Transport¶
Core protocol implementation
-
class
paramiko.transport.
Transport
(sock, default_window_size=2097152, default_max_packet_size=32768, gss_kex=False, gss_deleg_creds=True, disabled_algorithms=None, server_sig_algs=True)¶ An SSH Transport attaches to a stream (usually a socket), negotiates an encrypted session, authenticates, and then creates stream tunnels, called
channels
, across the session. Multiple channels can be multiplexed across a single session (and often are, in the case of port forwardings).Instances of this class may be used as context managers.
-
__init__
(sock, default_window_size=2097152, default_max_packet_size=32768, gss_kex=False, gss_deleg_creds=True, disabled_algorithms=None, server_sig_algs=True)¶ Create a new SSH session over an existing socket, or socket-like object. This only creates the
Transport
object; it doesn’t begin the SSH session yet. Useconnect
orstart_client
to begin a client session, orstart_server
to begin a server session.If the object is not actually a socket, it must have the following methods:
send(str)
: Writes from 1 tolen(str)
bytes, and returns an int representing the number of bytes written. Returns 0 or raisesEOFError
if the stream has been closed.recv(int)
: Reads from 1 toint
bytes and returns them as a string. Returns 0 or raisesEOFError
if the stream has been closed.close()
: Closes the socket.settimeout(n)
: Sets a (float) timeout on I/O operations.
For ease of use, you may also pass in an address (as a tuple) or a host string as the
sock
argument. (A host string is a hostname with an optional port (separated by":"
) which will be converted into a tuple of(hostname, port)
.) A socket will be connected to this address and used for communication. Exceptions from thesocket
call may be thrown in this case.Note
Modifying the the window and packet sizes might have adverse effects on your channels created from this transport. The default values are the same as in the OpenSSH code base and have been battle tested.
Parameters: - sock (socket) – a socket or socket-like object to create the session over.
- default_window_size (int) – sets the default window size on the transport. (defaults to 2097152)
- default_max_packet_size (int) – sets the default max packet size on the transport. (defaults to 32768)
- gss_kex (bool) – Whether to enable GSSAPI key exchange when GSSAPI is in play.
Default:
False
. - gss_deleg_creds (bool) – Whether to enable GSSAPI credential delegation when GSSAPI is in
play. Default:
True
. - disabled_algorithms (dict) –
If given, must be a dictionary mapping algorithm type to an iterable of algorithm identifiers, which will be disabled for the lifetime of the transport.
Keys should match the last word in the class’ builtin algorithm tuple attributes, such as
"ciphers"
to disable names within_preferred_ciphers
; or"kex"
to disable something defined inside_preferred_kex
. Values should exactly match members of the matching attribute.For example, if you need to disable
diffie-hellman-group16-sha512
key exchange (perhaps because your code talks to a server which implements it differently from Paramiko), specifydisabled_algorithms={"kex": ["diffie-hellman-group16-sha512"]}
. - server_sig_algs (bool) – Whether to send an extra message to compatible clients, in server
mode, with a list of supported pubkey algorithms. Default:
True
.
Changed in version 1.15: Added the
default_window_size
anddefault_max_packet_size
arguments.Changed in version 1.15: Added the
gss_kex
andgss_deleg_creds
kwargs.Changed in version 2.6: Added the
disabled_algorithms
kwarg.Changed in version 2.9: Added the
server_sig_algs
kwarg.
-
__repr__
()¶ Returns a string representation of this object, for debugging.
-
atfork
()¶ Terminate this Transport without closing the session. On posix systems, if a Transport is open during process forking, both parent and child will share the underlying socket, but only one process can use the connection (without corrupting the session). Use this method to clean up a Transport object without disrupting the other process.
New in version 1.5.3.
-
get_security_options
()¶ Return a
SecurityOptions
object which can be used to tweak the encryption algorithms this transport will permit (for encryption, digest/hash operations, public keys, and key exchanges) and the order of preference for them.
-
set_gss_host
(gss_host, trust_dns=True, gssapi_requested=True)¶ Normalize/canonicalize
self.gss_host
depending on various factors.Parameters: - gss_host (str) – The explicitly requested GSS-oriented hostname to connect to (i.e.
what the host’s name is in the Kerberos database.) Defaults to
self.hostname
(which will be the ‘real’ target hostname and/or host portion of given socket object.) - trust_dns (bool) – Indicates whether or not DNS is trusted; if true, DNS will be used
to canonicalize the GSS hostname (which again will either be
gss_host
or the transport’s default hostname.) (Defaults to True due to backwards compatibility.) - gssapi_requested (bool) – Whether GSSAPI key exchange or authentication was even requested.
