RFC 1510
The Kerberos Network Authentication Service (V5)
3.2. The Client/Server Authentication Exchange Summary Message direction Message type Section Client to Application server KRB_AP_REQ 5.5.1 [optional] Application server to client KRB_AP_REP or 5.5.2 KRB_ERROR 5.9.1 The client/server authentication (CS) exchange is used by network applications to authenticate the client to the server and vice versa. The client must have already acquired credentials for the server using the AS or TGS exchange. 3.2.1. The KRB_AP_REQ message The KRB_AP_REQ contains authentication information which should be part of the first message in an authenticated transaction. It contains a ticket, an authenticator, and some additional bookkeeping information (see section 5.5.1 for the exact format). The ticket by itself is insufficient to authenticate a client, since tickets are passed across the network in cleartext(Tickets contain both an encrypted and unencrypted portion, so cleartext here refers to the entire unit, which can be copied from one message and replayed in another without any cryptographic skill.), so the authenticator is used to prevent invalid replay of tickets by proving to the server that the client knows the session key of the ticket and thus is entitled to use it. The KRB_AP_REQ message is referred to elsewhere as the "authentication header." 3.2.2. Generation of a KRB_AP_REQ message When a client wishes to initiate authentication to a server, it obtains (either through a credentials cache, the AS exchange, or the
TGS exchange) a ticket and session key for the desired service. The client may re-use any tickets it holds until they expire. The client then constructs a new Authenticator from the the system time, its name, and optionally an application specific checksum, an initial sequence number to be used in KRB_SAFE or KRB_PRIV messages, and/or a session subkey to be used in negotiations for a session key unique to this particular session. Authenticators may not be re-used and will be rejected if replayed to a server (Note that this can make applications based on unreliable transports difficult to code correctly, if the transport might deliver duplicated messages. In such cases, a new authenticator must be generated for each retry.). If a sequence number is to be included, it should be randomly chosen so that even after many messages have been exchanged it is not likely to collide with other sequence numbers in use. The client may indicate a requirement of mutual authentication or the use of a session-key based ticket by setting the appropriate flag(s) in the ap-options field of the message. The Authenticator is encrypted in the session key and combined with the ticket to form the KRB_AP_REQ message which is then sent to the end server along with any additional application-specific information. See section A.9 for pseudocode. 3.2.3. Receipt of KRB_AP_REQ message Authentication is based on the server's current time of day (clocks must be loosely synchronized), the authenticator, and the ticket. Several errors are possible. If an error occurs, the server is expected to reply to the client with a KRB_ERROR message. This message may be encapsulated in the application protocol if its "raw" form is not acceptable to the protocol. The format of error messages is described in section 5.9.1. The algorithm for verifying authentication information is as follows. If the message type is not KRB_AP_REQ, the server returns the KRB_AP_ERR_MSG_TYPE error. If the key version indicated by the Ticket in the KRB_AP_REQ is not one the server can use (e.g., it indicates an old key, and the server no longer possesses a copy of the old key), the KRB_AP_ERR_BADKEYVER error is returned. If the USE- SESSION-KEY flag is set in the ap-options field, it indicates to the server that the ticket is encrypted in the session key from the server's ticket-granting ticket rather than its secret key (This is used for user-to-user authentication as described in [6]). Since it is possible for the server to be registered in multiple realms, with different keys in each, the srealm field in the unencrypted portion of the ticket in the KRB_AP_REQ is used to specify which secret key the server should use to decrypt that ticket. The KRB_AP_ERR_NOKEY
error code is returned if the server doesn't have the proper key to decipher the ticket. The ticket is decrypted using the version of the server's key specified by the ticket. If the decryption routines detect a modification of the ticket (each encryption system must provide safeguards to detect modified ciphertext; see section 6), the KRB_AP_ERR_BAD_INTEGRITY error is returned (chances are good that different keys were used to encrypt and decrypt). The authenticator is decrypted using the session key extracted from the decrypted ticket. If decryption shows it to have been modified, the KRB_AP_ERR_BAD_INTEGRITY error is returned. The name and realm of the client from the ticket are compared against the same fields in the authenticator. If they don't match, the KRB_AP_ERR_BADMATCH error is returned (they might not match, for example, if the wrong session key was used to encrypt the authenticator). The addresses in the ticket (if any) are then searched for an address matching the operating-system reported address of the client. If no match is found or the server insists on ticket addresses but none are present in the ticket, the KRB_AP_ERR_BADADDR error is returned. If the local (server) time and the client time in the authenticator differ by more than the allowable clock skew (e.g., 5 minutes), the KRB_AP_ERR_SKEW error is returned. If the server name, along with the client name, time and microsecond fields from the Authenticator match any recently-seen such tuples, the KRB_AP_ERR_REPEAT error is returned (Note that the rejection here is restricted to authenticators from the same principal to the same server. Other client principals communicating with the same server principal should not be have their authenticators rejected if the time and microsecond fields happen to match some other client's authenticator.). The server must remember any authenticator presented within the allowable clock skew, so that a replay attempt is guaranteed to fail. If a server loses track of any authenticator presented within the allowable clock skew, it must reject all requests until the clock skew interval has passed. This assures that any lost or re-played authenticators will fall outside the allowable clock skew and can no longer be successfully replayed (If this is not done, an attacker could conceivably record the ticket and authenticator sent over the network to a server, then disable the client's host, pose as the disabled host, and replay the ticket and authenticator to subvert the authentication.). If a sequence number is provided in the authenticator, the server saves it for later use in processing KRB_SAFE and/or KRB_PRIV messages. If a subkey is present, the server either saves it for later use or uses it to help generate its own choice for a subkey to be returned in a KRB_AP_REP message.
