMAC*(HASH, KMB, CB, IDB)
{pubKeyB, signB} = DECIPHER(KCB, CB, IDB)
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, formB})
VERIFY(signB, pubKeyB, macB)
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA, formA})
signA = SIGN(signKeyA, macA)
IDA = CIPHER(KCA, CA, {pubKeyA, signA})
MA = *HMAC*(HASH, KMA, CA, IDA)
IDA
--------->
MA, NB
*assert* MA = *HMAC*(HASH, KMA, CA, IDA)
{pubKeyA, signA} = DECIPHER(KCA, CA, IDA)
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA, formA})
VERIFY(signA, pubKeyA, macA)

This protocol is similar to the Online ESession-I Negotiation above, except that Bob's identity is protected from active attacks (by by delaying communicating his identity to Alice until he has authenticated her). The optional use of SAS, retained secrets and other secrets means the protocol may be used without any public keys. The differences between this protocol and Online ESession-I Negotiation are highlighted.

```
```**ALICE** **BOB**
NA = *random*()
*for* g,p ∈ options
x = *random*()
e = gx mod p
He = SHA256(e)
formA = {He1...HeZ, options, NA}
formA
------------>
chosen = {p,g,HASH,CIPHER,SIGN,SASGEN,isPKA,isPKB...} = *choose*(options)
He = *choose*(He1...HeZ, p)
NB = *random*()
CA = *random*()
CB = CA XOR 2n-1
y = *random*()
d = gy mod p
formB = {CA, chosen, d, NA, NB}
formB
<------------
*assert* chosen ∈ options
x = *choose*(x1...xZ, p)
e = *choose*(e1...eZ, p)
CB = CA XOR 2n-1
*assert* 1 < d < p-1
K = HASH(dx mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
RSH1A...RSHZA = *HMAC*(HASH, NA, RS1A...RSZA)
formA2 = {RSH1A...RSHZA, e, NB}
*if* isPKB *equals false then:*
macA = *HMAC*(HASH, KSA, {NB, NA, e, formA, formA2})
IDA = CIPHER(KCA, CA, macA)
*else:*
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA, formA, formA2})
signA = SIGN(signKeyA, macA)
IDA = CIPHER(KCA, CA, {pubKeyA, signA})
MA = *HMAC*(HASH, KMA, CA, IDA)
SAS = SASGEN(MA, formB)
IDA, MA
------------>
formA2
*assert* He = SHA256(e)
SAS = SASGEN(MA, formB)
SAS
<===========>
*assert* 1 < e < p-1
K = HASH(ey mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
*assert* MA = *HMAC*(HASH, KMA, CA, IDA)
*if* isPKB *equals false then:*
macA = DECIPHER(KCA, CA, IDA)
*assert* macA = *HMAC*(HASH, KSA, {NB, NA, e, formA, formA2})
*else:*
{pubKeyA, signA} = DECIPHER(KCA, CA, IDA)
macA = *HMAC*(HASH, KSA, {NB, NA, e, pubKeyA, formA, formA2})
VERIFY(signA, pubKeyA, macA)
SRS = *choose*(RS1B...RSZB, RSH1A...RSHZA, NA)
K = HASH(K | SRS | OSS)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
*if* SRS *equals false then:*
SRS = *random*()
SRSH = *HMAC*(HASH, SRS, "Shared Retained Secret")
*retain*(*HMAC*(HASH, K, "New Retained Secret"))
formB2 = {NA, SRSH}
*if* isPKA *equals false then:*
macB = *HMAC*(HASH, KSB, {NA, NB, d, formB, formB2})
IDB = CIPHER(KCB, CB, macB)
*else:*
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, formB, formB2})
signB = SIGN(signKeyB, macB)
IDB = CIPHER(KCB, CB, {pubKeyB, signB})
MB = *HMAC*(HASH, KMB, CB, IDB)
IDB, MB
<------------
formB2
SRS = *choose*(RS1A...RSZA, SRSH)
K = HASH(K | SRS | OSS)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
*retain*(*HMAC*(HASH, K, "New Retained Secret"))
*assert* MB = *HMAC*(HASH, KMB, CB, IDB)
*if* isPKA *equals false then:*
macB = DECIPHER(KCB, CB, IDB)
*assert* macB = *HMAC*(HASH, KSB, {NA, NB, d, formB, formB2})
*else:*
{pubKeyB, signB} = DECIPHER(KCB, CB, IDB)
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, formB, formB2})
VERIFY(signB, pubKeyB, macB)

Bob uses this protocol to send stanzas to Alice when she is Offline. Note: Since the full SIGMA protocol cannot be used if Alice is offline, her identity is not protected at all.

