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|
Internet Engineering Task Force K. Jaganathan
Internet-Draft L. Zhu
Intended status: Informational J. Brezak
Expires: January 31, 2007 Microsoft Corporation
July 30, 2006
The RC4-HMAC Kerberos Encryption Types Used by Microsoft Windows
draft-jaganathan-rc4-hmac-03.txt
Status of this Memo
By submitting this Internet-Draft, each author represents that any
applicable patent or other IPR claims of which he or she is aware
have been or will be disclosed, and any of which he or she becomes
aware will be disclosed, in accordance with Section 6 of BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF), its areas, and its working groups. Note that
other groups may also distribute working documents as Internet-
Drafts.
Internet-Drafts are draft documents valid for a maximum of six months
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material or to cite them other than as "work in progress."
The list of current Internet-Drafts can be accessed at
http://www.ietf.org/ietf/1id-abstracts.txt.
The list of Internet-Draft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html.
This Internet-Draft will expire on January 31, 2007.
Copyright Notice
Copyright (C) The Internet Society (2006).
Abstract
The Microsoft Windows 2000 implementation of Kerberos introduces a
new encryption type based on the RC4 encryption algorithm and using
an MD5 HMAC for checksum. This is offered as an alternative to using
the existing DES based encryption types.
The RC4-HMAC encryption types are used to ease upgrade of existing
Windows NT environments, provide strong crypto (128-bit key lengths),
Jaganathan, et al. Expires January 31, 2007 [Page 1]
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and provide exportable (meet United States government export
restriction requirements) encryption. This document describes the
implementation of those encryption types.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Key Generation . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Basic Operations . . . . . . . . . . . . . . . . . . . . . . . 4
4. Checksum Types . . . . . . . . . . . . . . . . . . . . . . . . 6
5. Encryption Types . . . . . . . . . . . . . . . . . . . . . . . 6
6. Key Strength Negotiation . . . . . . . . . . . . . . . . . . . 8
7. GSSAPI Kerberos V5 Mechanism Type . . . . . . . . . . . . . . 8
7.1. Mechanism Specific Changes . . . . . . . . . . . . . . . . 8
7.2. GSSAPI MIC Semantics . . . . . . . . . . . . . . . . . . . 10
7.3. GSSAPI WRAP Semantics . . . . . . . . . . . . . . . . . . 12
8. Security Considerations . . . . . . . . . . . . . . . . . . . 15
9. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 15
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 16
11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11.1. Normative References . . . . . . . . . . . . . . . . . . . 16
11.2. Informative References . . . . . . . . . . . . . . . . . . 16
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 16
Intellectual Property and Copyright Statements . . . . . . . . . . 18
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1. Introduction
The Microsoft Windows 2000 implementation of Kerberos contains new
encryption and checksum types for two reasons: for export reasons
early in the development process, 56 bit DES encryption could not be
exported, and because upon upgrade from Windows NT 4.0 to Windows
2000, accounts will not have the appropriate DES keying material to
do the standard DES encryption. Furthermore, 3DES is not available
for export, and there was a desire to use a single flavor of
encryption in the product for both US and international products.
As a result, there are two new encryption types and one new checksum
type introduced in Microsoft Windows 2000.
Note that these cryptosystems aren't intended to be complete,
general-purpose Kerberos encryption or checksum systems as defined in
[RFC3961]: there is no one-one mapping between the operations in this
documents and the primitives described in [RFC3961].
2. Key Generation
On upgrade from existing Windows NT domains, the user accounts would
not have a DES based key available to enable the use of DES base
encryption types specified in [RFC4120] [RFC3961]. The key used for
RC4-HMAC is the same as the existing Windows NT key (NT Password
Hash) for compatibility reasons. Once the account password is
changed, the DES based keys are created and maintained. Once the DES
keys are available DES based encryption types can be used with
Kerberos.
The RC4-HMAC String to key function is defined as follow:
String2Key(password)
K = MD4(UNICODE(password))
The RC4-HMAC keys are generated by using the Windows UNICODE version
of the password. Each Windows UNICODE character is encoded in
little-endian format of 2 octets each. Then performing an MD4
[RFC1320] hash operation on just the UNICODE characters of the
password (not including the terminating zero octets).