The server computes the age of the ticket: local (server) time minus the start time inside the Ticket. If the start time is later than the current time by more than the allowable clock skew or if the INVALID flag is set in the ticket, the KRB_AP_ERR_TKT_NYV error is returned. Otherwise, if the current time is later than end time by more than the allowable clock skew, the KRB_AP_ERR_TKT_EXPIRED error is returned. If all these checks succeed without an error, the server is assured that the client possesses the credentials of the principal named in the ticket and thus, the client has been authenticated to the server. See section A.10 for pseudocode. 3.2.4. Generation of a KRB_AP_REP message Typically, a client's request will include both the authentication information and its initial request in the same message, and the server need not explicitly reply to the KRB_AP_REQ. However, if mutual authentication (not only authenticating the client to the server, but also the server to the client) is being performed, the KRB_AP_REQ message will have MUTUAL-REQUIRED set in its ap-options field, and a KRB_AP_REP message is required in response. As with the error message, this message may be encapsulated in the application protocol if its "raw" form is not acceptable to the application's protocol. The timestamp and microsecond field used in the reply must be the client's timestamp and microsecond field (as provided in the authenticator). [Note: In the Kerberos version 4 protocol, the timestamp in the reply was the client's timestamp plus one. This is not necessary in version 5 because version 5 messages are formatted in such a way that it is not possible to create the reply by judicious message surgery (even in encrypted form) without knowledge of the appropriate encryption keys.] If a sequence number is to be included, it should be randomly chosen as described above for the authenticator. A subkey may be included if the server desires to negotiate a different subkey. The KRB_AP_REP message is encrypted in the session key extracted from the ticket. See section A.11 for pseudocode. 3.2.5. Receipt of KRB_AP_REP message If a KRB_AP_REP message is returned, the client uses the session key from the credentials obtained for the server (Note that for encrypting the KRB_AP_REP message, the sub-session key is not used, even if present in the Authenticator.) to decrypt the message, and verifies that the timestamp and microsecond fields match those in the Authenticator it sent to the server. If they match, then the client is assured that the server is genuine. The sequence number and subkey (if present) are retained for later use. See section A.12 for
pseudocode. 3.2.6. Using the encryption key After the KRB_AP_REQ/KRB_AP_REP exchange has occurred, the client and server share an encryption key which can be used by the application. The "true session key" to be used for KRB_PRIV, KRB_SAFE, or other application-specific uses may be chosen by the application based on the subkeys in the KRB_AP_REP message and the authenticator (Implementations of the protocol may wish to provide routines to choose subkeys based on session keys and random numbers and to orchestrate a negotiated key to be returned in the KRB_AP_REP message.). In some cases, the use of this session key will be implicit in the protocol; in others the method of use must be chosen from a several alternatives. We leave the protocol negotiations of how to use the key (e.g., selecting an encryption or checksum type) to the application programmer; the Kerberos protocol does not constrain the implementation options. With both the one-way and mutual authentication exchanges, the peers should take care not to send sensitive information to each other without proper assurances. In particular, applications that require privacy or integrity should use the KRB_AP_REP or KRB_ERROR responses from the server to client to assure both client and server of their peer's identity. If an application protocol requires privacy of its messages, it can use the KRB_PRIV message (section 3.5). The KRB_SAFE message (section 3.4) can be used to assure integrity. 3.3. The Ticket-Granting Service (TGS) Exchange Summary Message direction Message type Section 1. Client to Kerberos KRB_TGS_REQ 5.4.1 2. Kerberos to client KRB_TGS_REP or 5.4.2 KRB_ERROR 5.9.1 The TGS exchange between a client and the Kerberos Ticket-Granting Server is initiated by a client when it wishes to obtain authentication credentials for a given server (which might be registered in a remote realm), when it wishes to renew or validate an existing ticket, or when it wishes to obtain a proxy ticket. In the first case, the client must already have acquired a ticket for the Ticket-Granting Service using the AS exchange (the ticket-granting ticket is usually obtained when a client initially authenticates to the system, such as when a user logs in). The message format for the TGS exchange is almost identical to that for the AS exchange. The primary difference is that encryption and decryption in the TGS
exchange does not take place under the client's key. Instead, the session key from the ticket-granting ticket or renewable ticket, or sub-session key from an Authenticator is used. As is the case for all application servers, expired tickets are not accepted by the TGS, so once a renewable or ticket-granting ticket expires, the client must use a separate exchange to obtain valid tickets. The TGS exchange consists of two messages: A request (KRB_TGS_REQ) from the client to the Kerberos Ticket-Granting Server, and a reply (KRB_TGS_REP or KRB_ERROR). The KRB_TGS_REQ message includes information authenticating the client plus a request for credentials. The authentication information consists of the authentication header (KRB_AP_REQ) which includes the client's previously obtained ticket- granting, renewable, or invalid ticket. In the ticket-granting ticket and proxy cases, the request may include one or more of: a list of network addresses, a collection of typed authorization data to be sealed in the ticket for authorization use by the application server, or additional tickets (the use of which are described later). The TGS reply (KRB_TGS_REP) contains the requested credentials, encrypted in the session key from the ticket-granting ticket or renewable ticket, or if present, in the subsession key from the Authenticator (part of the authentication header). The KRB_ERROR message contains an error code and text explaining what went wrong. The KRB_ERROR message is not encrypted. The KRB_TGS_REP message contains information which can be used to detect replays, and to associate it with the message to which it replies. The KRB_ERROR message also contains information which can be used to associate it with the message to which it replies, but the lack of encryption in the KRB_ERROR message precludes the ability to detect replays or fabrications of such messages. 3.3.1. Generation of KRB_TGS_REQ message Before sending a request to the ticket-granting service, the client must determine in which realm the application server is registered [Note: This can be accomplished in several ways. It might be known beforehand (since the realm is part of the principal identifier), or it might be stored in a nameserver. Presently, however, this information is obtained from a configuration file. If the realm to be used is obtained from a nameserver, there is a danger of being spoofed if the nameservice providing the realm name is not authenticated. This might result in the use of a realm which has been compromised, and would result in an attacker's ability to compromise the authentication of the application server to the client.]. If the client does not already possess a ticket-granting ticket for the appropriate realm, then one must be obtained. This is first attempted by requesting a ticket-granting ticket for the destination realm from the local Kerberos server (using the
KRB_TGS_REQ message recursively). The Kerberos server may return a TGT for the desired realm in which case one can proceed. Alternatively, the Kerberos server may return a TGT for a realm which is "closer" to the desired realm (further along the standard hierarchical path), in which case this step must be repeated with a Kerberos server in the realm specified in the returned TGT. If neither are returned, then the request must be retried with a Kerberos server for a realm higher in the hierarchy. This request will itself require a ticket-granting ticket for the higher realm which must be obtained by recursively applying these directions. Once the client obtains a ticket-granting ticket for the appropriate realm, it determines which Kerberos servers serve that realm, and contacts one. The list might be obtained through a configuration file or network service; as long as the secret keys exchanged by realms are kept secret, only denial of service results from a false Kerberos server. As in the AS exchange, the client may specify a number of options in the KRB_TGS_REQ message. The client prepares the KRB_TGS_REQ message, providing an authentication header as an element of the padata field, and including the same fields as used in the KRB_AS_REQ message along with several optional fields: the enc-authorization- data field for application server use and additional tickets required by some options. In preparing the authentication header, the client can select a sub- session key under which the response from the Kerberos server will be encrypted (If the client selects a sub-session key, care must be taken to ensure the randomness of the selected subsession key. One approach would be to generate a random number and XOR it with the session key from the ticket-granting ticket.). If the sub-session key is not specified, the session key from the ticket-granting ticket will be used. If the enc-authorization-data is present, it must be encrypted in the sub-session key, if present, from the authenticator portion of the authentication header, or if not present in the session key from the ticket-granting ticket. Once prepared, the message is sent to a Kerberos server for the destination realm. See section A.5 for pseudocode. 3.3.2. Receipt of KRB_TGS_REQ message The KRB_TGS_REQ message is processed in a manner similar to the KRB_AS_REQ message, but there are many additional checks to be performed. First, the Kerberos server must determine which server the accompanying ticket is for and it must select the appropriate key to decrypt it. For a normal KRB_TGS_REQ message, it will be for the
