SPAKE Pre-Authentication
draft-ietf-kitten-krb-spake-preauth-04
The information below is for an old version of the document.
| Document | Type | Active Internet-Draft (kitten WG) | |
|---|---|---|---|
| Authors | Nathaniel McCallum , Simo Sorce , Robbie Harwood , Greg Hudson | ||
| Last updated | 2018-01-24 | ||
| Replaces | draft-mccallum-kitten-krb-spake-preauth | ||
| Stream | Internet Engineering Task Force (IETF) | ||
| Formats | plain text xml htmlized pdfized bibtex | ||
| Reviews |
GENART Last Call review
(of
-07)
Almost Ready
OPSDIR Last Call Review
Incomplete, due 2020-05-26
SECDIR Last Call Review
Incomplete, due 2020-05-26
|
||
| Stream | WG state | WG Document | |
| Associated WG milestone |
|
||
| Document shepherd | (None) | ||
| IESG | IESG state | I-D Exists | |
| Consensus boilerplate | Unknown | ||
| Telechat date | (None) | ||
| Responsible AD | (None) | ||
| Send notices to | (None) |
draft-ietf-kitten-krb-spake-preauth-04
Internet Engineering Task Force N. McCallum
Internet-Draft S. Sorce
Updates: 3961 (if approved) R. Harwood
Intended status: Standards Track Red Hat, Inc.
Expires: July 28, 2018 G. Hudson
MIT
January 24, 2018
SPAKE Pre-Authentication
draft-ietf-kitten-krb-spake-preauth-04
Abstract
This document defines a new pre-authentication mechanism for the
Kerberos protocol that uses a password authenticated key exchange.
This document has three goals. First, increase the security of
Kerberos pre-authentication exchanges by making offline brute-force
attacks infeasible. Second, enable the use of second factor
authentication without relying on FAST. This is achieved using the
existing trust relationship established by the shared first factor.
Third, make Kerberos pre-authentication more resilient against time
synchronization errors by removing the need to transfer an encrypted
timestamp from the client.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at http://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on July 28, 2018.
Copyright Notice
Copyright (c) 2018 IETF Trust and the persons identified as the
document authors. All rights reserved.
McCallum, et al. Expires July 28, 2018 [Page 1]
Internet-Draft SPAKE Pre-Authentication January 2018
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Properties of PAKE . . . . . . . . . . . . . . . . . . . 3
1.2. PAKE Algorithm Selection . . . . . . . . . . . . . . . . 3
1.3. PAKE and Two-Factor Authentication . . . . . . . . . . . 4
1.4. SPAKE Overview . . . . . . . . . . . . . . . . . . . . . 5
2. Document Conventions . . . . . . . . . . . . . . . . . . . . 5
3. Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1. PA-ETYPE-INFO2 . . . . . . . . . . . . . . . . . . . . . 6
3.2. Cookie Support . . . . . . . . . . . . . . . . . . . . . 6
3.3. More Pre-Authentication Data Required . . . . . . . . . . 6
4. Update to Checksum Specifications . . . . . . . . . . . . . . 6
5. SPAKE Pre-Authentication Message Protocol . . . . . . . . . . 7
5.1. First Pass . . . . . . . . . . . . . . . . . . . . . . . 7
5.2. Second Pass . . . . . . . . . . . . . . . . . . . . . . . 8
5.3. Third Pass . . . . . . . . . . . . . . . . . . . . . . . 9
5.4. Subsequent Passes . . . . . . . . . . . . . . . . . . . . 10
5.5. Reply Key Strengthening . . . . . . . . . . . . . . . . . 10
5.6. Optimizations . . . . . . . . . . . . . . . . . . . . . . 11
6. SPAKE Parameters and Conversions . . . . . . . . . . . . . . 11
7. Transcript Checksum . . . . . . . . . . . . . . . . . . . . . 12
8. Key Derivation . . . . . . . . . . . . . . . . . . . . . . . 13
9. Second Factor Types . . . . . . . . . . . . . . . . . . . . . 14
10. Security Considerations . . . . . . . . . . . . . . . . . . . 14
10.1. Unauthenticated Plaintext . . . . . . . . . . . . . . . 14
10.2. Side Channels . . . . . . . . . . . . . . . . . . . . . 14
10.3. KDC State . . . . . . . . . . . . . . . . . . . . . . . 15
10.4. Dictionary Attacks . . . . . . . . . . . . . . . . . . . 16
10.5. Brute Force Attacks . . . . . . . . . . . . . . . . . . 16
10.6. Denial of Service Attacks . . . . . . . . . . . . . . . 17
10.7. Reply-Key Encryption Type . . . . . . . . . . . . . . . 17
10.8. KDC Authentication . . . . . . . . . . . . . . . . . . . 17
11. Assigned Constants . . . . . . . . . . . . . . . . . . . . . 17
12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 17
12.1. Kerberos Second Factor Types . . . . . . . . . . . . . . 18
12.1.1. Registration Template . . . . . . . . . . . . . . . 18
12.1.2. Initial Registry Contents . . . . . . . . . . . . . 18
McCallum, et al. Expires July 28, 2018 [Page 2]
Internet-Draft SPAKE Pre-Authentication January 2018
12.2. Kerberos SPAKE Groups . . . . . . . . . . . . . . . . . 19
12.2.1. Registration Template . . . . . . . . . . . . . . . 19
12.2.2. Initial Registry Contents . . . . . . . . . . . . . 19
13. References . . . . . . . . . . . . . . . . . . . . . . . . . 21
13.1. Normative References . . . . . . . . . . . . . . . . . . 21
13.2. Non-normative References . . . . . . . . . . . . . . . . 22
Appendix A. ASN.1 Module . . . . . . . . . . . . . . . . . . . . 23
Appendix B. SPAKE M and N Value Selection . . . . . . . . . . . 24
Appendix C. Test Vectors . . . . . . . . . . . . . . . . . . . . 24
Appendix D. Acknowledgements . . . . . . . . . . . . . . . . . . 31
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 31
1. Introduction
When a client uses PA-ENC-TIMESTAMP (or similar schemes, or the KDC
does not require preauthentication), a passive attacker that observes
either the AS-REQ or AS-REP can perform an offline brute-force attack
against the transferred ciphertext. When the client principal's
long-term key is based on a password, offline dictionary attacks can
successfuly recover the key, with only modest effort needed if the
password is weak.
1.1. Properties of PAKE
Password authenticated key exchange (PAKE) algorithms provide several
properties which are useful to overcome this problem and make them
ideal for use as a Kerberos pre-authentication mechanism.
1. Each side of the exchange contributes entropy.
2. Passive attackers cannot determine the shared key.
3. Active attackers cannot perform a man-in-the-middle attack.
These properties of PAKE allow us to establish high-entropy
encryption keys resistant to offline brute force attack, even when
the passwords used are weak (low-entropy).
1.2. PAKE Algorithm Selection
The SPAKE algorithm works by encrypting the public keys of a Diffie-
Hellman key exchange with a shared secret. SPAKE was selected for
this pre-authentication mechanism for the following properties:
1. Because SPAKE's encryption method ensures that the result is a
member of the underlying group, it can be used with elliptic
curve cryptography, which is believed to provide equivalent
McCallum, et al. Expires July 28, 2018 [Page 3]
Internet-Draft SPAKE Pre-Authentication January 2018
security levels to finite-field DH key exchange at much smaller
key sizes.
2. It can compute the shared key after just one message from each
party.
3. It requires a small number of group operations, and can therefore
be implemented simply and efficiently.
1.3. PAKE and Two-Factor Authentication
Using PAKE in a pre-authentication mechanism also has another benefit
when used as a component of two-factor authentication (2FA). 2FA
methods often require the secure transfer of plaintext material to
the KDC for verification. This includes one-time passwords,
challenge/response signatures and biometric data. Attempting to
encrypt this data using the long-term secret results in packets that
are vulnerable to offline brute-force attack if either authenticated
encryption is used or if the plaintext is distinguishable from random
data. This is a problem that PAKE solves for first factor
authentication. So a similar technique can be used with PAKE to
encrypt second-factor data.
