Network Working Group B. Lloyd
Request for Comments: 1334 L&A
W. Simpson
Daydreamer
October 1992
PPP Authentication Protocols
Status of this Memo
This RFCspecifies an IAB standards track protocol for the Internet
community, and requests discussion and suggestions for improvements.
Please refer to the current edition of the "IAB Official Protocol
Standards" for the standardization state and status of this protocol.
Distribution of this memo is unlimited.
Abstract
The Point-to-Point Protocol (PPP) [1] provides a standard method of
encapsulating Network Layer protocol information over point-to-point
links. PPP also defines an extensible Link Control Protocol, which
allows negotiation of an Authentication Protocol for authenticating
its peer before allowing Network Layer protocols to transmit over the
link.
This document defines two protocols for Authentication: the PassWord
Authentication Protocol and the Challenge-Handshake Authentication
Protocol. This memo is the prodUCt of the Point-to-Point Protocol
Working Group of the Internet Engineering Task Force (IETF).
Comments on this memo should be submitted to the ietf-ppp@ucdavis.edu
mailing list.
Table of Contents
1. Introduction ............................................... 2
1.1 Specification Requirements ................................. 2
1.2 Terminology ................................................ 3
2. Password Authentication Protocol ............................ 3
2.1 Configuration Option Format ................................ 4
2.2 Packet Format .............................................. 5
2.2.1 Authenticate-Request ..................................... 5
2.2.2 Authenticate-Ack and Authenticate-Nak .................... 7
3. Challenge-Handshake Authentication Protocol.................. 8
3.1 Configuration Option Format ................................ 9
3.2 Packet Format .............................................. 10
3.2.1 Challenge and Response ................................... 11
3.2.2 Success and Failure ...................................... 13
SECURITY CONSIDERATIONS ........................................ 14
REFERENCES ..................................................... 15
ACKNOWLEDGEMENTS ............................................... 16
CHAIR'S ADDRESS ................................................ 16
AUTHOR'S ADDRESS ............................................... 16
1. Introduction
PPP has three main components:
1. A method for encapsulating datagrams over serial links.
2. A Link Control Protocol (LCP) for establishing, configuring,
and testing the data-link connection.
3. A family of Network Control Protocols (NCPs) for establishing
and configuring different network-layer protocols.
In order to establish communications over a point-to-point link, each
end of the PPP link must first send LCP packets to configure the data
link during Link Establishment phase. After the link has been
established, PPP provides for an optional Authentication phase before
proceeding to the Network-Layer Protocol phase.
By default, authentication is not mandatory. If authentication of
the link is desired, an implementation MUST specify the
Authentication-Protocol Configuration Option during Link
Establishment phase.
These authentication protocols are intended for use primarily by
hosts and routers that connect to a PPP network server via switched
circuits or dial-up lines, but might be applied to dedicated links as
well. The server can use the identification of the connecting host
or router in the selection of options for network layer negotiations.
This document defines the PPP authentication protocols. The Link
Establishment and Authentication phases, and the Authentication-
Protocol Configuration Option, are defined in The Point-to-Point
Protocol (PPP) [1].
1.1. Specification Requirements
In this document, several words are used to signify the requirements
of the specification. These words are often capitalized.
MUST
This word, or the adjective "required", means that the definition
is an absolute requirement of the specification.
MUST NOT
This phrase means that the definition is an absolute prohibition
of the specification.
SHOULD
This word, or the adjective "recommended", means that there may
exist valid reasons in particular circumstances to ignore this
item, but the full implications should be understood and carefully
weighed before choosing a different course.
MAY
This word, or the adjective "optional", means that this item is
one of an allowed set of alternatives. An implementation which
does not include this option MUST be prepared to interoperate with
another implementation which does include the option.
1.2. Terminology
This document frequently uses the following terms:
authenticator
The end of the link requiring the authentication. The
authenticator specifies the authentication protocol to be used in
the Configure-Request during Link Establishment phase.
peer
The other end of the point-to-point link; the end which is being
authenticated by the authenticator.
silently discard
This means the implementation discards the packet without further
processing. The implementation SHOULD provide the capability of
logging the error, including the contents of the silently
discarded packet, and SHOULD record the event in a statistics
counter.