ticket granting service, and the TGS's key will be used. If the TGT was issued by another realm, then the appropriate inter-realm key must be used. If the accompanying ticket is not a ticket granting ticket for the current realm, but is for an application server in the current realm, the RENEW, VALIDATE, or PROXY options are specified in the request, and the server for which a ticket is requested is the server named in the accompanying ticket, then the KDC will decrypt the ticket in the authentication header using the key of the server for which it was issued. If no ticket can be found in the padata field, the KDC_ERR_PADATA_TYPE_NOSUPP error is returned. Once the accompanying ticket has been decrypted, the user-supplied checksum in the Authenticator must be verified against the contents of the request, and the message rejected if the checksums do not match (with an error code of KRB_AP_ERR_MODIFIED) or if the checksum is not keyed or not collision-proof (with an error code of KRB_AP_ERR_INAPP_CKSUM). If the checksum type is not supported, the KDC_ERR_SUMTYPE_NOSUPP error is returned. If the authorization-data are present, they are decrypted using the sub-session key from the Authenticator. If any of the decryptions indicate failed integrity checks, the KRB_AP_ERR_BAD_INTEGRITY error is returned. 3.3.3. Generation of KRB_TGS_REP message The KRB_TGS_REP message shares its format with the KRB_AS_REP (KRB_KDC_REP), but with its type field set to KRB_TGS_REP. The detailed specification is in section 5.4.2. The response will include a ticket for the requested server. The Kerberos database is queried to retrieve the record for the requested server (including the key with which the ticket will be encrypted). If the request is for a ticket granting ticket for a remote realm, and if no key is shared with the requested realm, then the Kerberos server will select the realm "closest" to the requested realm with which it does share a key, and use that realm instead. This is the only case where the response from the KDC will be for a different server than that requested by the client. By default, the address field, the client's name and realm, the list of transited realms, the time of initial authentication, the expiration time, and the authorization data of the newly-issued ticket will be copied from the ticket-granting ticket (TGT) or renewable ticket. If the transited field needs to be updated, but the transited type is not supported, the KDC_ERR_TRTYPE_NOSUPP error is returned.
If the request specifies an endtime, then the endtime of the new ticket is set to the minimum of (a) that request, (b) the endtime from the TGT, and (c) the starttime of the TGT plus the minimum of the maximum life for the application server and the maximum life for the local realm (the maximum life for the requesting principal was already applied when the TGT was issued). If the new ticket is to be a renewal, then the endtime above is replaced by the minimum of (a) the value of the renew_till field of the ticket and (b) the starttime for the new ticket plus the life (endtimestarttime) of the old ticket. If the FORWARDED option has been requested, then the resulting ticket will contain the addresses specified by the client. This option will only be honored if the FORWARDABLE flag is set in the TGT. The PROXY option is similar; the resulting ticket will contain the addresses specified by the client. It will be honored only if the PROXIABLE flag in the TGT is set. The PROXY option will not be honored on requests for additional ticket-granting tickets. If the requested start time is absent or indicates a time in the past, then the start time of the ticket is set to the authentication server's current time. If it indicates a time in the future, but the POSTDATED option has not been specified or the MAY-POSTDATE flag is not set in the TGT, then the error KDC_ERR_CANNOT_POSTDATE is returned. Otherwise, if the ticket-granting ticket has the MAYPOSTDATE flag set, then the resulting ticket will be postdated and the requested starttime is checked against the policy of the local realm. If acceptable, the ticket's start time is set as requested, and the INVALID flag is set. The postdated ticket must be validated before use by presenting it to the KDC after the starttime has been reached. However, in no case may the starttime, endtime, or renew- till time of a newly-issued postdated ticket extend beyond the renew-till time of the ticket-granting ticket. If the ENC-TKT-IN-SKEY option has been specified and an additional ticket has been included in the request, the KDC will decrypt the additional ticket using the key for the server to which the additional ticket was issued and verify that it is a ticket-granting ticket. If the name of the requested server is missing from the request, the name of the client in the additional ticket will be used. Otherwise the name of the requested server will be compared to the name of the client in the additional ticket and if different, the request will be rejected. If the request succeeds, the session key from the additional ticket will be used to encrypt the new ticket that is issued instead of using the key of the server for which the new ticket will be used (This allows easy implementation of user-to- user authentication [6], which uses ticket-granting ticket session keys in lieu of secret server keys in situations where such secret
keys could be easily compromised.). If the name of the server in the ticket that is presented to the KDC as part of the authentication header is not that of the ticket- granting server itself, and the server is registered in the realm of the KDC, If the RENEW option is requested, then the KDC will verify that the RENEWABLE flag is set in the ticket and that the renew_till time is still in the future. If the VALIDATE option is rqeuested, the KDC will check that the starttime has passed and the INVALID flag is set. If the PROXY option is requested, then the KDC will check that the PROXIABLE flag is set in the ticket. If the tests succeed, the KDC will issue the appropriate new ticket. Whenever a request is made to the ticket-granting server, the presented ticket(s) is(are) checked against a hot-list of tickets which have been canceled. This hot-list might be implemented by storing a range of issue dates for "suspect tickets"; if a presented ticket had an authtime in that range, it would be rejected. In this way, a stolen ticket-granting ticket or renewable ticket cannot be used to gain additional tickets (renewals or otherwise) once the theft has been reported. Any normal ticket obtained before it was reported stolen will still be valid (because they require no interaction with the KDC), but only until their normal expiration time. The ciphertext part of the response in the KRB_TGS_REP message is encrypted in the sub-session key from the Authenticator, if present, or the session key key from the ticket-granting ticket. It is not encrypted using the client's secret key. Furthermore, the client's key's expiration date and the key version number fields are left out since these values are stored along with the client's database record, and that record is not needed to satisfy a request based on a ticket-granting ticket. See section A.6 for pseudocode. 3.3.3.1. Encoding the transited field If the identity of the server in the TGT that is presented to the KDC as part of the authentication header is that of the ticket-granting service, but the TGT was issued from another realm, the KDC will look up the inter-realm key shared with that realm and use that key to decrypt the ticket. If the ticket is valid, then the KDC will honor the request, subject to the constraints outlined above in the section describing the AS exchange. The realm part of the client's identity will be taken from the ticket-granting ticket. The name of the realm that issued the ticket-granting ticket will be added to the transited field of the ticket to be issued. This is accomplished by reading the transited field from the ticket-granting ticket (which is treated as an unordered set of realm names), adding the new realm to the set,
then constructing and writing out its encoded (shorthand) form (this
may involve a rearrangement of the existing encoding).