In the OTP pre-authentication [RFC6560] specification, this problem
is mitigated by using FAST, which uses a secondary trust relationship
to create a secure encryption channel within which pre-authentication
data can be sent. However, the requirement for a secondary trust
relationship has proven to be cumbersome to deploy and often
introduces third parties into the trust chain (such as certification
authorities). These requirements lead to a scenario where FAST
cannot be enabled by default without sufficient configuration. SPAKE
pre-authentication, in contrast, can create a secure encryption
channel implicitly, using the key exchange to negotiate a high-
entropy encryption key. This key can then be used to securely
encrypt 2FA plaintext data without the need for a secondary trust
relationship. Further, if the second factor verifiers are sent at
the same time as the first factor verifier, and the KDC is careful to
prevent timing attacks, then an online brute-force attack cannot be
used to attack the factors separately.
For these reasons, this draft departs from the advice given in
Section 1 of RFC 6113 [RFC6113] which states that "Mechanism
designers should design FAST factors, instead of new pre-
authentication mechanisms outside of FAST." However, this pre-
authentication mechanism does not intend to replace FAST, and may be
used with it to further conceal the metadata of the Kerberos
messages.
McCallum, et al. Expires July 28, 2018 [Page 4]
Internet-Draft SPAKE Pre-Authentication January 2018
1.4. SPAKE Overview
The SPAKE algorithm can be broadly described in a series of four
steps:
1. Calculation and exchange of the public key
2. Calculation of the shared secret (K)
3. Derivation of an encryption key (K')
4. Verification of the derived encryption key (K')
Higher level protocols must define their own verification step. In
the case of this mechanism, verification happens implicitly by a
successful decryption of the 2FA data.
This mechanism provides its own method of deriving encryption keys
from the calculated shared secret K, for several reasons: to fit
within the framework of [RFC3961], to ensure negotiation integrity
using a transcript checksum, to derive different keys for each use,
and to bind the KDC-REQ-BODY to the pre-authentication exchange.
2. Document Conventions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
This document refers to numerous terms and protocol messages defined
in [RFC4120].
The terms "encryption type", "required checksum mechanism", and
"get_mic" are defined in [RFC3961].
The terms "FAST", "PA-FX-COOKIE", "KDC_ERR_PREAUTH_EXPIRED",
"KDC_ERR_MORE_PREAUTH_DATA_REQUIRED", "KDC_ERR_PREAUTH_FAILED", "pre-
authentication facility", and "authentication set" are defined in
[RFC6113].
The [SPAKE] paper defines SPAKE as a family of two key exchange
algorithms differing only in derivation of the final key. This
mechanism uses a derivation similar to the second algorithm (SPAKE2)
with differences in detail. For simplicity, this document refers to
the algorithm as "SPAKE". The normative reference for this algorithm
is [I-D.irtf-cfrg-spake2].
McCallum, et al. Expires July 28, 2018 [Page 5]
Internet-Draft SPAKE Pre-Authentication January 2018
The terms "ASN.1" and "DER" are defined in [CCITT.X680.2002] and
[CCITT.X690.2002] respectively.
3. Prerequisites
3.1. PA-ETYPE-INFO2
This mechanism requires the initial KDC pre-authentication state to
contain a singular reply key. Therefore, a KDC which offers SPAKE
pre-authentication as a stand-alone mechanism MUST supply a PA-ETYPE-
INFO2 value containing a single ETYPE-INFO2-ENTRY, as described in
[RFC6113] section 2.1. PA-ETYPE-INFO2 is specified in [RFC4120]
section 5.2.7.5.
3.2. Cookie Support
KDCs which implement SPAKE pre-authentication MUST have some secure
mechanism for retaining state between AS-REQs. For stateless KDC
implementations, this method will most commonly be an encrypted PA-
FX-COOKIE. Clients which implement SPAKE pre-authentication MUST
support PA-FX-COOKIE, as described in [RFC6113] section 5.2.
3.3. More Pre-Authentication Data Required
Both KDCs and clients which implement SPAKE pre-authentication MUST
support the use of KDC_ERR_MORE_PREAUTH_DATA_REQUIRED, as described
in [RFC6113] section 5.2.
4. Update to Checksum Specifications
[RFC3961] section 4 specifies the Kerberos checksum algorithm
profile. It does not require checksums to be deterministic. In
practice, DES-based checksum types (deprecated by [RFC6649]) use a
random confounder; all other current checksum types are
deterministic.
Future checksum types required by an encryption type MUST be
deterministic. All future checksum types SHOULD be deterministic.
This mechanism requires a deterministic checksum type for the
transcript checksum. Therefore, a KDC MUST NOT offer this mechanism
if the initial reply key is of type des-cbc-crc, des-cbc-md4, or des-
cbc-md5.
McCallum, et al. Expires July 28, 2018 [Page 6]
Internet-Draft SPAKE Pre-Authentication January 2018
5. SPAKE Pre-Authentication Message Protocol
This mechanism uses the reply key and provides the Client
Authentication and Strengthening Reply Key pre-authentication
facilities ([RFC6113] section 3). When the mechanism completes
successfully, the client will have proved knowledge of the original
reply key and possibly a second factor, and the reply key will be
strengthened to a more uniform distribution based on the PAKE
exchange. This mechanism also ensures the integrity of the KDC-REQ-
BODY contents. This mechanism can be used in an authentication set;
no pa-hint value is required or defined.
This mechanism negotiates a choice of group for the SPAKE algorithm.
Groups are defined in the IANA "Kerberos SPAKE Groups" registry
created by this document. Clients and KDCs MUST implement the
edwards25519 group, but MAY choose not to offer or accept it by
default.
This section will describe the flow of messages when performing SPAKE
pre-authentication. We will begin by explaining the most verbose
version of the protocol which all implementations MUST support. Then
we will describe several optional optimizations to reduce round-
trips.
Mechanism messages are communicated using PA-DATA elements within the
padata field of KDC-REQ messages or within the METHOD-DATA in the
e-data field of KRB-ERROR messages. All PA-DATA elements for this
mechanism MUST use the following padata-type:
PA-SPAKE 151
The padata-value for all PA-SPAKE PA-DATA values MUST be empty or
contain a DER encoding for the ASN.1 type PA-SPAKE.
PA-SPAKE ::= CHOICE {
support [0] SPAKESupport,
challenge [1] SPAKEChallenge,
response [2] SPAKEResponse,
encdata [3] EncryptedData,
...
}
5.1. First Pass
The SPAKE pre-authentication exchange begins when the client sends an
initial authentication service request (AS-REQ) without pre-
authentication data. Upon receipt of this AS-REQ, a KDC which
requires pre-authentication and supports SPAKE SHOULD reply with a
McCallum, et al. Expires July 28, 2018 [Page 7]
Internet-Draft SPAKE Pre-Authentication January 2018
KDC_ERR_PREAUTH_REQUIRED error, with METHOD-DATA containing an empty
PA-SPAKE PA-DATA element (possibly in addition to other PA-DATA
elements). This message indicates to the client that the KDC
supports SPAKE pre-authentication.
5.2. Second Pass
Once the client knows that the KDC supports SPAKE pre-authentication
and the client desires to use it, the client will generate a new AS-
REQ message containing a PA-SPAKE PA-DATA element using the support
choice. This message indicates to the KDC which groups the client
prefers for the SPAKE operation. The group numbers are defined in
the IANA "Kerberos SPAKE Groups" registry created by this document.
The groups sequence is ordered from the most preferred group to the
least preferred group.
SPAKESupport ::= SEQUENCE {
groups [0] SEQUENCE (SIZE(1..MAX)) OF Int32,
...
}
The client and KDC initialize a transcript checksum (Section 7) and
update it with the DER-encoded PA-SPAKE message.
Upon receipt of the support message, the KDC will select a group.
The KDC SHOULD choose a group from the groups provided by the support
message. However, if the support message does not contain any group
that is supported by the KDC, the KDC MAY select another group in
hopes that the client might support it. Otherwise, the KDC MUST
respond with a KDC_ERR_PREAUTH_FAILED error.
Once the KDC has selected a group, the KDC will reply to the client
with a KDC_ERR_MORE_PREAUTH_DATA_REQUIRED error containing a PA-SPAKE
PA-DATA element using the challenge choice. The client and KDC
update the transcript checksum with the DER-encoded PA-SPAKE message.
SPAKEChallenge ::= SEQUENCE {
group [0] Int32,
pubkey [1] OCTET STRING,
factors [2] SEQUENCE (SIZE(1..MAX)) OF SPAKESecondFactor,
...