For an account with a password of "foo", this String2Key("foo") will
return:
0xac, 0x8e, 0x65, 0x7f, 0x83, 0xdf, 0x82, 0xbe,
0xea, 0x5d, 0x43, 0xbd, 0xaf, 0x78, 0x00, 0xcc
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3. Basic Operations
The MD5 HMAC function is defined in [RFC2104]. It is used in this
encryption type for checksum operations. Refer to [RFC2104] for
details on its operation. In this document this function is referred
to as HMAC(Key, Data) returning the checksum using the specified key
on the data.
The basic MD5 hash operation is used in this encryption type and
defined in [RFC1321]. In this document this function is referred to
as MD5(Data) returning the checksum of the data.
RC4 is a stream cipher licensed by RSA Data Security . In this
document the function is referred to as RC4(Key, Data) returning the
encrypted data using the specified key on the data.
These encryption types use key derivation. With each message, the
message type (T) is used as a component of the keying material. This
table summarizes the different key derivation values used in the
various operations. Note that these differ from the key derivations
used in other Kerberos encryption types. T = the message type,
encoded as a little-endian four byte integer.
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1. AS-REQ PA-ENC-TIMESTAMP padata timestamp, encrypted with
the client key (T=1)
2. AS-REP Ticket and TGS-REP Ticket (includes TGS session key
or application session key), encrypted with the service key
(T=2)
3. AS-REP encrypted part (includes TGS session key or
application session key), encrypted with the client key (T=8)
4. TGS-REQ KDC-REQ-BODY AuthorizationData, encrypted with the
TGS session key (T=4)
5. TGS-REQ KDC-REQ-BODY AuthorizationData, encrypted with the
TGS authenticator subkey (T=5)
6. TGS-REQ PA-TGS-REQ padata AP-REQ Authenticator cksum,
keyed with the TGS session key (T=6)
7. TGS-REQ PA-TGS-REQ padata AP-REQ Authenticator (includes
TGS authenticator subkey), encrypted with the TGS session key
T=7)
8. TGS-REP encrypted part (includes application session key),
encrypted with the TGS session key (T=8)
9. TGS-REP encrypted part (includes application session key),
encrypted with the TGS authenticator subkey (T=8)
10. AP-REQ Authenticator cksum, keyed with the application
session key (T=10)
11. AP-REQ Authenticator (includes application authenticator
subkey), encrypted with the application session key (T=11)
12. AP-REP encrypted part (includes application session
subkey), encrypted with the application session key (T=12)
13. KRB-PRIV encrypted part, encrypted with a key chosen by
the application. Also for data encrypted with GSS Wrap (T=13)
14. KRB-CRED encrypted part, encrypted with a key chosen by
the application (T=14)
15. KRB-SAFE cksum, keyed with a key chosen by the
application. Also for data signed in GSS MIC (T=15)
Relative to RFC-1964 key uses:
T = 0 in the generation of sequence number for the MIC token
T = 0 in the generation of sequence number for the WRAP token
T = 0 in the generation of encrypted data for the WRAPPED token
All strings in this document are ASCII unless otherwise specified.
The lengths of ASCII encoded character strings include the trailing
terminator character (0). The concat(a,b,c,...) function will return
the logical concatenation (left to right) of the values of the
arguments. The nonce(n) function returns a pseudo-random number of
"n" octets.
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4. Checksum Types
There is one checksum type used in this encryption type. The
Kerberos constant for this type is:
#define KERB_CHECKSUM_HMAC_MD5 (-138)
The function is defined as follows:
K - is the Key
T - the message type, encoded as a little-endian four byte integer
CHKSUM(K, T, data)
Ksign = HMAC(K, "signaturekey") //includes zero octet at end
tmp = MD5(concat(T, data))
CHKSUM = HMAC(Ksign, tmp)
5. Encryption Types
There are two encryption types used in these encryption types. The
Kerberos constants for these types are:
#define KERB_ETYPE_RC4_HMAC 23
#define KERB_ETYPE_RC4_HMAC_EXP 24
The basic encryption function is defined as follow:
T = the message type, encoded as a little-endian four byte integer.