If not, this is a no-op and nothing happens
(and
self.gss_host
is not set.) (Defaults to True due to backwards compatibility.)
Returns: None
.- gss_host (str) – The explicitly requested GSS-oriented hostname to connect to (i.e.
what the host’s name is in the Kerberos database.) Defaults to
-
start_client
(event=None, timeout=None)¶ Negotiate a new SSH2 session as a client. This is the first step after creating a new
Transport
. A separate thread is created for protocol negotiation.If an event is passed in, this method returns immediately. When negotiation is done (successful or not), the given
Event
will be triggered. On failure,is_active
will returnFalse
.(Since 1.4) If
event
isNone
, this method will not return until negotiation is done. On success, the method returns normally. Otherwise an SSHException is raised.After a successful negotiation, you will usually want to authenticate, calling
auth_password
orauth_publickey
.Note
connect
is a simpler method for connecting as a client.Note
After calling this method (or
start_server
orconnect
), you should no longer directly read from or write to the original socket object.Parameters: - event (threading.Event) – an event to trigger when negotiation is complete (optional)
- timeout (float) – a timeout, in seconds, for SSH2 session negotiation (optional)
Raises: SSHException
– if negotiation fails (and noevent
was passed in)
-
start_server
(event=None, server=None)¶ Negotiate a new SSH2 session as a server. This is the first step after creating a new
Transport
and setting up your server host key(s). A separate thread is created for protocol negotiation.If an event is passed in, this method returns immediately. When negotiation is done (successful or not), the given
Event
will be triggered. On failure,is_active
will returnFalse
.(Since 1.4) If
event
isNone
, this method will not return until negotiation is done. On success, the method returns normally. Otherwise an SSHException is raised.After a successful negotiation, the client will need to authenticate. Override the methods
get_allowed_auths
,check_auth_none
,check_auth_password
, andcheck_auth_publickey
in the givenserver
object to control the authentication process.After a successful authentication, the client should request to open a channel. Override
check_channel_request
in the givenserver
object to allow channels to be opened.Note
After calling this method (or
start_client
orconnect
), you should no longer directly read from or write to the original socket object.Parameters: - event (threading.Event) – an event to trigger when negotiation is complete.
- server (ServerInterface) – an object used to perform authentication and create
channels
Raises: SSHException
– if negotiation fails (and noevent
was passed in)
-
add_server_key
(key)¶ Add a host key to the list of keys used for server mode. When behaving as a server, the host key is used to sign certain packets during the SSH2 negotiation, so that the client can trust that we are who we say we are. Because this is used for signing, the key must contain private key info, not just the public half. Only one key of each type (RSA or DSS) is kept.
Parameters: key (PKey) – the host key to add, usually an RSAKey
orDSSKey
.
-
get_server_key
()¶ Return the active host key, in server mode. After negotiating with the client, this method will return the negotiated host key. If only one type of host key was set with
add_server_key
, that’s the only key that will ever be returned. But in cases where you have set more than one type of host key (for example, an RSA key and a DSS key), the key type will be negotiated by the client, and this method will return the key of the type agreed on. If the host key has not been negotiated yet,None
is returned. In client mode, the behavior is undefined.Returns: host key ( PKey
) of the type negotiated by the client, orNone
.
-
static
load_server_moduli
(filename=None)¶ (optional) Load a file of prime moduli for use in doing group-exchange key negotiation in server mode. It’s a rather obscure option and can be safely ignored.
In server mode, the remote client may request “group-exchange” key negotiation, which asks the server to send a random prime number that fits certain criteria. These primes are pretty difficult to compute, so they can’t be generated on demand. But many systems contain a file of suitable primes (usually named something like
/etc/ssh/moduli
). If you callload_server_moduli
and it returnsTrue
, then this file of primes has been loaded and we will support “group-exchange” in server mode. Otherwise server mode will just claim that it doesn’t support that method of key negotiation.Parameters: filename (str) – optional path to the moduli file, if you happen to know that it’s not in a standard location. Returns: True if a moduli file was successfully loaded; False otherwise. Note
This has no effect when used in client mode.