}
The group field indicates the KDC-selected group used for all SPAKE
calculations as defined in the IANA "Kerberos SPAKE Groups" registry
created by this document.
McCallum, et al. Expires July 28, 2018 [Page 8]
Internet-Draft SPAKE Pre-Authentication January 2018
The pubkey field indicates the KDC's public key generated using the M
constant in the SPAKE algorithm, with inputs and conversions as
specified in Section 6.
The factors field contains an unordered list of second factors which
can be used to complete the authentication. Each second factor is
represented by a SPAKESecondFactor.
SPAKESecondFactor ::= SEQUENCE {
type [0] Int32,
data [1] OCTET STRING OPTIONAL
}
The type field is a unique integer which identifies the second factor
type. The factors field of SPAKEChallenge MUST NOT contain more than
one SPAKESecondFactor with the same type value.
The data field contains optional challenge data. The contents in
this field will depend upon the second factor type chosen.
5.3. Third Pass
Upon receipt of the challenge message, the client will complete its
part of of the SPAKE algorithm, generating a public key and computing
the shared secret K. The client will then choose one of the second
factor types listed in the factors field of the challenge message and
gather whatever data is required for the chosen second factor type,
possibly using the associated challenge data. Finally, the client
will send an AS-REQ containing a PA-SPAKE PA-DATA element using the
response choice.
SPAKEResponse ::= SEQUENCE {
pubkey [0] OCTET STRING,
factor [1] EncryptedData, -- SPAKESecondFactor
...
}
The client and KDC will update the transcript checksum with the
pubkey value, and use the resulting checksum for all encryption key
derivations.
The pubkey field indicates the client's public key generated using
the N constant in the SPAKE algorithm, with inputs and conversions as
specified in Section 6.
The factor field indicates the client's chosen second factor data.
The key for this field is K'[1] as specified in Section 8. The key
usage number for the encryption is KEY_USAGE_SPAKE_FACTOR. The plain
McCallum, et al. Expires July 28, 2018 [Page 9]
Internet-Draft SPAKE Pre-Authentication January 2018
text inside the EncryptedData is an encoding of SPAKESecondFactor.
Once decoded, the SPAKESecondFactor contains the type of the second
factor and any optional data used. The contents of the data field
will depend on the second factor type chosen. The client MUST NOT
send a response containing a second factor type which was not listed
in the factors field of the challenge message.
When the KDC receives the response message from the client, it will
use the pubkey to compute the SPAKE result, derive K'[1], and decrypt
the factors field. If decryption is successful, the first factor is
successfully validated. The KDC then validates the second factor.
If either factor fails to validate, the KDC SHOULD respond with a
KDC_ERR_PREAUTH_FAILED error.
If validation of the second factor requires further round-trips, the
KDC MUST reply to the client with KDC_ERR_MORE_PREAUTH_DATA_REQUIRED
containing a PA-SPAKE PA-DATA element using the encdata choice. The
key for the EncryptedData value is K'[2] as specified in Section 8,
and the key usage number is KEY_USAGE_SPAKE_FACTOR. The plain text
of this message contains a DER-encoded SPAKESecondFactor message. As
before, the type field of this message will contain the second factor
type, and the data field will optionally contain second factor type
specific data.
KEY_USAGE_SPAKE_FACTOR 65
5.4. Subsequent Passes
Any number of additional round trips may occur using the encdata
choice. The contents of the plaintexts are specific to the second
factor type. If a client receives a PA-SPAKE PA-DATA element using
the encdata choice from the KDC, it MUST reply with a subsequent AS-
REQ with a PA-SPAKE PA-DATA using the encdata choice, or abort the AS
exchange.
The key for client-originated encdata messages in subsequent passes
is K'[3] as specified in Section 8 for the first subsequent pass,
K'[5] for the second, and so on. The key for KDC-originated encdata
messages is K'[4] for the first subsequent pass, K'[6] for the
second, and so on.
5.5. Reply Key Strengthening
When the KDC has successfully validated both factors, the reply key
is strengthened and the mechanism is complete. To strengthen the
reply key, the client and KDC replace it with K'[0] as specified in
Section 8. The KDC then replies with a KDC-REP message, or continues
McCallum, et al. Expires July 28, 2018 [Page 10]
Internet-Draft SPAKE Pre-Authentication January 2018
on to the next mechanism in the authentication set. There is no
final PA-SPAKE PA-DATA message from the KDC to the client.
Reply key strengthening occurs only once at the end of the exchange.
The client and KDC MUST use the initial reply key as the base key for
all K'[n] derivations.
5.6. Optimizations
The full protocol has two possible optimizations.
First, the KDC MAY reply to the initial AS-REQ (containing no pre-
authentication data) with a PA-SPAKE PA-DATA element using the
challenge choice, instead of an empty padata-value. In this case,
the KDC optimistically selects a group which the client may not
support. If the group chosen by the challenge message is supported
by the client, the client MUST skip to the third pass by issuing an
AS-REQ with a PA-SPAKE message using the response choice. If the
KDC's chosen group is not supported by the client, the client MUST
initialize and update the transcript checksum with the KDC's
challenge message, and then continue to the second pass. Clients
MUST support this optimization.
Second, clients MAY skip the first pass and send an AS-REQ with a PA-
SPAKE PA-DATA element using the support choice. If the KDC accepts
the support message and generates a challenge, it MUST include a PA-
ETYPE-INFO2 value within the METHOD-DATA of the
KDC_ERR_MORE_PREAUTH_DATA_REQUIRED error response, as the client may
not otherwise be able to compute the initial reply key. If the KDC
cannot continue with SPAKE (either because initial reply key type is
incompatible with SPAKE or because it does not support any of the
client's groups) but can offer other pre-authentication mechanisms,
it MUST respond with a KDC_ERR_PREAUTH_FAILED error containing
METHOD-DATA. A client supporting this optimization MUST continue
after a KDC_ERR_PREAUTH_FAILED error as described in [RFC6113]
section 2. KDCs MUST support this optimization.
6. SPAKE Parameters and Conversions
Group elements are converted to octet strings using the serialization
method defined in the IANA "Kerberos SPAKE Groups" registry created
by this document.
The SPAKE algorithm requires constants M and N for each group. These
constants are defined in the IANA "Kerberos SPAKE Groups" registry
created by this document.
McCallum, et al. Expires July 28, 2018 [Page 11]
Internet-Draft SPAKE Pre-Authentication January 2018
The SPAKE algorithm requires a shared secret input w to be used as a
scalar multiplier (see [I-D.irtf-cfrg-spake2] section 2). This value
MUST be produced from the initial reply key as follows:
1. Determine the length of the multiplier octet string as defined in
the IANA "Kerberos SPAKE Groups" registry created by this
document.
2. Compose a pepper string by concatenating the string "SPAKEsecret"
and the group number as a big-endian four-byte unsigned binary
number.
3. Produce an octet string of the required length using PRF+(K,
pepper), where K is the initial reply key and PRF+ is defined in
[RFC6113] section 5.1.
4. Convert the octet string to a multiplier scalar using the
multiplier conversion method defined in the IANA "Kerberos SPAKE
Groups" registry created by this document.
The KDC chooses a secret scalar value x and the client chooses a
secret scalar value y. As required by the SPAKE algorithm, these
values are chosen randomly and uniformly. The KDC and client MUST
NOT reuse x or y values for authentications involving different
initial reply keys (see Section 10.3).
7. Transcript Checksum
The transcript checksum is an octet string of length equal to the
output length of the required checksum type of the encryption type of
the initial reply key. The initial value consists of all bits set to
zero.
When the transcript checksum is updated with an octet string input,
the new value is the get_mic result computed over the concatenation
of the old value and the input, for the required checksum type of the
initial reply key's encryption type, using the initial reply key and
the key usage number KEY_USAGE_SPAKE_TRANSCRIPT.
In the normal message flow or with the second optimization described
in Section 5.6, the transcript checksum is first updated with the
client's support message, then the KDC's challenge message, and
finally with the client's pubkey value. It therefore incorporates
the client's supported groups, the KDC's chosen group, the KDC's
initial second-factor messages, and the client and KDC public values.
Once the transcript checksum is finalized, it is used without change
for all key derivations (Section 8).
McCallum, et al. Expires July 28, 2018 [Page 12]
Internet-Draft SPAKE Pre-Authentication January 2018
If the first optimization described in Section 5.6 is used
successfully, the transcript checksum is updated only with the KDC's
challenge message and the client's pubkey value.