Note that the ticket-granting service does not add the name of its
own realm. Instead, its responsibility is to add the name of the
previous realm. This prevents a malicious Kerberos server from
intentionally leaving out its own name (it could, however, omit other
realms' names).
The names of neither the local realm nor the principal's realm are to
be included in the transited field. They appear elsewhere in the
ticket and both are known to have taken part in authenticating the
principal. Since the endpoints are not included, both local and
single-hop inter-realm authentication result in a transited field
that is empty.
Because the name of each realm transited is added to this field,
it might potentially be very long. To decrease the length of this
field, its contents are encoded. The initially supported encoding is
optimized for the normal case of inter-realm communication: a
hierarchical arrangement of realms using either domain or X.500 style
realm names. This encoding (called DOMAIN-X500-COMPRESS) is now
described.
Realm names in the transited field are separated by a ",". The ",",
"\", trailing "."s, and leading spaces (" ") are special characters,
and if they are part of a realm name, they must be quoted in the
transited field by preceding them with a "\".
A realm name ending with a "." is interpreted as being prepended to
the previous realm. For example, we can encode traversal of EDU,
MIT.EDU, ATHENA.MIT.EDU, WASHINGTON.EDU, and CS.WASHINGTON.EDU as:
"EDU,MIT.,ATHENA.,WASHINGTON.EDU,CS.".
Note that if ATHENA.MIT.EDU, or CS.WASHINGTON.EDU were endpoints,
that they would not be included in this field, and we would have:
"EDU,MIT.,WASHINGTON.EDU"
A realm name beginning with a "/" is interpreted as being appended to
the previous realm (For the purpose of appending, the realm preceding
the first listed realm is considered to be the null realm ("")). If
it is to stand by itself, then it should be preceded by a space ("
"). For example, we can encode traversal of /COM/HP/APOLLO, /COM/HP,
/COM, and /COM/DEC as:
"/COM,/HP,/APOLLO, /COM/DEC".
Like the example above, if /COM/HP/APOLLO and /COM/DEC are endpoints,
they they would not be included in this field, and we would have:
"/COM,/HP"
A null subfield preceding or following a "," indicates that all
realms between the previous realm and the next realm have been
traversed (For the purpose of interpreting null subfields, the
client's realm is considered to precede those in the transited field,
and the server's realm is considered to follow them.). Thus, ","
means that all realms along the path between the client and the
server have been traversed. ",EDU, /COM," means that that all realms
from the client's realm up to EDU (in a domain style hierarchy) have
been traversed, and that everything from /COM down to the server's
realm in an X.500 style has also been traversed. This could occur if
the EDU realm in one hierarchy shares an inter-realm key directly
with the /COM realm in another hierarchy.
3.3.4. Receipt of KRB_TGS_REP message
When the KRB_TGS_REP is received by the client, it is processed in
the same manner as the KRB_AS_REP processing described above. The
primary difference is that the ciphertext part of the response must
be decrypted using the session key from the ticket-granting ticket
rather than the client's secret key. See section A.7 for pseudocode.
3.4. The KRB_SAFE Exchange
The KRB_SAFE message may be used by clients requiring the ability to
detect modifications of messages they exchange. It achieves this by
including a keyed collisionproof checksum of the user data and some
control information. The checksum is keyed with an encryption key
(usually the last key negotiated via subkeys, or the session key if
no negotiation has occured).
3.4.1. Generation of a KRB_SAFE message
When an application wishes to send a KRB_SAFE message, it collects
its data and the appropriate control information and computes a
checksum over them. The checksum algorithm should be some sort of
keyed one-way hash function (such as the RSA-MD5-DES checksum
algorithm specified in section 6.4.5, or the DES MAC), generated
using the sub-session key if present, or the session key. Different
algorithms may be selected by changing the checksum type in the
message. Unkeyed or non-collision-proof checksums are not suitable
for this use.
The control information for the KRB_SAFE message includes both a
timestamp and a sequence number. The designer of an application using the KRB_SAFE message must choose at least one of the two mechanisms. This choice should be based on the needs of the application protocol. Sequence numbers are useful when all messages sent will be received by one's peer. Connection state is presently required to maintain the session key, so maintaining the next sequence number should not present an additional problem. If the application protocol is expected to tolerate lost messages without them being resent, the use of the timestamp is the appropriate replay detection mechanism. Using timestamps is also the appropriate mechanism for multi-cast protocols where all of one's peers share a common sub-session key, but some messages will be sent to a subset of one's peers. After computing the checksum, the client then transmits the information and checksum to the recipient in the message format specified in section 5.6.1. 3.4.2. Receipt of KRB_SAFE message When an application receives a KRB_SAFE message, it verifies it as follows. If any error occurs, an error code is reported for use by the application. The message is first checked by verifying that the protocol version and type fields match the current version and KRB_SAFE, respectively. A mismatch generates a KRB_AP_ERR_BADVERSION or KRB_AP_ERR_MSG_TYPE error. The application verifies that the checksum used is a collisionproof keyed checksum, and if it is not, a KRB_AP_ERR_INAPP_CKSUM error is generated. The recipient verifies that the operating system's report of the sender's address matches the sender's address in the message, and (if a recipient address is specified or the recipient requires an address) that one of the recipient's addresses appears as the recipient's address in the message. A failed match for either case generates a KRB_AP_ERR_BADADDR error. Then the timestamp and usec and/or the sequence number fields are checked. If timestamp and usec are expected and not present, or they are present but not current, the KRB_AP_ERR_SKEW error is generated. If the server name, along with the client name, time and microsecond fields from the Authenticator match any recently-seen such tuples, the KRB_AP_ERR_REPEAT error is generated. If an incorrect sequence number is included, or a sequence number is expected but not present, the KRB_AP_ERR_BADORDER error is generated. If neither a timestamp and usec or a sequence number is present, a KRB_AP_ERR_MODIFIED error is generated.