2. Password Authentication Protocol
The Password Authentication Protocol (PAP) provides a simple method
for the peer to establish its identity using a 2-way handshake. This
is done only upon initial link establishment.
After the Link Establishment phase is complete, an Id/Password pair
is repeatedly sent by the peer to the authenticator until
authentication is acknowledged or the connection is terminated.
PAP is not a strong authentication method. Passwords are sent over
the circuit "in the clear", and there is no protection from playback
or repeated trial and error attacks. The peer is in control of the
frequency and timing of the attempts.
Any implementations which include a stronger authentication method
(such as CHAP, described below) MUST offer to negotiate that method
prior to PAP.
This authentication method is most appropriately used where a
plaintext password must be available to simulate a login at a remote
host. In such use, this method provides a similar level of security
to the usual user login at the remote host.
Implementation Note: It is possible to limit the eXPosure of the
plaintext password to transmission over the PPP link, and avoid
sending the plaintext password over the entire network. When the
remote host password is kept as a one-way transformed value, and
the algorithm for the transform function is implemented in the
local server, the plaintext password SHOULD be locally transformed
before comparison with the transformed password from the remote
host.
2.1. Configuration Option Format
A summary of the Authentication-Protocol Configuration Option format
to negotiate the Password Authentication Protocol is shown below.
The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Type Length Authentication-Protocol
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Type
3
Length
4
Authentication-Protocol
c023 (hex) for Password Authentication Protocol.
Data
There is no Data field.
2.2. Packet Format
Exactly one Password Authentication Protocol packet is encapsulated
in the Information field of a PPP Data Link Layer frame where the
protocol field indicates type hex c023 (Password Authentication
Protocol). A summary of the PAP packet format is shown below. The
fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code Identifier Length
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Data ...
+-+-+-+-+
Code
The Code field is one octet and identifies the type of PAP packet.
PAP Codes are assigned as follows:
1 Authenticate-Request
2 Authenticate-Ack
3 Authenticate-Nak
Identifier
The Identifier field is one octet and aids in matching requests
and replies.
Length
The Length field is two octets and indicates the length of the PAP
packet including the Code, Identifier, Length and Data fields.
Octets outside the range of the Length field should be treated as
Data Link Layer padding and should be ignored on reception.
Data
The Data field is zero or more octets. The format of the Data
field is determined by the Code field.
2.2.1. Authenticate-Request
Description
The Authenticate-Request packet is used to begin the Password
Authentication Protocol. The link peer MUST transmit a PAP packet
with the Code field set to 1 (Authenticate-Request) during the
Authentication phase. The Authenticate-Request packet MUST be
repeated until a valid reply packet is received, or an optional
retry counter expires.
The authenticator SHOULD expect the peer to send an Authenticate-
Request packet. Upon reception of an Authenticate-Request packet,
some type of Authenticate reply (described below) MUST be
returned.
Implementation Note: Because the Authenticate-Ack might be
lost, the authenticator MUST allow repeated Authenticate-
Request packets after completing the Authentication phase.
Protocol phase MUST return the same reply Code returned when
the Authentication phase completed (the message portion MAY be
different). Any Authenticate-Request packets received during
any other phase MUST be silently discarded.
When the Authenticate-Nak is lost, and the authenticator
terminates the link, the LCP Terminate-Request and Terminate-
Ack provide an alternative indication that authentication
failed.
A summary of the Authenticate-Request packet format is shown below.
The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code Identifier Length
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Peer-ID Length Peer-Id ...
+-+-+-+-+-+-+-+-+-+-+-+-+
Passwd-Length Password ...
+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code
1 for Authenticate-Request.
Identifier
The Identifier field is one octet and aids in matching requests
and replies. The Identifier field MUST be changed each time an
Authenticate-Request packet is issued.
Peer-ID-Length
The Peer-ID-Length field is one octet and indicates the length of
the Peer-ID field.
Peer-ID
The Peer-ID field is zero or more octets and indicates the name of
the peer to be authenticated.
Passwd-Length
The Passwd-Length field is one octet and indicates the length of
the Password field.
Password
The Password field is zero or more octets and indicates the
password to be used for authentication.