If first optimization is used unsuccessfully (i.e. the client does
not accept the KDC's selected group), the transcript checksum is
updated with the KDC's optimistic challenge message, then with the
client's support message, then the KDC's second challenge message,
and finally with the client's pubkey value.
KEY_USAGE_SPAKE_TRANSCRIPT 66
8. Key Derivation
Implementations MUST NOT use the SPAKE result (denoted by K in
Section 2 of SPAKE [I-D.irtf-cfrg-spake2]) directly for any
cryptographic operation. Instead, the SPAKE result is used to derive
keys K'[n] as defined in this section. This method differs slightly
from the method used to generate K' in Section 3 of SPAKE
[I-D.irtf-cfrg-spake2].
An input string is assembled by concatenating the following values:
o The fixed string "SPAKEkey".
o The group number as a big-endian four-byte unsigned binary number.
o The encryption type of the initial reply key as a big-endian four-
byte unsigned binary number.
o The SPAKE result K, converted to an octet string as specified in
Section 6.
o The transcript checksum.
o The KDC-REQ-BODY encoding for the request being sent or responded
to. Within a FAST channel, the inner KDC-REQ-BODY encoding MUST
be used.
o The value n as a big-endian four-byte unsigned binary number.
The derived key K'[n] has the same encryption type as the initial
reply key, and has the value random-to-key(PRF+(initial-reply-key,
input-string)). PRF+ is defined in [RFC6113] section 5.1.
McCallum, et al. Expires July 28, 2018 [Page 13]
Internet-Draft SPAKE Pre-Authentication January 2018
9. Second Factor Types
This document defines one second factor type:
SF-NONE 1
This second factor type indicates that no second factor is used.
Whenever a SPAKESecondFactor is used with SF-NONE, the data field
MUST be omitted. The SF-NONE second factor always successfully
validates.
10. Security Considerations
All of the security considerations from SPAKE [I-D.irtf-cfrg-spake2]
apply here as well.
10.1. Unauthenticated Plaintext
This mechanism includes unauthenticated plaintext in the support and
challenge messages. Beginning with the third pass, the integrity of
this plaintext is ensured by incorporating the transcript checksum
into the derivation of the final reply key and second factor
encryption keys. Downgrade attacks on support and challenge messages
will result in the client and KDC deriving different reply keys and
EncryptedData keys. The KDC-REQ-BODY contents are also incorporated
into key derivation, ensuring their integrity. The unauthenticated
plaintext in the KDC-REP message is not protected by this mechanism.
Unless FAST is used, the factors field of a challenge message is not
integrity-protected until the response is verified. Second factor
types MUST account for this when specifying the semantics of the data
field. Second factor data in the challenge should not be included in
user prompts, as it could be modified by an attacker to contain
misleading or offensive information.
Subsequent factor data, including the data in the response, are
encrypted in a derivative of the shared secret K. Therefore, it is
not possible to exploit the untrustworthiness of the challenge to
turn the client into an encryption or signing oracle, unless the
attacker knows the client's long-term key.
10.2. Side Channels
An implementation of this pre-authentication mechanism can have the
property of indistinguishability, meaning that an attacker who
guesses a long-term key and a second factor value cannot determine
whether one of the factors was correct unless both are correct.
Indistinguishability is only maintained if the second factor can be
McCallum, et al. Expires July 28, 2018 [Page 14]
Internet-Draft SPAKE Pre-Authentication January 2018
validated solely based on the data in the response; the use of
additional round trips will reveal to the attacker whether the long-
term key is correct. Indistinguishability also requires that there
are no side channels. When processing a response message, whether or
not the KDC successfully decrypts the factor field, it must reply
with the same error fields, take the same amount of time, and make
the same observable communications to other servers.
Both the size of the EncryptedData and the number of EncryptedData
messages used for second-factor data (including the factor field of
the SPAKEResponse message and messages using the encdata PA-SPAKE
choice) may reveal information about the second factor used in an
authentication. Care should be taken to keep second factor messages
as small and as few as possible.
Any side channels in the creation of the shared secret input w, or in
the multiplications wM and wN, could allow an attacker to recover the
client long-term key. Implementations MUST take care to avoid side
channels, particularly timing channels. Generation of the secret
scalar values x and y need not take constant time, but the amount of
time taken MUST NOT provide information about the resulting value.
The conversion of the scalar multiplier for the SPAKE w parameter may
produce a multiplier that is larger than the order of the group.
Some group implementations may be unable to handle such a multiplier.
Others may silently accept such a multiplier, but proceed to perform
multiplication that is not constant time. This is a minor risk in
all known groups, but is a major risk for P-521 due to the extra
seven high bits in the input octet string. A common solution to this
problem is achieved by reducing the multiplier modulo the group
order, taking care to ensure constant time operation.
10.3. KDC State
A stateless KDC implementation generally must use a PA-FX-COOKIE
value to remember its private scalar value x and the transcript
checksum. The KDC MUST maintain confidentiality and integrity of the
cookie value, perhaps by encrypting it in a key known only to the
realm's KDCs. Cookie values may be replayed by attackers. The KDC
SHOULD limit the time window of replays using a timestamp, and SHOULD
prevent cookie values from being applied to other pre-authentication
mechanisms or other client principals. Within the validity period of
a cookie, an attacker can replay the final message of a pre-
authentication exchange to any of the realm's KDCs and make it appear
that the client has authenticated.
If an x or y value is reused for pre-authentications involving two
different client long-term keys, an attacker who observes both
McCallum, et al. Expires July 28, 2018 [Page 15]
Internet-Draft SPAKE Pre-Authentication January 2018
authentications and knows one of the long-term keys can conduct an
offline dictionary attack to recover the other one.
This pre-authentication mechanism is not designed to provide forward
secrecy. Nevertheless, some measure of forward secrecy may result
depending on implementation choices. A passive attacker who
determines the client long-term key after the exchange generally will
not be able to recover the ticket session key; however, an attacker
who also determines the PA-FX-COOKIE encryption key (if the KDC uses
an encrypted cookie) will be able to recover the ticket session key.
The KDC can mitigate this risk by periodically rotating the cookie
encryption key. If the KDC or client retains the x or y value for
reuse with the same client long-term key, an attacker who recovers
the x or y value and the long-term key will be able to recover the
ticket session key.
10.4. Dictionary Attacks
Although this pre-authentication mechanism is designed to prevent an
offline dictionary attack by an active attacker posing as the KDC,
such an attacker can attempt to downgrade the client to encrypted
timestamp. Client implementations SHOULD provide a configuration
option to disable encrypted timestamp on a per-realm basis to
mitigate this attack.
If the user enters the wrong password, the client might fall back to
encrypted timestamp after receiving a KDC_ERR_PREAUTH_FAILED error
from the KDC, if encrypted timestamp is offered by the KDC and not
disabled by client configuration. This fallback will enable a
passive attacker to mount an offline dictionary attack against the
incorrect password, which may be similar to the correct password.
Client implementations SHOULD assume that encrypted timestamp and
encrypted challenge are unlikely to succeed if SPAKE pre-
authentication fails in the second pass and no second factor was
used.
Like any other pre-authentication mechanism using the client long-
term key, this pre-authentication mechanism does not prevent online
password guessing attacks. The KDC is made aware of unsuccessful
guesses, and can apply facilities such as password lockout to
mitigate the risk of online attacks.
10.5. Brute Force Attacks
The selected group's resistance to offline brute-force attacks may
not correspond to the size of the reply key. For performance
reasons, a KDC MAY select a group whose brute-force work factor is
less than the reply key length. A passive attacker who solves the
McCallum, et al. Expires July 28, 2018 [Page 16]
Internet-Draft SPAKE Pre-Authentication January 2018
group discrete logarithm problem after the exchange will be able to
conduct an offline attack against the client long-term key. Although
the use of password policies and costly, salted string-to-key
functions may increase the cost of such an attack, the resulting cost
will likely not be higher than the cost of solving the group discrete
logarithm.
10.6. Denial of Service Attacks
Elliptic curve group operations are more computationally expensive
than secret-key operations. As a result, the use of this mechanism
may affect the KDC's performance under normal load and its resistance
to denial of service attacks.