Finally, the checksum is computed over the data and control information, and if it doesn't match the received checksum, a KRB_AP_ERR_MODIFIED error is generated. If all the checks succeed, the application is assured that the message was generated by its peer and was not modified in transit. 3.5. The KRB_PRIV Exchange The KRB_PRIV message may be used by clients requiring confidentiality and the ability to detect modifications of exchanged messages. It achieves this by encrypting the messages and adding control information. 3.5.1. Generation of a KRB_PRIV message When an application wishes to send a KRB_PRIV message, it collects its data and the appropriate control information (specified in section 5.7.1) and encrypts them under an encryption key (usually the last key negotiated via subkeys, or the session key if no negotiation has occured). As part of the control information, the client must choose to use either a timestamp or a sequence number (or both); see the discussion in section 3.4.1 for guidelines on which to use. After the user data and control information are encrypted, the client transmits the ciphertext and some "envelope" information to the recipient. 3.5.2. Receipt of KRB_PRIV message When an application receives a KRB_PRIV message, it verifies it as follows. If any error occurs, an error code is reported for use by the application. The message is first checked by verifying that the protocol version and type fields match the current version and KRB_PRIV, respectively. A mismatch generates a KRB_AP_ERR_BADVERSION or KRB_AP_ERR_MSG_TYPE error. The application then decrypts the ciphertext and processes the resultant plaintext. If decryption shows the data to have been modified, a KRB_AP_ERR_BAD_INTEGRITY error is generated. The recipient verifies that the operating system's report of the sender's address matches the sender's address in the message, and (if a recipient address is specified or the recipient requires an address) that one of the recipient's addresses appears as the recipient's address in the message. A failed match for either case generates a KRB_AP_ERR_BADADDR error. Then the timestamp and usec and/or the sequence number fields are checked. If timestamp and usec are expected and not present, or they are present but not current, the KRB_AP_ERR_SKEW error is generated. If the server name, along with
the client name, time and microsecond fields from the Authenticator match any recently-seen such tuples, the KRB_AP_ERR_REPEAT error is generated. If an incorrect sequence number is included, or a sequence number is expected but not present, the KRB_AP_ERR_BADORDER error is generated. If neither a timestamp and usec or a sequence number is present, a KRB_AP_ERR_MODIFIED error is generated. If all the checks succeed, the application can assume the message was generated by its peer, and was securely transmitted (without intruders able to see the unencrypted contents). 3.6. The KRB_CRED Exchange The KRB_CRED message may be used by clients requiring the ability to send Kerberos credentials from one host to another. It achieves this by sending the tickets together with encrypted data containing the session keys and other information associated with the tickets. 3.6.1. Generation of a KRB_CRED message When an application wishes to send a KRB_CRED message it first (using the KRB_TGS exchange) obtains credentials to be sent to the remote host. It then constructs a KRB_CRED message using the ticket or tickets so obtained, placing the session key needed to use each ticket in the key field of the corresponding KrbCredInfo sequence of the encrypted part of the the KRB_CRED message. Other information associated with each ticket and obtained during the KRB_TGS exchange is also placed in the corresponding KrbCredInfo sequence in the encrypted part of the KRB_CRED message. The current time and, if specifically required by the application the nonce, s- address, and raddress fields, are placed in the encrypted part of the KRB_CRED message which is then encrypted under an encryption key previosuly exchanged in the KRB_AP exchange (usually the last key negotiated via subkeys, or the session key if no negotiation has occured). 3.6.2. Receipt of KRB_CRED message When an application receives a KRB_CRED message, it verifies it. If any error occurs, an error code is reported for use by the application. The message is verified by checking that the protocol version and type fields match the current version and KRB_CRED, respectively. A mismatch generates a KRB_AP_ERR_BADVERSION or KRB_AP_ERR_MSG_TYPE error. The application then decrypts the ciphertext and processes the resultant plaintext. If decryption shows the data to have been modified, a KRB_AP_ERR_BAD_INTEGRITY error is generated.