2.2.2. Authenticate-Ack and Authenticate-Nak
Description
If the Peer-ID/Password pair received in an Authenticate-Request
is both recognizable and acceptable, then the authenticator MUST
transmit a PAP packet with the Code field set to 2 (Authenticate-
Ack).
If the Peer-ID/Password pair received in a Authenticate-Request is
not recognizable or acceptable, then the authenticator MUST
transmit a PAP packet with the Code field set to 3 (Authenticate-
Nak), and SHOULD take action to terminate the link.
A summary of the Authenticate-Ack and Authenticate-Nak packet format
is shown below. The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code Identifier Length
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Msg-Length Message ...
+-+-+-+-+-+-+-+-+-+-+-+-+-
Code
2 for Authenticate-Ack;
3 for Authenticate-Nak.
Identifier
The Identifier field is one octet and aids in matching requests
and replies. The Identifier field MUST be copied from the
Identifier field of the Authenticate-Request which caused this
reply.
Msg-Length
The Msg-Length field is one octet and indicates the length of the
Message field.
Message
The Message field is zero or more octets, and its contents are
implementation dependent. It is intended to be human readable,
and MUST NOT affect operation of the protocol. It is recommended
that the message contain displayable ASCII characters 32 through
126 decimal. Mechanisms for extension to other character sets are
the topic of future research.
3. Challenge-Handshake Authentication Protocol
The Challenge-Handshake Authentication Protocol (CHAP) is used to
periodically verify the identity of the peer using a 3-way handshake.
This is done upon initial link establishment, and MAY be repeated
anytime after the link has been established.
After the Link Establishment phase is complete, the authenticator
sends a "challenge" message to the peer. The peer responds with a
value calculated using a "one-way hash" function. The authenticator
checks the response against its own calculation of the expected hash
value. If the values match, the authentication is acknowledged;
otherwise the connection SHOULD be terminated.
CHAP provides protection against playback attack through the use of
an incrementally changing identifier and a variable challenge value.
The use of repeated challenges is intended to limit the time of
exposure to any single attack. The authenticator is in control of
the frequency and timing of the challenges.
This authentication method depends upon a "secret" known only to the
authenticator and that peer. The secret is not sent over the link.
This method is most likely used where the same secret is easily
Accessed from both ends of the link.
Implementation Note: CHAP requires that the secret be available in
plaintext form. To avoid sending the secret over other links in
the network, it is recommended that the challenge and response
values be examined at a central server, rather than each network
access server. Otherwise, the secret SHOULD be sent to such
servers in a reversably encrypted form.
The CHAP algorithm requires that the length of the secret MUST be at
least 1 octet. The secret SHOULD be at least as large and
unguessable as a well-chosen password. It is preferred that the
secret be at least the length of the hash value for the hashing
algorithm chosen (16 octets for MD5). This is to ensure a
sufficiently large range for the secret to provide protection against
exhaustive search attacks.
The one-way hash algorithm is chosen such that it is computationally
infeasible to determine the secret from the known challenge and
response values.
The challenge value SHOULD satisfy two criteria: uniqueness and
unpredictability. Each challenge value SHOULD be unique, since
repetition of a challenge value in conjunction with the same secret
would permit an attacker to reply with a previously intercepted
response. Since it is expected that the same secret MAY be used to
authenticate with servers in disparate geographic regions, the
challenge SHOULD exhibit global and temporal uniqueness. Each
challenge value SHOULD also be unpredictable, least an attacker trick
a peer into responding to a predicted future challenge, and then use
the response to masquerade as that peer to an authenticator.
Although protocols such as CHAP are incapable of protecting against
realtime active wiretapping attacks, generation of unique
unpredictable challenges can protect against a wide range of active
attacks.
A discussion of sources of uniqueness and probability of divergence
is included in the Magic-Number Configuration Option [1].
3.1. Configuration Option Format
A summary of the Authentication-Protocol Configuration Option format
to negotiate the Challenge-Handshake Authentication Protocol is shown
below. The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Type Length Authentication-Protocol
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Algorithm
+-+-+-+-+-+-+-+-+
Type
3
Length
5
Authentication-Protocol
c223 (hex) for Challenge-Handshake Authentication Protocol.