-
close
()¶ Close this session, and any open channels that are tied to it.
-
get_remote_server_key
()¶ Return the host key of the server (in client mode).
Note
Previously this call returned a tuple of
(key type, key string)
. You can get the same effect by callingPKey.get_name
for the key type, andstr(key)
for the key string.Raises: SSHException
– if no session is currently active.Returns: public key ( PKey
) of the remote server
-
is_active
()¶ Return true if this session is active (open).
Returns: True if the session is still active (open); False if the session is closed
-
open_session
(window_size=None, max_packet_size=None, timeout=None)¶ Request a new channel to the server, of type
"session"
. This is just an alias for callingopen_channel
with an argument of"session"
.Note
Modifying the the window and packet sizes might have adverse effects on the session created. The default values are the same as in the OpenSSH code base and have been battle tested.
Parameters: Returns: a new
Channel
Raises: SSHException
– if the request is rejected or the session ends prematurelyChanged in version 1.13.4/1.14.3/1.15.3: Added the
timeout
argument.Changed in version 1.15: Added the
window_size
andmax_packet_size
arguments.
-
open_x11_channel
(src_addr=None)¶ Request a new channel to the client, of type
"x11"
. This is just an alias foropen_channel('x11', src_addr=src_addr)
.Parameters: src_addr (tuple) – the source address ( (str, int)
) of the x11 server (port is the x11 port, ie. 6010)Returns: a new Channel
Raises: SSHException
– if the request is rejected or the session ends prematurely
-
open_forward_agent_channel
()¶ Request a new channel to the client, of type
"auth-agent@openssh.com"
.This is just an alias for
open_channel('auth-agent@openssh.com')
.Returns: a new Channel
Raises: SSHException
– if the request is rejected or the session ends prematurely
-
open_forwarded_tcpip_channel
(src_addr, dest_addr)¶ Request a new channel back to the client, of type
forwarded-tcpip
.This is used after a client has requested port forwarding, for sending incoming connections back to the client.
Parameters: - src_addr – originator’s address
- dest_addr – local (server) connected address
-
open_channel
(kind, dest_addr=None, src_addr=None, window_size=None, max_packet_size=None, timeout=None)¶ Request a new channel to the server.
Channels
are socket-like objects used for the actual transfer of data across the session. You may only request a channel after negotiating encryption (usingconnect
orstart_client
) and authenticating.Note
Modifying the the window and packet sizes might have adverse effects on the channel created. The default values are the same as in the OpenSSH code base and have been battle tested.
Parameters: - kind (str) – the kind of channel requested (usually
"session"
,"forwarded-tcpip"
,"direct-tcpip"
, or"x11"
) - dest_addr (tuple) – the destination address (address + port tuple) of this port
forwarding, if
kind
is"forwarded-tcpip"
or"direct-tcpip"
(ignored for other channel types) - src_addr – the source address of this port forwarding, if
kind
is"forwarded-tcpip"
,"direct-tcpip"
, or"x11"
- window_size (int) – optional window size for this session.
- max_packet_size (int) – optional max packet size for this session.
- timeout (float) – optional timeout opening a channel, default 3600s (1h)
Returns: a new
Channel
on successRaises: SSHException
– if the request is rejected, the session ends prematurely or there is a timeout openning a channelChanged in version 1.15: Added the
window_size
andmax_packet_size
arguments.- kind (str) – the kind of channel requested (usually
-
request_port_forward
(address, port, handler=None)¶ Ask the server to forward TCP connections from a listening port on the server, across this SSH session.
If a handler is given, that handler is called from a different thread whenever a forwarded connection arrives. The handler parameters are:
handler( channel, (origin_addr, origin_port), (server_addr, server_port), )
where
server_addr
andserver_port
are the address and port that the server was listening on.If no handler is set, the default behavior is to send new incoming forwarded connections into the accept queue, to be picked up via
accept
.Parameters: Returns: the port number (
int
) allocated by the serverRaises: SSHException
– if the server refused the TCP forward request
-
cancel_port_forward
(address, port)¶ Ask the server to cancel a previous port-forwarding request. No more connections to the given address & port will be forwarded across this ssh connection.