If present or required, the recipient verifies that the operating system's report of the sender's address matches the sender's address in the message, and that one of the recipient's addresses appears as the recipient's address in the message. A failed match for either case generates a KRB_AP_ERR_BADADDR error. The timestamp and usec fields (and the nonce field if required) are checked next. If the timestamp and usec are not present, or they are present but not current, the KRB_AP_ERR_SKEW error is generated. If all the checks succeed, the application stores each of the new tickets in its ticket cache together with the session key and other information in the corresponding KrbCredInfo sequence from the encrypted part of the KRB_CRED message. 4. The Kerberos Database The Kerberos server must have access to a database containing the principal identifiers and secret keys of principals to be authenticated (The implementation of the Kerberos server need not combine the database and the server on the same machine; it is feasible to store the principal database in, say, a network name service, as long as the entries stored therein are protected from disclosure to and modification by unauthorized parties. However, we recommend against such strategies, as they can make system management and threat analysis quite complex.). 4.1. Database contents A database entry should contain at least the following fields: Field Value name Principal's identifier key Principal's secret key p_kvno Principal's key version max_life Maximum lifetime for Tickets max_renewable_life Maximum total lifetime for renewable Tickets The name field is an encoding of the principal's identifier. The key field contains an encryption key. This key is the principal's secret key. (The key can be encrypted before storage under a Kerberos "master key" to protect it in case the database is compromised but the master key is not. In that case, an extra field must be added to indicate the master key version used, see below.) The p_kvno field is the key version number of the principal's secret key. The max_life field contains the maximum allowable lifetime (endtime - starttime) for any Ticket issued for this principal. The max_renewable_life
field contains the maximum allowable total lifetime for any renewable Ticket issued for this principal. (See section 3.1 for a description of how these lifetimes are used in determining the lifetime of a given Ticket.) A server may provide KDC service to several realms, as long as the database representation provides a mechanism to distinguish between principal records with identifiers which differ only in the realm name. When an application server's key changes, if the change is routine (i.e., not the result of disclosure of the old key), the old key should be retained by the server until all tickets that had been issued using that key have expired. Because of this, it is possible for several keys to be active for a single principal. Ciphertext encrypted in a principal's key is always tagged with the version of the key that was used for encryption, to help the recipient find the proper key for decryption. When more than one key is active for a particular principal, the principal will have more than one record in the Kerberos database. The keys and key version numbers will differ between the records (the rest of the fields may or may not be the same). Whenever Kerberos issues a ticket, or responds to a request for initial authentication, the most recent key (known by the Kerberos server) will be used for encryption. This is the key with the highest key version number. 4.2. Additional fields Project Athena's KDC implementation uses additional fields in its database: Field Value K_kvno Kerberos' key version expiration Expiration date for entry attributes Bit field of attributes mod_date Timestamp of last modification mod_name Modifying principal's identifier The K_kvno field indicates the key version of the Kerberos master key under which the principal's secret key is encrypted. After an entry's expiration date has passed, the KDC will return an error to any client attempting to gain tickets as or for the principal. (A database may want to maintain two expiration dates: one for the principal, and one for the principal's current key. This allows password aging to work independently of the principal's
expiration date. However, due to the limited space in the responses, the KDC must combine the key expiration and principal expiration date into a single value called "key_exp", which is used as a hint to the user to take administrative action.) The attributes field is a bitfield used to govern the operations involving the principal. This field might be useful in conjunction with user registration procedures, for site-specific policy implementations (Project Athena currently uses it for their user registration process controlled by the system-wide database service, Moira [7]), or to identify the "string to key" conversion algorithm used for a principal's key. (See the discussion of the padata field in section 5.4.2 for details on why this can be useful.) Other bits are used to indicate that certain ticket options should not be allowed in tickets encrypted under a principal's key (one bit each): Disallow issuing postdated tickets, disallow issuing forwardable tickets, disallow issuing tickets based on TGT authentication, disallow issuing renewable tickets, disallow issuing proxiable tickets, and disallow issuing tickets for which the principal is the server. The mod_date field contains the time of last modification of the entry, and the mod_name field contains the name of the principal which last modified the entry. 4.3. Frequently Changing Fields Some KDC implementations may wish to maintain the last time that a request was made by a particular principal. Information that might be maintained includes the time of the last request, the time of the last request for a ticket-granting ticket, the time of the last use of a ticket-granting ticket, or other times. This information can then be returned to the user in the last-req field (see section 5.2). Other frequently changing information that can be maintained is the latest expiration time for any tickets that have been issued using each key. This field would be used to indicate how long old keys must remain valid to allow the continued use of outstanding tickets. 4.4. Site Constants The KDC implementation should have the following configurable constants or options, to allow an administrator to make and enforce policy decisions: + The minimum supported lifetime (used to determine whether the KDC_ERR_NEVER_VALID error should be returned). This constant should reflect reasonable expectations of round-trip time to the
KDC, encryption/decryption time, and processing time by the client
and target server, and it should allow for a minimum "useful"
lifetime.
+ The maximum allowable total (renewable) lifetime of a ticket
(renew_till - starttime).
+ The maximum allowable lifetime of a ticket (endtime - starttime).
+ Whether to allow the issue of tickets with empty address fields
(including the ability to specify that such tickets may only be
issued if the request specifies some authorization_data).
+ Whether proxiable, forwardable, renewable or post-datable tickets
are to be issued.
5. Message Specifications
The following sections describe the exact contents and encoding of
protocol messages and objects. The ASN.1 base definitions are
presented in the first subsection. The remaining subsections specify
the protocol objects (tickets and authenticators) and messages.
Specification of encryption and checksum techniques, and the fields
related to them, appear in section 6.
5.1. ASN.1 Distinguished Encoding Representation
All uses of ASN.1 in Kerberos shall use the Distinguished Encoding
Representation of the data elements as described in the X.509
specification, section 8.7 [8].
5.2. ASN.1 Base Definitions
The following ASN.1 base definitions are used in the rest of this
section. Note that since the underscore character (_) is not
permitted in ASN.1 names, the hyphen (-) is used in its place for the
purposes of ASN.1 names.
Realm ::= GeneralString
PrincipalName ::= SEQUENCE {
name-type[0] INTEGER,
name-string[1] SEQUENCE OF GeneralString
}
Kerberos realms are encoded as GeneralStrings. Realms shall not
contain a character with the code 0 (the ASCII NUL). Most realms
will usually consist of several components separated by periods (.),
in the style of Internet Domain Names, or separated by slashes (/) in
the style of X.500 names. Acceptable forms for realm names are
specified in section 7. A PrincipalName is a typed sequence of
components consisting of the following sub-fields:
name-type This field specifies the type of name that follows.
Pre-defined values for this field are
specified in section 7.2. The name-type should be
treated as a hint. Ignoring the name type, no two
names can be the same (i.e., at least one of the
components, or the realm, must be different).
This constraint may be eliminated in the future.
name-string This field encodes a sequence of components that
form a name, each component encoded as a General
String. Taken together, a PrincipalName and a Realm
form a principal identifier. Most PrincipalNames
will have only a few components (typically one or two).
KerberosTime ::= GeneralizedTime
-- Specifying UTC time zone (Z)
The timestamps used in Kerberos are encoded as GeneralizedTimes. An
encoding shall specify the UTC time zone (Z) and shall not include
any fractional portions of the seconds. It further shall not include
any separators. Example: The only valid format for UTC time 6
minutes, 27 seconds after 9 pm on 6 November 1985 is 19851106210627Z.
HostAddress ::= SEQUENCE {
addr-type[0] INTEGER,
address[1] OCTET STRING
}
HostAddresses ::= SEQUENCE OF SEQUENCE {
addr-type[0] INTEGER,
address[1] OCTET STRING
}
The host adddress encodings consists of two fields:
addr-type This field specifies the type of address that
follows. Pre-defined values for this field are
specified in section 8.1.
address This field encodes a single address of type addr-type.