Algorithm
The Algorithm field is one octet and indicates the one-way hash
method to be used. The most up-to-date values of the CHAP
Algorithm field are specified in the most recent "Assigned
Numbers" RFC[2]. Current values are assigned as follows:
0-4 unused (reserved)
5 MD5 [3]
3.2. Packet Format
Exactly one Challenge-Handshake Authentication Protocol packet is
encapsulated in the Information field of a PPP Data Link Layer frame
where the protocol field indicates type hex c223 (Challenge-Handshake
Authentication Protocol). A summary of the CHAP packet format is
shown below. The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code Identifier Length
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Data ...
+-+-+-+-+
Code
The Code field is one octet and identifies the type of CHAP
packet. CHAP Codes are assigned as follows:
1 Challenge
2 Response
3 Success
4 Failure
Identifier
The Identifier field is one octet and aids in matching challenges,
responses and replies.
Length
The Length field is two octets and indicates the length of the
CHAP packet including the Code, Identifier, Length and Data
fields. Octets outside the range of the Length field should be
treated as Data Link Layer padding and should be ignored on
reception.
Data
The Data field is zero or more octets. The format of the Data
field is determined by the Code field.
3.2.1. Challenge and Response
Description
The Challenge packet is used to begin the Challenge-Handshake
Authentication Protocol. The authenticator MUST transmit a CHAP
packet with the Code field set to 1 (Challenge). Additional
Challenge packets MUST be sent until a valid Response packet is
received, or an optional retry counter expires.
A Challenge packet MAY also be transmitted at any time during the
Network-Layer Protocol phase to ensure that the connection has not
been altered.
The peer SHOULD expect Challenge packets during the Authentication
phase and the Network-Layer Protocol phase. Whenever a Challenge
packet is received, the peer MUST transmit a CHAP packet with the
Code field set to 2 (Response).
Whenever a Response packet is received, the authenticator compares
the Response Value with its own calculation of the expected value.
Based on this comparison, the authenticator MUST send a Success or
Failure packet (described below).
Implementation Note: Because the Success might be lost, the
authenticator MUST allow repeated Response packets after
completing the Authentication phase. To prevent discovery of
alternative Names and Secrets, any Response packets received
having the current Challenge Identifier MUST return the same
reply Code returned when the Authentication phase completed
(the message portion MAY be different). Any Response packets
received during any other phase MUST be silently discarded.
When the Failure is lost, and the authenticator terminates the
link, the LCP Terminate-Request and Terminate-Ack provide an
alternative indication that authentication failed.
A summary of the Challenge and Response packet format is shown below.
The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code Identifier Length
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Value-Size Value ...
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Name ...
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code
1 for Challenge;
2 for Response.
Identifier
The Identifier field is one octet. The Identifier field MUST be
changed each time a Challenge is sent.
The Response Identifier MUST be copied from the Identifier field
of the Challenge which caused the Response.
Value-Size
This field is one octet and indicates the length of the Value
field.
Value
The Value field is one or more octets. The most significant octet
is transmitted first.
The Challenge Value is a variable stream of octets. The
importance of the uniqueness of the Challenge Value and its
relationship to the secret is described above. The Challenge
Value MUST be changed each time a Challenge is sent. The length
of the Challenge Value depends upon the method used to generate
the octets, and is independent of the hash algorithm used.
The Response Value is the one-way hash calculated over a stream of
octets consisting of the Identifier, followed by (concatenated
with) the "secret", followed by (concatenated with) the Challenge
Value. The length of the Response Value depends upon the hash
algorithm used (16 octets for MD5).
Name
The Name field is one or more octets representing the
identification of the system transmitting the packet. There are
no limitations on the content of this field. For example, it MAY
contain ASCII character strings or globally unique identifiers in
ASN.1 syntax. The Name should not be NUL or CR/LF terminated.
The size is determined from the Length field.
Since CHAP may be used to authenticate many different systems, the
content of the name field(s) may be used as a key to locate the
proper secret in a database of secrets. This also makes it
possible to support more than one name/secret pair per system.
3.2.2. Success and Failure
Description
If the Value received in a Response is equal to the expected
value, then the implementation MUST transmit a CHAP packet with
the Code field set to 3 (Success).
If the Value received in a Response is not equal to the expected
value, then the implementation MUST transmit a CHAP packet with
the Code field set to 4 (Failure), and SHOULD take action to
terminate the link.