The diagram is split into three phases. First Alice publishes her ESession options before going offline. Later Bob completes the key exchange (and sends her encrypted stanzas that are not shown below) these are all stored by Alice's server. Finally when Alice comes online again she verifies and calculates the decryption key.

The differences between this offline protocol and the Online ESession-I Negotiation protocol above are highlighted in the diagram below.

```
```**ALICE** **ALICE'S SERVER** **BOB**
NA = *random*()
*for* g,p ∈ options
x = *random*()
e = gx mod p
formA = {e1...eZ, options, NA}
signsA = *multi_sign*(signKeysA, formA)
*retain*(NA, x1...xZ, expireTime)
formA
-------->
signsA
*retain*(formA, signsA)
---------------------------------------------------------------------------------------------------------
*retrieve*(formA, signsA)
formA
-------->
signsA
*verify_one*(signsA, pubKeysA, formA)
chosen = {p,g,HASH,CIPHER,SIGN...} = *choose*(options)
e = *choose*(e1...eZ, p)
CA = *random*()
y = *random*()
d = gy mod p
CB = CA XOR 2n-1
NB = *random*()
formB = {CA, chosen, d, NA, NB}
*assert* 1 < e < p-1
K = HASH(ey mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, formB})
signB = SIGN(signKeyB, macB)
IDB = CIPHER(KCB, CB, {pubKeyB, signB})
MB = *HMAC*(HASH, KMB, CB, IDB)
formB
<--------
IDB, MB
*retain*(formB,IDB,MB)
---------------------------------------------------------------------------------------------------------
*retrieve*(formB,IDB,MB)(formB,IDB,MB)
---------------------------------------------------------------------------------------------------------
*retrieve*(formB,IDB,MB)(formB,IDB,MB)
---------------------------------------------------------------------------------------------------------
*retrieve*(formB,IDB,MB)(formB,IDB,MB)
---------------------------------------------------------------------------------------------------------
*retrieve*(formB,IDB,MB)
formB
<--------
IDB, MB
*retrieve*(NA, x1...xZ, expireTime)
*assert* now < expireTime
*assert* chosen ∈ options
x = *choose*(x1...xZ, p)
e = gx mod p
CB = CA XOR 2n-1
*assert* 1 < d < p-1
K = HASH(dx mod p)
KCA = *HMAC*(HASH, K, "Initiator Cipher Key")
KCB = *HMAC*(HASH, K, "Responder Cipher Key")
KMA = *HMAC*(HASH, K, "Initiator MAC Key")
KMB = *HMAC*(HASH, K, "Responder MAC Key")
KSA = *HMAC*(HASH, K, "Initiator SIGMA Key")
KSB = *HMAC*(HASH, K, "Responder SIGMA Key")
*assert* MB = *HMAC*(HASH, KMB, CB, IDB)
{pubKeyB, signB} = DECIPHER(KCB, CB, IDB)
macB = *HMAC*(HASH, KSB, {NA, NB, d, pubKeyB, formB})
VERIFY(signB, pubKeyB, macB)

Note: KMB is necessary only to allow Bob to terminate the ESession if he comes online before Alice terminates it. The calculation of KCB and KSB is not strictly necessary.

The security considerations are described in Encrypted Session Negotiation and Offline Encrypted Sessions.

This document requires no interaction with the Internet Assigned Numbers Authority (IANA)

This document requires no interaction with the XMPP Registrar

The author would like to thank: Ian Goldberg for the time he spent reviewing an early version of this protocol and for his invaluable suggestions and comments; and Hugo Krawczyk for his general advice and encouragment. The author of this document is entirely responsable for any errors it contains.