10.7. Reply-Key Encryption Type
This mechanism does not upgrade the encryption type of the initial
reply key, and relies on that encryption type for confidentiality,
integrity, and pseudo-random functions. If the client long-term key
uses a weak encryption type, an attacker might be able to subvert the
exchange, and the replaced reply key will also be of the same weak
encryption type.
10.8. KDC Authentication
This mechanism does not directly provide the KDC Authentication pre-
authentication facility, because it does not send a key confirmation
from the KDC to the client. When used as a stand-alone mechanism,
the traditional KDC authentication provided by the KDC-REP enc-part
still applies.
11. Assigned Constants
The following key usage values are assigned for this mechanism:
KEY_USAGE_SPAKE_TRANSCRIPT 65
KEY_USAGE_SPAKE_FACTOR 66
12. IANA Considerations
IANA has assigned the following number for PA-SPAKE in the "Pre-
authentication and Typed Data" registry:
+----------+-------+-----------------+
| Type | Value | Reference |
+----------+-------+-----------------+
| PA-SPAKE | 151 | [this document] |
+----------+-------+-----------------+
McCallum, et al. Expires July 28, 2018 [Page 17]
Internet-Draft SPAKE Pre-Authentication January 2018
The notes for the "Kerberos Checksum Type Numbers" registry should be
updated with the following addition: "If the checksum algorithm is
non-deterministic, see [this document] Section 4."
This document establishes two registries with the following
procedure, in accordance with [RFC5226]:
Registry entries are to be evaluated using the Specification Required
method. All specifications must be be published prior to entry
inclusion in the registry. There will be a three-week review period
by Designated Experts on the krb5-spake-review@ietf.org mailing list.
Prior to the end of the review period, the Designated Experts must
approve or deny the request. This decision is to be conveyed to both
the IANA and the list, and should include reasonably detailed
explanation in the case of a denial as well as whether the request
can be resubmitted.
12.1. Kerberos Second Factor Types
This section species the IANA "Kerberos Second Factor Types"
registry. This registry records the number, name, and reference for
each second factor protocol.
12.1.1. Registration Template
ID Number: This is a value that uniquely identifies this entry. It
is a signed integer in range -2147483648 to 2147483647, inclusive.
Positive values must be assigned only for algorithms specified in
accordance with these rules for use with Kerberos and related
protocols. Negative values should be used for private and
experimental algorithms only. Zero is reserved and must not be
assigned.
Name: Brief, unique, human-readable name for this algorithm.
Reference: URI or otherwise unique identifier for where the details
of this algorithm can be found. It should be as specific as
reasonably possible.
12.1.2. Initial Registry Contents
o ID Number: 1
o Name: NONE
o Reference: this draft.
McCallum, et al. Expires July 28, 2018 [Page 18]
Internet-Draft SPAKE Pre-Authentication January 2018
12.2. Kerberos SPAKE Groups
This section specifies the IANA "Kerberos SPAKE Groups" registry.
This registry records the number, name, specification, serialization,
multiplier length, multiplier conversion, SPAKE M constant and SPAKE
N constant.
12.2.1. Registration Template
ID Number: This is a value that uniquely identifies this entry. It
is a signed integer in range -2147483648 to 2147483647, inclusive.
Positive values must be assigned only for algorithms specified in
accordance with these rules for use with Kerberos and related
protocols. Negative values should be used for private and
experimental use only. Zero is reserved and must not be assigned.
Values should be assigned in increasing order.
Name: Brief, unique, human readable name for this entry.
Specification: Reference to the definition of the group parameters
and operations.
Serialization: Reference to the definition of the method used to
serialize group elements.
Multiplier Length: The length of the input octet string to
multiplication operations.
Multiplier Conversion: Reference to the definition of the method
used to convert an octet string to a multiplier scalar.
SPAKE M Constant: The serialized value of the SPAKE M constant in
hexadecimal notation.
SPAKE N Constant: The serialized value of the SPAKE N constant in
hexadecimal notation.
12.2.2. Initial Registry Contents
McCallum, et al. Expires July 28, 2018 [Page 19]
Internet-Draft SPAKE Pre-Authentication January 2018
o ID Number: 1
o Name: edwards25519
o Specification: [RFC7748] section 4.1 (edwards25519)
o Serialization: [RFC8032] section 3.1
o Multiplier Length: 32
o Multiplier Conversion: [RFC8032] section 3.1
o SPAKE M Constant:
d048032c6ea0b6d697ddc2e86bda85a33adac920f1bf18e1b0c6d166a5cecdaf
o SPAKE N Constant:
d3bfb518f44f3430f29d0c92af503865a1ed3281dc69b35dd868ba85f886c4ab
o ID Number: 2
o Name: P-256
o Specification: [SEC2] section 2.4.2
o Serialization: [SEC1] section 2.3.3 (compressed).
o Multiplier Length: 32
o Multiplier Conversion: [SEC1] section 2.3.8.
o SPAKE M Constant:
02886e2f97ace46e55ba9dd7242579f2993b64e16ef3dcab95afd497333d8fa12f
o SPAKE N Constant:
03d8bbd6c639c62937b04d997f38c3770719c629d7014d49a24b4f98baa1292b49
o ID Number: 3
o Name: P-384
o Specification: [SEC2] section 2.5.1
o Serialization: [SEC1] section 2.3.3 (compressed).
o Multiplier Length: 48
o Multiplier Conversion: [SEC1] section 2.3.8.
o SPAKE M Constant:
030ff0895ae5ebf6187080a82d82b42e2765e3b2f8749c7e05eba3664
34b363d3dc36f15314739074d2eb8613fceec2853
o SPAKE N Constant:
02c72cf2e390853a1c1c4ad816a62fd15824f56078918f43f922ca215
18f9c543bb252c5490214cf9aa3f0baab4b665c10
McCallum, et al. Expires July 28, 2018 [Page 20]
Internet-Draft SPAKE Pre-Authentication January 2018
o ID Number: 4
o Name: P-521
o Specification: [SEC2] section 2.6.1
o Serialization: [SEC1] section 2.3.3 (compressed).
o Multiplier Length: 66
o Multiplier Conversion: [SEC1] section 2.3.8.
o SPAKE M Constant:
02003f06f38131b2ba2600791e82488e8d20ab889af753a41806c5db1
8d37d85608cfae06b82e4a72cd744c719193562a653ea1f119eef9356907edc9b5
6979962d7aa
o SPAKE N Constant:
0200c7924b9ec017f3094562894336a53c50167ba8c5963876880542b
c669e494b2532d76c5b53dfb349fdf69154b9e0048c58a42e8ed04cef052a3bc34
9d95575cd25
13. References
13.1. Normative References
[CCITT.X680.2002]
International Telephone and Telegraph Consultative
Committee, "Abstract Syntax Notation One (ASN.1):
Specification of basic notation", CCITT Recommendation
X.680, July 2002.
[CCITT.X690.2002]
International Telephone and Telegraph Consultative
Committee, "ASN.1 encoding rules: Specification of basic
encoding Rules (BER), Canonical encoding rules (CER) and
Distinguished encoding rules (DER)", CCITT Recommendation
X.690, July 2002.
[I-D.irtf-cfrg-spake2]
Ladd, W., "SPAKE2, a PAKE", draft-irtf-cfrg-spake2-01
(work in progress), February 2015.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/
RFC2119, March 1997, <https://www.rfc-editor.org/info/
rfc2119>.
[RFC3961] Raeburn, K., "Encryption and Checksum Specifications for
Kerberos 5", RFC 3961, DOI 10.17487/RFC3961, February
2005, <https://www.rfc-editor.org/info/rfc3961>.
McCallum, et al. Expires July 28, 2018 [Page 21]
Internet-Draft SPAKE Pre-Authentication January 2018
[RFC4120] Neuman, C., Yu, T., Hartman, S., and K. Raeburn, "The
Kerberos Network Authentication Service (V5)", RFC 4120,
DOI 10.17487/RFC4120, July 2005, <https://www.rfc-
editor.org/info/rfc4120>.
[RFC5226] Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", RFC 5226, DOI
10.17487/RFC5226, May 2008, <https://www.rfc-
editor.org/info/rfc5226>.
[RFC6113] Hartman, S. and L. Zhu, "A Generalized Framework for
Kerberos Pre-Authentication", RFC 6113, DOI 10.17487/
RFC6113, April 2011, <https://www.rfc-editor.org/info/
rfc6113>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/info/rfc7748>.