A summary of the Success and Failure packet format is shown below.
The fields are transmitted from left to right.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Code Identifier Length
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Message ...
+-+-+-+-+-+-+-+-+-+-+-+-+-
Code
3 for Success;
4 for Failure.
Identifier
The Identifier field is one octet and aids in matching requests
and replies. The Identifier field MUST be copied from the
Identifier field of the Response which caused this reply.
Message
The Message field is zero or more octets, and its contents are
implementation dependent. It is intended to be human readable,
and MUST NOT affect operation of the protocol. It is recommended
that the message contain displayable ASCII characters 32 through
126 decimal. Mechanisms for extension to other character sets are
the topic of future research. The size is determined from the
Length field.
Security Considerations
Security issues are the primary topic of this RFC.
The interaction of the authentication protocols within PPP are
highly implementation dependent. This is indicated by the use of
SHOULD throughout the document.
For example, upon failure of authentication, some implementations
do not terminate the link. Instead, the implementation limits the
kind of traffic in the Network-Layer Protocols to a filtered
subset, which in turn allows the user opportunity to update
secrets or send mail to the network administrator indicating a
problem.
There is no provision for re-tries of failed authentication.
However, the LCP state machine can renegotiate the authentication
protocol at any time, thus allowing a new attempt. It is
recommended that any counters used for authentication failure not
be reset until after successful authentication, or subsequent
termination of the failed link.
There is no requirement that authentication be full duplex or that
the same protocol be used in both directions. It is perfectly
acceptable for different protocols to be used in each direction.
This will, of course, depend on the specific protocols negotiated.
In practice, within or associated with each PPP server, there is a
database which associates "user" names with authentication
information ("secrets"). It is not anticipated that a particular
named user would be authenticated by multiple methods. This would
make the user vulnerable to attacks which negotiate the least
secure method from among a set (such as PAP rather than CHAP).
Instead, for each named user there should be an indication of
exactly one method used to authenticate that user name. If a user
needs to make use of different authentication method under
different circumstances, then distinct user names SHOULD be
employed, each of which identifies exactly one authentication
method.
Passwords and other secrets should be stored at the respective
ends such that access to them is as limited as possible. Ideally,
the secrets should only be accessible to the process requiring
access in order to perform the authentication.
The secrets should be distributed with a mechanism that limits the
number of entities that handle (and thus gain knowledge of) the
secret. Ideally, no unauthorized person should ever gain
knowledge of the secrets. It is possible to achieve this with
SNMP Security Protocols [4], but such a mechanism is outside the
scope of this specification.
Other distribution methods are currently undergoing research and
experimentation. The SNMP Security document also has an Excellent
overview of threats to network protocols.
References
[1] Simpson, W., "The Point-to-Point Protocol (PPP)", RFC1331,
Daydreamer, May 1992.
[2] Reynolds, J., and J. Postel, "Assigned Numbers", RFC1340,
USC/Information Sciences Institute, July 1992.
[3] Rivest, R., and S. Dusse, "The MD5 Message-Digest Algorithm", MIT
Laboratory for Computer Science and RSA Data Security, Inc. RFC
1321, April 1992.
[4] Galvin, J., McCloghrie, K., and J. Davin, "SNMP Security
Protocols", Trusted Information Systems, Inc., Hughes LAN
Systems, Inc., MIT Laboratory for Computer Science, RFC1352,
July 1992.
Acknowledgments
Some of the text in this document is taken from RFC1172, by Drew
Perkins of Carnegie Mellon University, and by Russ Hobby of the
University of California at Davis.
Special thanks to Dave Balenson, Steve Crocker, James Galvin, and
Steve Kent, for their extensive explanations and suggestions. Now,
if only we could get them to agree with each other.
Chair's Address
The working group can be contacted via the current chair:
Brian Lloyd
Lloyd & Associates
3420 Sudbury Road
Cameron Park, California 95682
Phone: (916) 676-1147
EMail:
brian@lloyd.com
Author's Address
Questions about this memo can also be directed to:
William Allen Simpson
Daydreamer
Computer Systems Consulting Services
P O Box 6205
East Lansing, MI 48826-6205
EMail: Bill.Simpson@um.cc.umich.edu