OCTET L40[14] = "fortybits";
The header field on the encrypted data in KDC messages is:
typedef struct _RC4_MDx_HEADER {
OCTET Checksum[16];
OCTET Confounder[8];
} RC4_MDx_HEADER, *PRC4_MDx_HEADER;
ENCRYPT (K, export, T, data)
{
struct EDATA {
struct HEADER {
OCTET Checksum[16];
OCTET Confounder[8];
} Header;
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OCTET Data[0];
} edata;
if (export){
*((DWORD *)(L40+10)) = T;
HMAC (K, L40, 10 + 4, K1);
}
else
{
HMAC (K, &T, 4, K1);
}
memcpy (K2, K1, 16);
if (export) memset (K1+7, 0xAB, 9);
nonce (edata.Confounder, 8);
memcpy (edata.Data, data);
edata.Checksum = HMAC (K2, edata);
K3 = HMAC (K1, edata.Checksum);
RC4 (K3, edata.Confounder);
RC4 (K3, data.Data);
}
DECRYPT (K, export, T, edata)
{
// edata looks like
struct EDATA {
struct HEADER {
OCTET Checksum[16];
OCTET Confounder[8];
} Header;
OCTET Data[0];
} edata;
if (export){
*((DWORD *)(L40+10)) = T;
HMAC (K, L40, 14, K1);
}
else
{
HMAC (K, &T, 4, K1);
}
memcpy (K2, K1, 16);
if (export) memset (K1+7, 0xAB, 9);
K3 = HMAC (K1, edata.Checksum);
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RC4 (K3, edata.Confounder);
RC4 (K3, edata.Data);
// verify generated and received checksums
checksum = HMAC (K2, concat(edata.Confounder, edata.Data));
if (checksum != edata.Checksum)
printf("CHECKSUM ERROR !!!!!!\n");
}
The KDC message is encrypted using the ENCRYPT function not including
the Checksum in the RC4_MDx_HEADER.
The character constant "fortybits" evolved from the time when a 40-
bit key length was all that was exportable from the United States.
It is now used to recognize that the key length is of "exportable"
length. In this description, the key size is actually 56-bits.
The pseudo-random operation [RFC3961] for both enctypes above is
defined as follows:
pseudo-random(K, S) = HMAC-SHA1(K, S)
where K is the protocol key and S is the input octet string. HMAC-
SHA1 is defined in [RFC2104] and the output of HMAC-SHA1 is the 20-
octet digest.
6. Key Strength Negotiation
A Kerberos client and server can negotiate over key length if they
are using mutual authentication. If the client is unable to perform
full strength encryption, it may propose a key in the "subkey" field
of the authenticator, using a weaker encryption type. The server
must then either return the same key or suggest its own key in the
subkey field of the AP reply message. The key used to encrypt data
is derived from the key returned by the server. If the client is
able to perform strong encryption but the server is not, it may
propose a subkey in the AP reply without first being sent a subkey in
the authenticator.
7. GSSAPI Kerberos V5 Mechanism Type
7.1. Mechanism Specific Changes
The GSSAPI per-message tokens also require new checksum and
encryption types. The GSS-API per-message tokens are adapted to
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support these new encryption types. See [RFC1964] Section 1.2.2.
The only support quality of protection is:
#define GSS_KRB5_INTEG_C_QOP_DEFAULT 0x0
When using this RC4 based encryption type, the sequence number is
always sent in big-endian rather than little-endian order.
The Windows 2000 implementation also defines new GSSAPI flags in the
initial token passed when initializing a security context. These
flags are passed in the checksum field of the authenticator. See
[RFC1964] Section 1.1.1.
GSS_C_DCE_STYLE - This flag was added for use with Microsoft's
implementation of DCE RPC, which initially expected three legs of
authentication. Setting this flag causes an extra AP reply to be
sent from the client back to the server after receiving the server's
AP reply. In addition, the context negotiation tokens do not have
GSSAPI per message tokens - they are raw AP messages that do not
include object identifiers.
#define GSS_C_DCE_STYLE 0x1000
GSS_C_IDENTIFY_FLAG - This flag allows the client to indicate to the
server that it should only allow the server application to identify
the client by name and ID, but not to impersonate the client.