[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/
RFC8032, January 2017, <https://www.rfc-editor.org/info/
rfc8032>.
[SEC1] Standards for Efficient Cryptography Group, "SEC 1:
Elliptic Curve Cryptography", May 2009.
[SEC2] Standards for Efficient Cryptography Group, "SEC 2:
Recommended Elliptic Curve Domain Parameters", January
2010.
13.2. Non-normative References
[RFC6560] Richards, G., "One-Time Password (OTP) Pre-
Authentication", RFC 6560, DOI 10.17487/RFC6560, April
2012, <https://www.rfc-editor.org/info/rfc6560>.
[RFC6649] Hornquist Astrand, L. and T. Yu, "Deprecate DES, RC4-HMAC-
EXP, and Other Weak Cryptographic Algorithms in Kerberos",
BCP 179, RFC 6649, DOI 10.17487/RFC6649, July 2012,
<https://www.rfc-editor.org/info/rfc6649>.
[SPAKE] Abdalla, M. and D. Pointcheval, "Simple Password-Based
Encrypted Key Exchange Protocols", February 2005.
McCallum, et al. Expires July 28, 2018 [Page 22]
Internet-Draft SPAKE Pre-Authentication January 2018
Appendix A. ASN.1 Module
KerberosV5SPAKE {
iso(1) identified-organization(3) dod(6) internet(1)
security(5) kerberosV5(2) modules(4) spake(8)
} DEFINITIONS EXPLICIT TAGS ::= BEGIN
IMPORTS
EncryptedData, Int32
FROM KerberosV5Spec2 { iso(1) identified-organization(3)
dod(6) internet(1) security(5) kerberosV5(2) modules(4)
krb5spec2(2) };
-- as defined in RFC 4120.
SPAKESupport ::= SEQUENCE {
groups [0] SEQUENCE (SIZE(1..MAX)) OF Int32,
...
}
SPAKEChallenge ::= SEQUENCE {
group [0] Int32,
pubkey [1] OCTET STRING,
factors [2] SEQUENCE (SIZE(1..MAX)) OF SPAKESecondFactor,
...
}
SPAKESecondFactor ::= SEQUENCE {
type [0] Int32,
data [1] OCTET STRING OPTIONAL
}
SPAKEResponse ::= SEQUENCE {
pubkey [0] OCTET STRING,
factor [1] EncryptedData, -- SPAKESecondFactor
...
}
PA-SPAKE ::= CHOICE {
support [0] SPAKESupport,
challenge [1] SPAKEChallenge,
response [2] SPAKEResponse,
encdata [3] EncryptedData,
...
}
END
McCallum, et al. Expires July 28, 2018 [Page 23]
Internet-Draft SPAKE Pre-Authentication January 2018
Appendix B. SPAKE M and N Value Selection
The M and N constants for the NIST groups are from
[I-D.irtf-cfrg-spake2] section 3.
The M and N constants for the edwards25519 group were generated using
the algorithm from [I-D.irtf-cfrg-spake2] section 3 and the seed
strings "edwards25519 point generation seed (M)" and "edwards25519
point generation seed (N)".
Appendix C. Test Vectors
For the following text vectors:
o The key is the string-to-key of "password" with the salt
"ATHENA.MIT.EDUraeburn" for the designated initial reply key
encryption type.
o x and y were chosen randomly within the order of the designated
group, then multiplied by the cofactor..
o The SPAKESupport message contains only the designated group's
number.
o The SPAKEChallenge message offers only the SF-NONE second factor
type.
o The KDC-REQ-BODY message contains no KDC options, the client
principal name "raeburn@ATHENA.MIT.EDU", the server principal name
"krbtgt/ATHENA.MIT.EDU", the realm "ATHENA.MIT.EDU", the till
field "19700101000000Z", the nonce zero, and an etype list
containing only the designated encryption type.
DES3 edwards25519
key: 850bb51358548cd05e86768c313e3bfef7511937dcf72c3e
w: a1f1a25cbd8e3092667e2fddba8ecd24f2c9cef124f7a3371ae81e11cad42a07
x: 201012d07bfd48ddfa33c4aac4fb1e229fb0d043cfe65ebfb14399091c71a723
y: 500b294797b8b042aca1bedc0f5931a4f52c537b3608b2d05cc8a2372f439f25
X: ec274df1920dc0f690c8741b794127233745444161016ef950ad75c51db58c3e
Y: d90974f1c42dac1cd4454561ac2d49af762f2ac87bf02436d461e7b661b43028
T: 18f511e750c97b592acd30db7d9e5fca660389102e6bf610c1bfbed4616c8362
S: 5d10705e0d1e43d5dbf30240ccfbde4a0230c70d4c79147ab0b317edad2f8ae7
K: 25bde0d875f0feb5755f45ba5e857889d916ecf7476f116aa31dc3e037ec4292
SPAKESupport: a0093007a0053003020101
Checksum after SPAKESupport: 9037756a58a060f80c13354b1a743a66837f1d4d
SPAKEChallenge: a1363034a003020101a122042018f511e750c97b592acd30
db7d9e5fca660389102e6bf610c1bfbed4616c8362a20930
073005a003020101
McCallum, et al. Expires July 28, 2018 [Page 24]
Internet-Draft SPAKE Pre-Authentication January 2018
Checksum after SPAKEChallenge: 145fbe58e8bd6bf84627
df10ee9954b7849fdc8c
Final checksum after pubkey: f08091064aa5cc32c5660d9a04efb84a1948381b
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020110
K'[0]: 8fcdad5da81f0b4962e91a67d598a2d9c84fc83b0104c868
K'[1]: abf286ce894523013ba89e3413f7c4ef43c1eca8efa7dadf
K'[2]: 6897524c86b5dc5ec7ecc1944cbc1aae7cbcc1643dcd989e
K'[3]: b0a22c32e37902e023192cefada1869b08e69429e9fe0243
RC4 edwards25519
key: 8846f7eaee8fb117ad06bdd830b7586c
w: 2713c1583c53861520b849bfef0525cd4fe82215b3ea6fcd896561d48048f40c
x: c8a62e7b626f44cad807b2d695450697e020d230a738c5cd5691cc781dce8754
y: 18fe7c1512708c7fd06db270361f04593775bc634ceaf45347e5c11c38aae017
X: b0bcbbdd25aa031f4608d0442dd4924be7731d49c089a8301859d77343ffb567
Y: 7d1ab8aeda1a2b1f9eab8d11c0fda60b616005d0f37d1224c5f12b8649f579a5
T: 7db465f1c08c64983a19f560bce966fe5306c4b447f70a5bca14612a92da1d63
S: 38f8d4568090148ebc9fd17c241b4cc2769505a7ca6f3f7104417b72b5b5cf54
K: 03e75edd2cd7e7677642dd68736e91700953ac55dc650e3c2a1b3b4acdb800f8
SPAKESupport: a0093007a0053003020101
Checksum after SPAKESupport: c8bb7fb72f6b142557fd5de9b1b8bb4c
SPAKEChallenge: a1363034a003020101a12204207db465f1c08c64983a19f5
60bce966fe5306c4b447f70a5bca14612a92da1d63a20930
073005a003020101
Checksum after SPAKEChallenge: 318afd9874400fffa744bc602615cde8
Final checksum after pubkey: 0853678dff8b9e5eb855c5e05420790c
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020117
K'[0]: 87a50a15f0dbd7c958e5bf1bbffee4f2
K'[1]: 1b4a484d4ac7dd18acf5ebc42d8e1b14
K'[2]: 8d6b89f491be1b532be6c6e8482328fe
K'[3]: 425c47073edd4a6f0067f08166d44c7a
AES128 edwards25519
key: fca822951813fb252154c883f5ee1cf4
w: 17c2a9030afb7c37839bd4ae7fdfeb179e99e710e464e62f1fb7c9b67936f30b
x: 50be049a5a570fa1459fb9f666e6fd80602e4e87790a0e567f12438a2c96c138
y: b877afe8612b406d96be85bd9f19d423e95be96c0e1e0b5824127195c3ed5917