Parameters:
-
open_sftp_client
()¶ Create an SFTP client channel from an open transport. On success, an SFTP session will be opened with the remote host, and a new
SFTPClient
object will be returned.Returns: a new SFTPClient
referring to an sftp session (channel) across this transport
-
send_ignore
(byte_count=None)¶ Send a junk packet across the encrypted link. This is sometimes used to add “noise” to a connection to confuse would-be attackers. It can also be used as a keep-alive for long lived connections traversing firewalls.
Parameters: byte_count (int) – the number of random bytes to send in the payload of the ignored packet – defaults to a random number from 10 to 41.
-
renegotiate_keys
()¶ Force this session to switch to new keys. Normally this is done automatically after the session hits a certain number of packets or bytes sent or received, but this method gives you the option of forcing new keys whenever you want. Negotiating new keys causes a pause in traffic both ways as the two sides swap keys and do computations. This method returns when the session has switched to new keys.
Raises: SSHException
– if the key renegotiation failed (which causes the session to end)
-
set_keepalive
(interval)¶ Turn on/off keepalive packets (default is off). If this is set, after
interval
seconds without sending any data over the connection, a “keepalive” packet will be sent (and ignored by the remote host). This can be useful to keep connections alive over a NAT, for example.Parameters: interval (int) – seconds to wait before sending a keepalive packet (or 0 to disable keepalives).
-
global_request
(kind, data=None, wait=True)¶ Make a global request to the remote host. These are normally extensions to the SSH2 protocol.
Parameters: Returns: a
Message
containing possible additional data if the request was successful (or an emptyMessage
ifwait
wasFalse
);None
if the request was denied.
-
accept
(timeout=None)¶ Return the next channel opened by the client over this transport, in server mode. If no channel is opened before the given timeout,
None
is returned.Parameters: timeout (int) – seconds to wait for a channel, or None
to wait foreverReturns: a new Channel
opened by the client
-
connect
(hostkey=None, username='', password=None, pkey=None, gss_host=None, gss_auth=False, gss_kex=False, gss_deleg_creds=True, gss_trust_dns=True)¶ Negotiate an SSH2 session, and optionally verify the server’s host key and authenticate using a password or private key. This is a shortcut for
start_client
,get_remote_server_key
, andTransport.auth_password
orTransport.auth_publickey
. Use those methods if you want more control.You can use this method immediately after creating a Transport to negotiate encryption with a server. If it fails, an exception will be thrown. On success, the method will return cleanly, and an encrypted session exists. You may immediately call
open_channel
oropen_session
to get aChannel
object, which is used for data transfer.Note
If you fail to supply a password or private key, this method may succeed, but a subsequent
open_channel
oropen_session
call may fail because you haven’t authenticated yet.Parameters: - hostkey (PKey) – the host key expected from the server, or
None
if you don’t want to do host key verification. - username (str) – the username to authenticate as.
- password (str) – a password to use for authentication, if you want to use password
authentication; otherwise
None
. - pkey (PKey) – a private key to use for authentication, if you want to use private
key authentication; otherwise
None
. - gss_host (str) – The target’s name in the kerberos database. Default: hostname
- gss_auth (bool) –
True
if you want to use GSS-API authentication. - gss_kex (bool) – Perform GSS-API Key Exchange and user authentication.
- gss_deleg_creds (bool) – Whether to delegate GSS-API client credentials.
- gss_trust_dns – Indicates whether or not the DNS is trusted to securely
canonicalize the name of the host being connected to (default
True
).
Raises: SSHException
– if the SSH2 negotiation fails, the host key supplied by the server is incorrect, or authentication fails.Changed in version 2.3: Added the
gss_trust_dns
argument.- hostkey (PKey) – the host key expected from the server, or
-
get_exception
()¶ Return any exception that happened during the last server request. This can be used to fetch more specific error information after using calls like
start_client
. The exception (if any) is cleared after this call.Returns: an exception, or None
if there is no stored exception.New in version 1.1.
-
set_subsystem_handler
(name, handler, *larg, **kwarg)¶ Set the handler class for a subsystem in server mode. If a request for this subsystem is made on an open ssh channel later, this handler will be constructed and called – see
SubsystemHandler
for more detailed documentation.Any extra parameters (including keyword arguments) are saved and passed to the
SubsystemHandler
constructor later.Parameters: - name (str) – name of the subsystem.