#define GSS_C_IDENTIFY_FLAG 0x2000
GSS_C_EXTENDED_ERROR_FLAG - Setting this flag indicates that the
client wants to be informed of extended error information. In
particular, Windows 2000 status codes may be returned in the data
field of a Kerberos error message. This allows the client to
understand a server failure more precisely. In addition, the server
may return errors to the client that are normally handled at the
application layer in the server, in order to let the client try to
recover. After receiving an error message, the client may attempt to
resubmit an AP request.
#define GSS_C_EXTENDED_ERROR_FLAG 0x4000
These flags are only used if a client is aware of these conventions
when using the SSPI on the Windows platform; they are not generally
used by default.
When NetBIOS addresses are used in the GSSAPI, they are identified by
the GSS_C_AF_NETBIOS value. This value is defined as:
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#define GSS_C_AF_NETBIOS 0x14
NetBios addresses are 16-octet addresses typically composed of 1 to
15 characters, trailing blank (ASCII char 20) filled, with a 16-th
octet of 0x0.
7.2. GSSAPI MIC Semantics
The GSSAPI checksum type and algorithm is defined in Section 5. Only
the first 8 octets of the checksum are used. The resulting checksum
is stored in the SGN_CKSUM field . See [RFC1964] Section 1.2 for
GSS_GetMIC() and GSS_Wrap(conf_flag=FALSE).
The GSS_GetMIC token has the following format:
Byte no Name Description
0..1 TOK_ID Identification field.
Tokens emitted by GSS_GetMIC() contain
the hex value 01 01 in this field.
2..3 SGN_ALG Integrity algorithm indicator.
11 00 - HMAC
4..7 Filler Contains ff ff ff ff
8..15 SND_SEQ Sequence number field.
16..23 SGN_CKSUM Checksum of "to-be-signed data",
calculated according to algorithm
specified in SGN_ALG field.
The MIC mechanism used for GSS MIC based messages is as follow:
GetMIC(Kss, direction, export, seq_num, data)
{
struct Token {
struct Header {
OCTET TOK_ID[2];
OCTET SGN_ALG[2];
OCTET Filler[4];
};
OCTET SND_SEQ[8];
OCTET SGN_CKSUM[8];
} Token;
Token.TOK_ID = 01 01;
Token.SGN_SLG = 11 00;
Token.Filler = ff ff ff ff;
// Create the sequence number
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if (direction == sender_is_initiator)
{
memset(Token.SEND_SEQ+4, 0xff, 4)
}
else if (direction == sender_is_acceptor)
{
memset(Token.SEND_SEQ+4, 0, 4)
}
Token.SEND_SEQ[0] = (seq_num & 0xff000000) >> 24;
Token.SEND_SEQ[1] = (seq_num & 0x00ff0000) >> 16;
Token.SEND_SEQ[2] = (seq_num & 0x0000ff00) >> 8;
Token.SEND_SEQ[3] = (seq_num & 0x000000ff);
// Derive signing key from session key
Ksign = HMAC(Kss, "signaturekey");
// length includes terminating null
// Generate checksum of message - SGN_CKSUM
// Key derivation salt = 15
Sgn_Cksum = MD5((int32)15, Token.Header, data);
// Save first 8 octets of HMAC Sgn_Cksum
Sgn_Cksum = HMAC(Ksign, Sgn_Cksum);
memcpy(Token.SGN_CKSUM, Sgn_Cksum, 8);
// Encrypt the sequence number
// Derive encryption key for the sequence number
// Key derivation salt = 0
if (exportable)
{
Kseq = HMAC(Kss, "fortybits", (int32)0);
// len includes terminating null
memset(Kseq+7, 0xab, 7)
}
else
{
Kseq = HMAC(Kss, (int32)0);
}
Kseq = HMAC(Kseq, Token.SGN_CKSUM);
// Encrypt the sequence number
RC4(Kseq, Token.SND_SEQ);
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}
7.3. GSSAPI WRAP Semantics
There are two encryption keys for GSSAPI message tokens, one that is
128 bits in strength, and one that is 56 bits in strength as defined
in Section 6.
All padding is rounded up to 1 byte. One byte is needed to say that
there is 1 byte of padding. The DES based mechanism type uses 8 byte
padding. See [RFC1964] Section 1.2.2.3.