The two forms differ slightly. HostAddress contains exactly one
address; HostAddresses contains a sequence of possibly many
addresses.
AuthorizationData ::= SEQUENCE OF SEQUENCE {
ad-type[0] INTEGER,
ad-data[1] OCTET STRING
}
ad-data This field contains authorization data to be
interpreted according to the value of the
corresponding ad-type field.
ad-type This field specifies the format for the ad-data
subfield. All negative values are reserved for
local use. Non-negative values are reserved for
registered use.
APOptions ::= BIT STRING {
reserved(0),
use-session-key(1),
mutual-required(2)
}
TicketFlags ::= BIT STRING {
reserved(0),
forwardable(1),
forwarded(2),
proxiable(3),
proxy(4),
may-postdate(5),
postdated(6),
invalid(7),
renewable(8),
initial(9),
pre-authent(10),
hw-authent(11)
}
KDCOptions ::= BIT STRING {
reserved(0),
forwardable(1),
forwarded(2),
proxiable(3),
proxy(4),
allow-postdate(5),
postdated(6),
unused7(7),
renewable(8),
unused9(9),
unused10(10),
unused11(11),
renewable-ok(27),
enc-tkt-in-skey(28),
renew(30),
validate(31)
}
LastReq ::= SEQUENCE OF SEQUENCE {
lr-type[0] INTEGER,
lr-value[1] KerberosTime
}
lr-type This field indicates how the following lr-value
field is to be interpreted. Negative values indicate
that the information pertains only to the
responding server. Non-negative values pertain to
all servers for the realm.
If the lr-type field is zero (0), then no information
is conveyed by the lr-value subfield. If the
absolute value of the lr-type field is one (1),
then the lr-value subfield is the time of last
initial request for a TGT. If it is two (2), then
the lr-value subfield is the time of last initial
request. If it is three (3), then the lr-value
subfield is the time of issue for the newest
ticket-granting ticket used. If it is four (4),
then the lr-value subfield is the time of the last
renewal. If it is five (5), then the lr-value
subfield is the time of last request (of any
type).
lr-value This field contains the time of the last request.
The time must be interpreted according to the contents
of the accompanying lr-type subfield.
See section 6 for the definitions of Checksum, ChecksumType,
EncryptedData, EncryptionKey, EncryptionType, and KeyType.
5.3. Tickets and Authenticators This section describes the format and encryption parameters for tickets and authenticators. When a ticket or authenticator is included in a protocol message it is treated as an opaque object. 5.3.1. Tickets A ticket is a record that helps a client authenticate to a service. A Ticket contains the following information: Ticket ::= [APPLICATION 1] SEQUENCE { tkt-vno[0] INTEGER, realm[1] Realm, sname[2] PrincipalName, enc-part[3] EncryptedData } -- Encrypted part of ticket EncTicketPart ::= [APPLICATION 3] SEQUENCE { flags[0] TicketFlags, key[1] EncryptionKey, crealm[2] Realm, cname[3] PrincipalName, transited[4] TransitedEncoding, authtime[5] KerberosTime, starttime[6] KerberosTime OPTIONAL, endtime[7] KerberosTime, renew-till[8] KerberosTime OPTIONAL, caddr[9] HostAddresses OPTIONAL, authorization-data[10] AuthorizationData OPTIONAL } -- encoded Transited field TransitedEncoding ::= SEQUENCE { tr-type[0] INTEGER, -- must be registered contents[1] OCTET STRING } The encoding of EncTicketPart is encrypted in the key shared by Kerberos and the end server (the server's secret key). See section 6 for the format of the ciphertext. tkt-vno This field specifies the version number for the ticket format. This document describes version number 5. realm This field specifies the realm that issued a ticket. It also serves to identify the realm part of the server's principal identifier. Since a Kerberos server can only issue tickets for servers within its realm, the two will
always be identical.
sname This field specifies the name part of the server's
identity.
enc-part This field holds the encrypted encoding of the
EncTicketPart sequence.
flags This field indicates which of various options were used or
requested when the ticket was issued. It is a bit-field,
where the selected options are indicated by the bit being
set (1), and the unselected options and reserved fields
being reset (0). Bit 0 is the most significant bit. The
encoding of the bits is specified in section 5.2. The
flags are described in more detail above in section 2. The
meanings of the flags are:
Bit(s) Name Description
0 RESERVED Reserved for future expansion of this
field.
1 FORWARDABLE The FORWARDABLE flag is normally only
interpreted by the TGS, and can be
ignored by end servers. When set,
this flag tells the ticket-granting
server that it is OK to issue a new
ticket- granting ticket with a
different network address based on
the presented ticket.
2 FORWARDED When set, this flag indicates that
the ticket has either been forwarded
or was issued based on authentication
involving a forwarded ticket-granting
ticket.
3 PROXIABLE The PROXIABLE flag is normally only
interpreted by the TGS, and can be
ignored by end servers. The PROXIABLE
flag has an interpretation identical
to that of the FORWARDABLE flag,
except that the PROXIABLE flag tells
the ticket-granting server that only
non- ticket-granting tickets may be
issued with different network
addresses.
4 PROXY When set, this flag indicates that a
ticket is a proxy.
5 MAY-POSTDATE The MAY-POSTDATE flag is normally
only interpreted by the TGS, and can
be ignored by end servers. This flag
tells the ticket-granting server that
a post- dated ticket may be issued
based on this ticket-granting ticket.
6 POSTDATED This flag indicates that this ticket
has been postdated. The end-service
can check the authtime field to see
when the original authentication
occurred.
7 INVALID This flag indicates that a ticket is
invalid, and it must be validated by
the KDC before use. Application
servers must reject tickets which
have this flag set.
8 RENEWABLE The RENEWABLE flag is normally only
interpreted by the TGS, and can
usually be ignored by end servers
(some particularly careful servers
may wish to disallow renewable
tickets). A renewable ticket can be
used to obtain a replacement ticket
that expires at a later date.
9 INITIAL This flag indicates that this ticket
was issued using the AS protocol, and
not issued based on a ticket-granting
ticket.
10 PRE-AUTHENT This flag indicates that during
initial authentication, the client
was authenticated by the KDC before a
ticket was issued. The strength of
the preauthentication method is not
indicated, but is acceptable to the
KDC.
11 HW-AUTHENT This flag indicates that the protocol
employed for initial authentication
required the use of hardware expected
to be possessed solely by the named
client. The hardware authentication
method is selected by the KDC and the
strength of the method is not
indicated.