- handler – subclass of
SubsystemHandler
that handles this subsystem.
-
is_authenticated
()¶ Return true if this session is active and authenticated.
Returns: True if the session is still open and has been authenticated successfully; False if authentication failed and/or the session is closed.
-
get_username
()¶ Return the username this connection is authenticated for. If the session is not authenticated (or authentication failed), this method returns
None
.Returns: username that was authenticated (a str
), orNone
.
Return the banner supplied by the server upon connect. If no banner is supplied, this method returns
None
.Returns: server supplied banner ( str
), orNone
.New in version 1.13.
-
auth_none
(username)¶ Try to authenticate to the server using no authentication at all. This will almost always fail. It may be useful for determining the list of authentication types supported by the server, by catching the
BadAuthenticationType
exception raised.Parameters: username (str) – the username to authenticate as Returns: list of auth types permissible for the next stage of authentication (normally empty) Raises: BadAuthenticationType
– if “none” authentication isn’t allowed by the server for this userRaises: SSHException
– if the authentication failed due to a network errorNew in version 1.5.
-
auth_password
(username, password, event=None, fallback=True)¶ Authenticate to the server using a password. The username and password are sent over an encrypted link.
If an
event
is passed in, this method will return immediately, and the event will be triggered once authentication succeeds or fails. On success,is_authenticated
will returnTrue
. On failure, you may useget_exception
to get more detailed error information.Since 1.1, if no event is passed, this method will block until the authentication succeeds or fails. On failure, an exception is raised. Otherwise, the method simply returns.
Since 1.5, if no event is passed and
fallback
isTrue
(the default), if the server doesn’t support plain password authentication but does support so-called “keyboard-interactive” mode, an attempt will be made to authenticate using this interactive mode. If it fails, the normal exception will be thrown as if the attempt had never been made. This is useful for some recent Gentoo and Debian distributions, which turn off plain password authentication in a misguided belief that interactive authentication is “more secure”. (It’s not.)If the server requires multi-step authentication (which is very rare), this method will return a list of auth types permissible for the next step. Otherwise, in the normal case, an empty list is returned.
Parameters: - username (str) – the username to authenticate as
- password (basestring) – the password to authenticate with
- event (threading.Event) – an event to trigger when the authentication attempt is complete (whether it was successful or not)
- fallback (bool) –
True
if an attempt at an automated “interactive” password auth should be made if the server doesn’t support normal password auth
Returns: list of auth types permissible for the next stage of authentication (normally empty)
Raises: BadAuthenticationType
– if password authentication isn’t allowed by the server for this user (and no event was passed in)Raises: AuthenticationException
– if the authentication failed (and no event was passed in)Raises: SSHException
– if there was a network error
-
auth_publickey
(username, key, event=None)¶ Authenticate to the server using a private key. The key is used to sign data from the server, so it must include the private part.
If an
event
is passed in, this method will return immediately, and the event will be triggered once authentication succeeds or fails. On success,is_authenticated
will returnTrue
. On failure, you may useget_exception
to get more detailed error information.Since 1.1, if no event is passed, this method will block until the authentication succeeds or fails. On failure, an exception is raised. Otherwise, the method simply returns.
If the server requires multi-step authentication (which is very rare), this method will return a list of auth types permissible for the next step. Otherwise, in the normal case, an empty list is returned.
Parameters: - username (str) – the username to authenticate as
- key (PKey) – the private key to authenticate with
- event (threading.Event) – an event to trigger when the authentication attempt is complete (whether it was successful or not)
Returns: list of auth types permissible for the next stage of authentication (normally empty)
Raises: BadAuthenticationType
– if public-key authentication isn’t allowed by the server for this user (and no event was passed in)Raises: AuthenticationException
– if the authentication failed (and no event was passed in)Raises: SSHException
– if there was a network error
-
auth_interactive
(username, handler, submethods='')¶ Authenticate to the server interactively. A handler is used to answer arbitrary questions from the server. On many servers, this is just a dumb wrapper around PAM.
This method will block until the authentication succeeds or fails, peroidically calling the handler asynchronously to get answers to authentication questions. The handler may be called more than once if the server continues to ask questions.