The RC4-HMAC GSS_Wrap() token has the following format:
Byte no Name Description
0..1 TOK_ID Identification field.
Tokens emitted by GSS_Wrap() contain
the hex value 02 01 in this field.
2..3 SGN_ALG Checksum algorithm indicator.
11 00 - HMAC
4..5 SEAL_ALG ff ff - none
00 00 - DES-CBC
10 00 - RC4
6..7 Filler Contains ff ff
8..15 SND_SEQ Encrypted sequence number field.
16..23 SGN_CKSUM Checksum of plaintext padded data,
calculated according to algorithm
specified in SGN_ALG field.
24..31 Confounder Random confounder
32..last Data encrypted or plaintext padded data
The encryption mechanism used for GSS wrap based messages is as
follow:
WRAP(Kss, encrypt, direction, export, seq_num, data)
{
struct Token { // 32 octets
struct Header {
OCTET TOK_ID[2];
OCTET SGN_ALG[2];
OCTET SEAL_ALG[2];
OCTET Filler[2];
};
OCTET SND_SEQ[8];
OCTET SGN_CKSUM[8];
OCTET Confounder[8];
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} Token;
Token.TOK_ID = 02 01;
Token.SGN_SLG = 11 00;
Token.SEAL_ALG = (no_encrypt)? ff ff : 10 00;
Token.Filler = ff ff;
// Create the sequence number
if (direction == sender_is_initiator)
{
memset(&Token.SEND_SEQ[4], 0xff, 4)
}
else if (direction == sender_is_acceptor)
{
memset(&Token.SEND_SEQ[4], 0, 4)
}
Token.SEND_SEQ[0] = (seq_num & 0xff000000) >> 24;
Token.SEND_SEQ[1] = (seq_num & 0x00ff0000) >> 16;
Token.SEND_SEQ[2] = (seq_num & 0x0000ff00) >> 8;
Token.SEND_SEQ[3] = (seq_num & 0x000000ff);
// Generate random confounder
nonce(&Token.Confounder, 8);
// Derive signing key from session key
Ksign = HMAC(Kss, "signaturekey");
// Generate checksum of message -
// SGN_CKSUM + Token.Confounder
// Key derivation salt = 15
Sgn_Cksum = MD5((int32)15, Token.Header,
Token.Confounder);
// Derive encryption key for data
// Key derivation salt = 0
for (i = 0; i < 16; i++) Klocal[i] = Kss[i] ^ 0xF0;
// XOR
if (exportable)
{
Kcrypt = HMAC(Klocal, "fortybits", (int32)0);
// len includes terminating null
memset(Kcrypt+7, 0xab, 7);
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}
else
{
Kcrypt = HMAC(Klocal, (int32)0);
}
// new encryption key salted with seq
Kcrypt = HMAC(Kcrypt, (int32)seq);
// Encrypt confounder (if encrypting)
if (encrypt)
RC4(Kcrypt, Token.Confounder);
// Sum the data buffer
Sgn_Cksum += MD5(data); // Append to checksum
// Encrypt the data (if encrypting)
if (encrypt)
RC4(Kcrypt, data);
// Save first 8 octets of HMAC Sgn_Cksum
Sgn_Cksum = HMAC(Ksign, Sgn_Cksum);
memcpy(Token.SGN_CKSUM, Sgn_Cksum, 8);
// Derive encryption key for the sequence number
// Key derivation salt = 0
if (exportable)
{
Kseq = HMAC(Kss, "fortybits", (int32)0);
// len includes terminating null
memset(Kseq+7, 0xab, 7)
}
else
{
Kseq = HMAC(Kss, (int32)0);
}
Kseq = HMAC(Kseq, Token.SGN_CKSUM);
// Encrypt the sequence number
RC4(Kseq, Token.SND_SEQ);
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// Encrypted message = Token + Data
}
The character constant "fortybits" evolved from the time when a 40-
bit key length was all that was exportable from the United States.
It is now used to recognize that the key length is of "exportable"
length. In this description, the key size is actually 56-bits.
8. Security Considerations
Care must be taken in implementing these encryption types because
they use a stream cipher. If a different IV is not used in each
direction when using a session key, the encryption is weak. By using
the sequence number as an IV, this is avoided.