X: e73a443c678913eb4a0cad5cbd3086cf82f65a5a91b611e01e949f5c52efd6dd
Y: 473c5b44ed2be9cb50afe1762b535b3930530489816ea6bd962622cccf39f6e8
T: 9e9311d985c1355e022d7c3c694ad8d6f7ad6d647b68a90b0fe46992818002da
McCallum, et al. Expires July 28, 2018 [Page 25]
Internet-Draft SPAKE Pre-Authentication January 2018
S: fbe08f7f96cd5d4139e7c9eccb95e79b8ace41e270a60198c007df18525b628e
K: c2f7f99997c585e6b686ceb62db42f17cc70932def3bb4cf009e36f22ea5473d
SPAKESupport: a0093007a0053003020101
Checksum after SPAKESupport: ce5052873534f00424e38897
SPAKEChallenge: a1363034a003020101a12204209e9311d985c1355e022d7c
3c694ad8d6f7ad6d647b68a90b0fe46992818002daa20930
073005a003020101
Checksum after SPAKEChallenge: 9c46dbbaa67fe262585e68f4
Final checksum after pubkey: 9eb1f4db71208adad0d6d9f1
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020111
K'[0]: 50de22f3b9cd6cd283b23396870ca246
K'[1]: b8e433cef3a84fff59f683b5206d3c86
K'[2]: 3c96a2da9575a297c4e831fe2ae625d8
K'[3]: 54ef2f63b25f66aed65f3d6c77030c6a
AES256 edwards25519
key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1
w: 35b35ca126156b5bf4ec8b90e9545060f2108f1b6aa97b381012b9400c9e3f0e
x: 88c6c0a4f0241ef217c9788f02c32d00b72e4310748cd8fb5f94717607e6417d
y: 88b859df58ef5c69bacdfe681c582754eaab09a74dc29cff50b328613c232f55
X: 23c48eaff2721051946313840723b38f563c59b92043d6ffd752f95781af0327
Y: 3d51486ec1d9be69bc45386bb675c013db87fd0488f6a9cacf6b43e8c81a0641
T: 6f301aacae1220e91be42868c163c5009aeea1e9d9e28afcfc339cda5e7105b5
S: 9e2cc32908fc46273279ec75354b4aeafa70c3d99a4d507175ed70d80b255dda
K: cf57f58f6e60169d2ecc8f20bb923a8e4c16e5bc95b9e64b5dc870da7026321b
SPAKESupport: a0093007a0053003020101
Checksum after SPAKESupport: 14b16e16da078fab9830a66c
SPAKEChallenge: a1363034a003020101a12204206f301aacae1220e91be428
68c163c5009aeea1e9d9e28afcfc339cda5e7105b5a20930
073005a003020101
Checksum after SPAKEChallenge: 667e82727168d0fef248c926
Final checksum after pubkey: 32bf15d0606762b6411a0f68
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020112
K'[0]: 9463038f091c0aed6f8186224b7da5cf
24557bf5c7fd6fe35526ce34a9eb5b05
K'[1]: 1900e226176d6730e9e4c1bf342fd954
df3fc65790f8c267c89b4a3026d0d164
K'[2]: b025fb4103dc29f233640540627331e1
b567c1a7f5a3a00d800c70f0ef213804
K'[3]: 840e2280e4d4c61c44c057e2c7c92207
McCallum, et al. Expires July 28, 2018 [Page 26]
Internet-Draft SPAKE Pre-Authentication January 2018
041dd205bd76b6dc50c9add16cc76c7b
AES256 P-256
key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1
w: eb2984af18703f94dd5288b8596cd36988d0d4e83bfb2b44de14d0e95e2090bd
x: 935ddd725129fb7c6288e1a5cc45782198a6416d1775336d71eacd0549a3e80e
y: e07405eb215663abc1f254b8adc0da7a16febaa011af923d79fdef7c42930b33
X: 03bc802165aea7dbd98cc155056249fe0a37a9c203a7c0f7e872d5bf687bd105e2
Y: 0340b8d91ce3852d0a12ae1f3e82c791fc86df6b346006431e968a1b869af7c735
T: 024f62078ceb53840d02612195494d0d0d88de21feeb81187c71cbf3d01e71788d
S: 021d07dc31266fc7cfd904ce2632111a169b7ec730e5f74a7e79700f86638e13c8
K: 0268489d7a9983f2fde69c6e6a1307e9d252259264f5f2dfc32f58cca19671e79b
SPAKESupport: a0093007a0053003020102
Checksum after SPAKESupport: 61f93e7f998dec5f54cac55c
SPAKEChallenge: a1373035a003020102a1230421024f62078ceb53840d0261
2195494d0d0d88de21feeb81187c71cbf3d01e71788da209
30073005a003020101
Checksum after SPAKEChallenge: 949916036d3c524608533206
Final checksum after pubkey: 1024bfe60a1e22b5bf2838c3
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020112
K'[0]: b3a882eccd2f31df46880f6235522a4d
87523a34442547778c46780f5b35800a
K'[1]: 6e18ebfd20a9a05af11b320eaab15870
93f3e21a5efcb261307786661330344d
K'[2]: 11e1a36e87c729a89bbda12cfa15652f
a1848c0ba9b72cb3e69562648744fb09
K'[3]: 9875d491c6d0bb7cbe6d374c368e1242
97e506becbf8ec6aa539a0d70b9e430a
AES256 P-384
key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1
w: 0304cfc55151c6bbe889653db96dbfe0ba4acafc024c1e8840cb3a486f6d80c1
6e1b8974016aa4b7fa43042a9b3825b1
x: f323ca74d344749096fd35d0adf20806e521460637176e84d977e9933c49d76f
cfc6e62585940927468ff53d864a7a50
y: 5b7c709acb175a5afb82860deabca8d0b341facdff0ac0f1a425799aa905d750
7e1ea9c573581a81467437419466e472
X: 0211e3334f117b76635dd802d4022f601680a1fd066a56606b7f246493a10351
7797b81789b225bd5bb1d9ae1da2962250
Y: 0383dfa413496e5e7599fc8c6430f8d6910d37cf326d81421bc92c0939b555c4
ca2ef6a993f6d3db8cb7407655ef60866e
T: 02a1524603ef14f184696f854229d3397507a66c63f841ba748451056be07879
ac298912387b1c5cdff6381c264701be57
S: 020d5adfdb92bc377041cf5837412574c5d13e0f4739208a4f0c859a0a302bc6
McCallum, et al. Expires July 28, 2018 [Page 27]
Internet-Draft SPAKE Pre-Authentication January 2018
a533440a245b9d97a0d34af5016a20053d
K: 0264aa8c61da9600dfb0beb5e46550d63740e4ef29e73f1a30d543eb43c25499
037ad16538586552761b093cf0e37c703a
SPAKESupport: a0093007a0053003020103
Checksum after SPAKESupport: a0024c7b5ff667ae074a9988
SPAKEChallenge: a1473045a003020103a133043102a1524603ef14f184696f
854229d3397507a66c63f841ba748451056be07879ac2989
12387b1c5cdff6381c264701be57a20930073005a003020101
Checksum after SPAKEChallenge: ecd0f64ed7c0d4e18fa4c5b4
Final checksum after pubkey: a238108c88afd856f04d3aa5
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020112
K'[0]: ff59fb5fb83c7bafe197b62c853eb7c3
a2902301dfe8326851626a0e9c714c47
K'[1]: e3c741ac7041feed0f0b5c36cb74c179
cb565e509b6d65594d0badafe318c4dc
K'[2]: 9c7a73087f22b52db38a14eb8292df61
54516eaadb7149b14d35864bdb85aa22
K'[3]: 75ea14f0f53ee8dbabd78f446462cfda
590d4ace0fa93708a00f26f26c565e56
AES256 P-521
key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1
w: 003a095a2b2386eff3eb15b735398da1caf95bc8425665d82370aff58b0471f3
4cce63791cfed967f0c94c16054b3e1703133681bece1e05219f5426bc944b0f
bfb3
x: 017c38701a14b490b6081dfc83524562be7fbb42e0b20426465e3e37952d30bc
ab0ed857010255d44936a1515607964a870c7c879b741d878f9f9cdf5a865306
f3f5
y: 003e2e2950656fa231e959acdd984d125e7fa59cec98126cbc8f3888447911eb