The handler is expected to be a callable that will handle calls of the form:
handler(title, instructions, prompt_list)
. Thetitle
is meant to be a dialog-window title, and theinstructions
are user instructions (both are strings).prompt_list
will be a list of prompts, each prompt being a tuple of(str, bool)
. The string is the prompt and the boolean indicates whether the user text should be echoed.A sample call would thus be:
handler('title', 'instructions', [('Password:', False)])
.The handler should return a list or tuple of answers to the server’s questions.
If the server requires multi-step authentication (which is very rare), this method will return a list of auth types permissible for the next step. Otherwise, in the normal case, an empty list is returned.
Parameters: Returns: list of auth types permissible for the next stage of authentication (normally empty).
Raises: BadAuthenticationType
– if public-key authentication isn’t allowed by the server for this userRaises: AuthenticationException
– if the authentication failedRaises: SSHException
– if there was a network errorNew in version 1.5.
-
auth_interactive_dumb
(username, handler=None, submethods='')¶ Autenticate to the server interactively but dumber. Just print the prompt and / or instructions to stdout and send back the response. This is good for situations where partial auth is achieved by key and then the user has to enter a 2fac token.
-
auth_gssapi_with_mic
(username, gss_host, gss_deleg_creds)¶ Authenticate to the Server using GSS-API / SSPI.
Parameters: Returns: list of auth types permissible for the next stage of authentication (normally empty)
Raises: BadAuthenticationType
– if gssapi-with-mic isn’t allowed by the server (and no event was passed in)Raises: AuthenticationException
– if the authentication failed (and no event was passed in)Raises: SSHException
– if there was a network error
-
auth_gssapi_keyex
(username)¶ Authenticate to the server with GSS-API/SSPI if GSS-API kex is in use.
Parameters: username (str) – The username to authenticate as. Returns: a list of auth types permissible for the next stage of authentication (normally empty) Raises: BadAuthenticationType
– if GSS-API Key Exchange was not performed (and no event was passed in)Raises: AuthenticationException
– if the authentication failed (and no event was passed in)Raises: SSHException
– if there was a network error
-
set_log_channel
(name)¶ Set the channel for this transport’s logging. The default is
"paramiko.transport"
but it can be set to anything you want. (See thelogging
module for more info.) SSH Channels will log to a sub-channel of the one specified.Parameters: name (str) – new channel name for logging New in version 1.1.
-
get_log_channel
()¶ Return the channel name used for this transport’s logging.
Returns: channel name as a str
New in version 1.2.
-
set_hexdump
(hexdump)¶ Turn on/off logging a hex dump of protocol traffic at DEBUG level in the logs. Normally you would want this off (which is the default), but if you are debugging something, it may be useful.
Parameters: hexdump (bool) – True
to log protocol traffix (in hex) to the log;False
otherwise.
-
get_hexdump
()¶ Return
True
if the transport is currently logging hex dumps of protocol traffic.Returns: True
if hex dumps are being logged, elseFalse
.New in version 1.4.
-
use_compression
(compress=True)¶ Turn on/off compression. This will only have an affect before starting the transport (ie before calling
connect
, etc). By default, compression is off since it negatively affects interactive sessions.Parameters: compress (bool) – True
to ask the remote client/server to compress traffic;False
to refuse compressionNew in version 1.5.2.
-
getpeername
()¶ Return the address of the remote side of this Transport, if possible.
This is effectively a wrapper around
getpeername
on the underlying socket. If the socket-like object has nogetpeername
method, then("unknown", 0)
is returned.Returns: the address of the remote host, if known, as a (str, int)
tuple.
-
-
class
paramiko.transport.
SecurityOptions
(transport)¶ Simple object containing the security preferences of an ssh transport. These are tuples of acceptable ciphers, digests, key types, and key exchange algorithms, listed in order of preference.
Changing the contents and/or order of these fields affects the underlying
Transport
(but only if you change them before starting the session). If you try to add an algorithm that paramiko doesn’t recognize,ValueError
will be raised. If you try to assign something besides a tuple to one of the fields,TypeError
will be raised.-
__repr__
()¶ Returns a string representation of this object, for debugging.
-
ciphers
¶ Symmetric encryption ciphers
-
digests
¶ Digest (one-way hash) algorithms
-
key_types
¶ Public-key algorithms
-
kex
¶ Key exchange algorithms
-
compression
¶ Compression algorithms
-