There are two classes of attack on RC4 described in [MIRONOV].
Strong distinguishers distinguish an RC4 keystream from randomness at
the start of the stream. Weak distinguishers can operate on any part
of the keystream, and the best ones, described in [FMcG] and
[MANTIN05], can exploit data from multiple, different keystreams. A
consequence of these is that encrypting the same data (for instance,
a password) sufficiently many times in separate RC4 keystreams can be
sufficient to leak information to an adversary. The encryption types
defined in this document defend against these by constructing a new
key stream for every message. However, it is RECOMMENDED not to use
the RC4 encryption types defined in this document for high-volume
connections.
Weaknesses in MD4 [BOER91] were demonstrated by Den Boer and
Bosselaers in 1991. In August 2004, Xiaoyun Wang et al reported MD4
collisions generated using hand calculation [WANG04].
Implementations based on Wang's algorithm can find collisions in real
time. However, the intended usage of MD4 described in this document
does not rely on the collision-resistant property of MD4.
Futhermore, MD4 is always used in the context of a keyed hash in this
document. Although no evidence has suggested keyed MD4 hashes are
vulnerable to collision-based attacks, no study has directly proved
that the HMAC-MD4 is secure: the existing study simply assumed that
the hash function used in HMAC is collision proof. It is thus
RECOMMENDED not to use the RC4 encryption types defined in this
document if alternative stronger encryption types, such as aes256-
cts-hmac-sha1-96 [RFC3962], are available.
9. Acknowledgements
The authors wish to thank Sam Hartman, Ken Raeburn and Qunli Li for
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their insightful comments.
10. IANA Considerations
This document has no actions for IANA.
11. References
11.1. Normative References
[RFC1320] Rivest, R., "The MD4 Message-Digest Algorithm", RFC 1320,
April 1992.
[RFC1321] Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321,
April 1992.
[RFC1964] Linn, J., "The Kerberos Version 5 GSS-API Mechanism",
RFC 1964, June 1996.
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
February 1997.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC3961] Raeburn, K., "Encryption and Checksum Specifications for
Kerberos 5", RFC 3961, February 2005.
[RFC3962] Raeburn, K., "Advanced Encryption Standard (AES)
Encryption for Kerberos 5", RFC 3962, February 2005.
[RFC4120] Neuman, C., Yu, T., Hartman, S., and K. Raeburn, "The
Kerberos Network Authentication Service (V5)", RFC 4120,
July 2005.
11.2. Informative References
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[BOER91] Boer, D. and A. Bosselaers, "An Attack on the Last Two
Rounds of MD4",
http://citeseer.ist.psu.edu/denboer91attack.html, 1991.
[FMcG] Fluhrer, S. and D. McGrew, "Statistical Analysis of the
Alleged RC4 Keystream Generator", Fast Software
Encryption: 7th International Workshop, FSE 2000, April
2000, <http://www.mindspring.com/~dmcgrew/rc4-03.pdf>.
[MANTIN01] Mantin, I., "Analysis of the Stream Cipher RC4", M.Sc.
Thesis, Weizmann Institute of Science, 2001, <http://
www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/Mantin1.zip>.
[MIRONOV] Mironov, I., "(Not So) Random Shuffles of RC4", Advances
in Cryptology -- CRYPTO 2002: 22nd Annual International
Cryptology Conference, August 2002,
<http://eprint.iacr.org/2002/067.pdf>.
[MANTIN05] Mantin, I., "Predicting and Distinguishing Attacks on RC4
Keystream Generator", Advances in Cryptology -- EUROCRYPT
2005: 24th Annual International Conference on the Theory
and Applications of Cryptographic Techniques, May 2005.
[WANG04] Wang, X., Lai, X., Feng, D., Chen H., and X. Yu,
"Cryptanalysis of Hash functions MD4 and RIPEMD",
http://www.infosec.sdu.edu.cn/paper/md4-ripemd-attck.pdf,
Augest, 2004.
Authors' Addresses
Karthik Jaganathan
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
US
Email: karthikj@microsoft.com
Larry Zhu
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
US
Email: lzhu@microsoft.com
John Brezak
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
US
Email: jbrezak@microsoft.com
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