cd49428a1c22d5fdb76a19fbeb1d9edfa3da6cf55b158b53031d05d51433ade9
b2b4
X: 03003e95272223b210b48cfd908b956a36add04a7ff443511432f94ddd87e064
1d680ba3b3d532c21fa6046192f6bfae7af81c4b803aa154e12459d1428f8f2f
56e9f2
Y: 030064916687960df496557ecab08298bf075429eca268c6dabbae24e258d568
c62841664dc8ecf545369f573ea84548faa22f118128c0a87e1d47315afabb77
3bb082
T: 02017d3de19a3ec53d0174905665ef37947d142535102cd9809c0dfbd0dfe007
353d54cf406ce2a59950f2bb540df6fbe75f8bbbef811c9ba06cc275adbd9675
6696ec
S: 02004d142d87477841f6ba053c8f651f3395ad264b7405ca5911fb9a55abd454
fef658a5f9ed97d1efac68764e9092fa15b9e0050880d78e95fd03abf5931791
6822b5
K: 03007c303f62f09282cc849490805bd4457a6793a832cbeb55df427db6a31e99
McCallum, et al. Expires July 28, 2018 [Page 28]
Internet-Draft SPAKE Pre-Authentication January 2018
b055d5dc99756d24d47b70ad8b6015b0fb8742a718462ed423b90fa3fe631ac1
3fa916
SPAKESupport: a0093007a0053003020104
Checksum after SPAKESupport: 1b69d116036e141e45d4f7d7
SPAKEChallenge: a1593057a003020104a145044302017d3de19a3ec53d0174
905665ef37947d142535102cd9809c0dfbd0dfe007353d54
cf406ce2a59950f2bb540df6fbe75f8bbbef811c9ba06cc2
75adbd96756696eca20930073005a003020101
Checksum after SPAKEChallenge: cac3da1e9ab1261723ece823
Final checksum after pubkey: 654493ca7e47f3c5200f4b84
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020112
K'[0]: c91635dfd1de3884b635b58b30d3cfd5
26fe78f8dade6f19e4eb2fb23ef594ca
K'[1]: 03d38e139bb3f66cc76c5da720f3bf11
4280f64ed708e69e96094bb62aa28f32
K'[2]: 515eaa3c45b08bc9d77468059e64a8e1
96cfcd15db92ad431cae5edbe721d07e
K'[3]: 898ae786e58391d8a00eb7a7cbddd005
3aff9147b42a3076d934608e70a6f0ff
AES256 edwards25519 with accepted optimistic challenge
key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1
w: 35b35ca126156b5bf4ec8b90e9545060f2108f1b6aa97b381012b9400c9e3f0e
x: 70937207344cafbc53c8a55070e399c584cbafce00b836980dd4e7e74fad2a64
y: 785d6801a2490df028903ac6449b105f2ff0db895b252953cdc2076649526103
X: 13841224ea50438c1d9457159d05f2b7cd9d05daf154888eeed223e79008b47c
Y: d01fc81d5ce20d6ea0939a6bb3e40ccd049f821baaf95e323a3657309ef75d61
T: 83523b35f1565006cbfc4f159885467c2fb9bc6fe23d36cb1da43d199f1a3118
S: 2a8f70f46cee9030700037b77f22cec7970dcc238e3e066d9d726baf183992c6
K: d3c5e4266aa6d1b2873a97ce8af91c7e4d7a7ac456acced7908d34c561ad8fa6
SPAKEChallenge: a1363034a003020101a122042083523b35f1565006cbfc4f
159885467c2fb9bc6fe23d36cb1da43d199f1a3118a20930
073005a003020101
Checksum after SPAKEChallenge: 0b1dc2059f7411b639295982
Final checksum after pubkey: 3990d78eb0abc055d1f69fcb
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
303130313030303030305aa703020100a8053003020112
K'[0]: 1e9b04bdbdaaffb340aa09c6cdf560fa
dcaadb7cb8762b22cd6e7c96753090b7
K'[1]: 7b959d40bd6c517a89278b008cf314e5
d947b181a3251d2832ab61a21c40d484
McCallum, et al. Expires July 28, 2018 [Page 29]
Internet-Draft SPAKE Pre-Authentication January 2018
K'[2]: 3e484bb86ab7f4ffc4b80a6f6d79692c
55daf2b78654b38c7f1d37b1d688d1f3
K'[3]: 23a331ddf33211859b82502295b0be4b
23a56057b77356d62a13985ca573dae1
AES256 P-521 with rejected optimistic edwards25519 challenge
key: 01b897121d933ab44b47eb5494db15e50eb74530dbdae9b634d65020ff5d88c1
w: 003a095a2b2386eff3eb15b735398da1caf95bc8425665d82370aff58b0471f3
4cce63791cfed967f0c94c16054b3e1703133681bece1e05219f5426bc944b0f
bfb3
x: 01687b59051bf40048d7c31d5a973d792fa12284b7a447e7f5938b5885ca0bb2
c3f0bd30291a55fea08e143e2e04bdd7d19b753c7c99032f06cab0d9c2aa8f83
7ef7
y: 01ded675ebf74fe30c9a53710f577e9cf84f09f6048fe245a4600004884cc167
733f9a9e43108fb83babe8754cd37cbd7025e28bc9ff870f084c7244f536285e
25b4
X: 03001bed88af987101ef52db5b8876f6287eb49a72163876c2cf99deb94f4c74
9bfd118f0f400833cc8daad81971fe40498e6075d8ba0a2acfac35eb9ec8530e
e0edd5
Y: 02007bd3bf214200795ea449852976f241c9f50f445f78ff2714fffe42983f25
cd9c9094ba3f9d7adadd6c251e9dc0991fc8210547e7769336a0ac406878fb94
be2f1f
T: 02014cb2e5b592ece5990f0ef30d308c061de1598bc4272b4a6599bed466fd15
21693642abcf4dbe36ce1a2d13967de45f6c4f8d0fa8e14428bf03fb96ef5f1e
d3e645
S: 02016c64995e804416f748fd5fa3aa678cbc7cbb596a4f523132dc8af7ce84e5
41f484a2c74808c6b21dcf7775baefa6753398425becc7b838b210ac5daa0cb0
b710e2
K: 0200997f4848ae2e7a98c23d14ac662030743ab37fccc2a45f1c721114f40bcc
80fe6ec6aba49868f8aea1aa994d50e81b86d3e4d3c1130c8695b68907c673d9
e5886a
Optimistic SPAKEChallenge: a1363034a003020102a122042047ca8c
24c3a4a70b6eca228322529dadcfa85c
f58faceecf5d5c02907b9e2deba20930
073005a003020101
Checksum after optimist SPAKEChallenge: 57eff4df899bc520010deb48
SPAKESupport: a0093007a0053003020104
Checksum after SPAKESupport: c2fe6c3c142c207d0bdbdd9c
SPAKEChallenge: a1593057a003020104a145044302014cb2e5b592ece5990f
0ef30d308c061de1598bc4272b4a6599bed466fd15216936
42abcf4dbe36ce1a2d13967de45f6c4f8d0fa8e14428bf03
fb96ef5f1ed3e645a20930073005a003020101
Checksum after SPAKEChallenge: c78a00b2d896b73dbed4969b
Final checksum after pubkey: 80a1da254a44641e0223a944
KDC-REQ-BODY: 3075a00703050000000000a1143012a003020101a10b3009
1b077261656275726ea2101b0e415448454e412e4d49542e
454455a3233021a003020102a11a30181b066b7262746774
1b0e415448454e412e4d49542e454455a511180f31393730
McCallum, et al. Expires July 28, 2018 [Page 30]
Internet-Draft SPAKE Pre-Authentication January 2018
303130313030303030305aa703020100a8053003020112
K'[0]: 567cb2ee046cc10cd29cd5bbe5998e5c
d4fca318075981087400c32c55299697
K'[1]: 57535deb12a3bcaac8389957d9065ee5
51a869148de1f457b232e12055ee9efa
K'[2]: 6d18f714b69242f1e556b2819f895926
9ee0da5b014785b4f1fabb3b7318b70c
K'[3]: a1d86d7d091800f191884e501974fa32
ca513a520197866d7c57e5c1296319e6
Appendix D. Acknowledgements
Nico Williams (Cryptonector)
Taylor Yu (MIT)
Authors' Addresses
Nathaniel McCallum
Red Hat, Inc.
EMail: npmccallum@redhat.com
Simo Sorce
Red Hat, Inc.
EMail: ssorce@redhat.com
Robbie Harwood
Red Hat, Inc.
EMail: rharwood@redhat.com
Greg Hudson
MIT
EMail: ghudson@mit.edu
McCallum, et al. Expires July 28, 2018 [Page 31]