12-31 RESERVED Reserved for future use.
key This field exists in the ticket and the KDC response and is
used to pass the session key from Kerberos to the
application server and the client. The field's encoding is
described in section 6.2.
crealm This field contains the name of the realm in which the
client is registered and in which initial authentication
took place.
cname This field contains the name part of the client's principal
identifier.
transited This field lists the names of the Kerberos realms that took
part in authenticating the user to whom this ticket was
issued. It does not specify the order in which the realms
were transited. See section 3.3.3.1 for details on how
this field encodes the traversed realms.
authtime This field indicates the time of initial authentication for
the named principal. It is the time of issue for the
original ticket on which this ticket is based. It is
included in the ticket to provide additional information to
the end service, and to provide the necessary information
for implementation of a `hot list' service at the KDC. An
end service that is particularly paranoid could refuse to
accept tickets for which the initial authentication
occurred "too far" in the past.
This field is also returned as part of the response from
the KDC. When returned as part of the response to initial
authentication (KRB_AS_REP), this is the current time on
the Kerberos server (It is NOT recommended that this time
value be used to adjust the workstation's clock since the
workstation cannot reliably determine that such a
KRB_AS_REP actually came from the proper KDC in a timely
manner.).
starttime This field in the ticket specifies the time after which the
ticket is valid. Together with endtime, this field
specifies the life of the ticket. If it is absent from
the ticket, its value should be treated as that of the
authtime field.
endtime This field contains the time after which the ticket will
not be honored (its expiration time). Note that individual
services may place their own limits on the life of a ticket
and may reject tickets which have not yet expired. As
such, this is really an upper bound on the expiration time
for the ticket.
renew-till This field is only present in tickets that have the
RENEWABLE flag set in the flags field. It indicates the
maximum endtime that may be included in a renewal. It can
be thought of as the absolute expiration time for the
ticket, including all renewals.
caddr This field in a ticket contains zero (if omitted) or more
(if present) host addresses. These are the addresses from
which the ticket can be used. If there are no addresses,
the ticket can be used from any location. The decision
by the KDC to issue or by the end server to accept zero-
address tickets is a policy decision and is left to the
Kerberos and end-service administrators; they may refuse to
issue or accept such tickets. The suggested and default
policy, however, is that such tickets will only be issued
or accepted when additional information that can be used to
restrict the use of the ticket is included in the
authorization_data field. Such a ticket is a capability.
Network addresses are included in the ticket to make it
harder for an attacker to use stolen credentials. Because
the session key is not sent over the network in cleartext,
credentials can't be stolen simply by listening to the
network; an attacker has to gain access to the session key
(perhaps through operating system security breaches or a
careless user's unattended session) to make use of stolen
tickets.
It is important to note that the network address from which
a connection is received cannot be reliably determined.
Even if it could be, an attacker who has compromised the
client's workstation could use the credentials from there.
Including the network addresses only makes it more
difficult, not impossible, for an attacker to walk off with
stolen credentials and then use them from a "safe"
location.
authorization-data The authorization-data field is used to pass
authorization data from the principal on whose behalf a
ticket was issued to the application service. If no
authorization data is included, this field will be left
out. The data in this field are specific to the end
service. It is expected that the field will contain the
names of service specific objects, and the rights to those
objects. The format for this field is described in section
5.2. Although Kerberos is not concerned with the format of
the contents of the subfields, it does carry type
information (ad-type).
By using the authorization_data field, a principal is able
to issue a proxy that is valid for a specific purpose. For
example, a client wishing to print a file can obtain a file
server proxy to be passed to the print server. By
specifying the name of the file in the authorization_data
field, the file server knows that the print server can only
use the client's rights when accessing the particular file
to be printed.
It is interesting to note that if one specifies the
authorization-data field of a proxy and leaves the host
addresses blank, the resulting ticket and session key can
be treated as a capability. See [9] for some suggested
uses of this field.
The authorization-data field is optional and does not have
to be included in a ticket.
5.3.2. Authenticators
An authenticator is a record sent with a ticket to a server to
certify the client's knowledge of the encryption key in the ticket,
to help the server detect replays, and to help choose a "true session
key" to use with the particular session. The encoding is encrypted
in the ticket's session key shared by the client and the server:
-- Unencrypted authenticator
Authenticator ::= [APPLICATION 2] SEQUENCE {
authenticator-vno[0] INTEGER,
crealm[1] Realm,
cname[2] PrincipalName,
cksum[3] Checksum OPTIONAL,
cusec[4] INTEGER,
ctime[5] KerberosTime,
subkey[6] EncryptionKey OPTIONAL,
seq-number[7] INTEGER OPTIONAL,
authorization-data[8] AuthorizationData OPTIONAL
}
authenticator-vno This field specifies the version number for the
format of the authenticator. This document specifies
version 5.
crealm and cname These fields are the same as those described for the
ticket in section 5.3.1.
cksum This field contains a checksum of the the application data
that accompanies the KRB_AP_REQ.
cusec This field contains the microsecond part of the client's
timestamp. Its value (before encryption) ranges from 0 to
999999. It often appears along with ctime. The two fields
are used together to specify a reasonably accurate
timestamp.
ctime This field contains the current time on the client's host.
subkey This field contains the client's choice for an encryption
key which is to be used to protect this specific
application session. Unless an application specifies
otherwise, if this field is left out the session key from
the ticket will be used.
seq-number This optional field includes the initial sequence number
to be used by the KRB_PRIV or KRB_SAFE messages when
sequence numbers are used to detect replays (It may also be
used by application specific messages). When included in
the authenticator this field specifies the initial sequence
number for messages from the client to the server. When
included in the AP-REP message, the initial sequence number
is that for messages from the server to the client. When
used in KRB_PRIV or KRB_SAFE messages, it is incremented by
one after each message is sent.
For sequence numbers to adequately support the detection of
replays they should be non-repeating, even across
connection boundaries. The initial sequence number should
be random and uniformly distributed across the full space
of possible sequence numbers, so that it cannot be guessed
by an attacker and so that it and the successive sequence
numbers do not repeat other sequences.
authorization-data This field is the same as described for the ticket
in section 5.3.1. It is optional and will only appear when
additional restrictions are to be placed on the use of a
ticket, beyond those carried in the ticket itself.
(page 49 continued on part 3)
