# `srp` — Secure Remote Password

The Secure Remote Password protocol (SRP) is a cryptographically strong authentication protocol for password-based, mutual authentication over an insecure network connection. Successful SRP authentication requires both sides of the connection to have knowledge of the user’s password. In addition to password verification, the SRP protocol also performs a secure key exchange during the authentication process. This key may be used to protect network traffic via symmetric key encryption.

SRP offers security and deployment advantages over other challenge-response protocols, such as Kerberos and SSL, in that it does not require trusted key servers or certificate infrastructures. Instead, small verification keys derived from each user’s password are stored and used by each SRP server application. SRP provides a near-ideal solution for many applications requiring simple and secure password authentication that does not rely on an external infrastructure.

Another favorable aspect of the SRP protocol is that compromized verification keys are of little value to an attacker. Possesion of a verification key does not allow a user to be impersonated and it cannot be used to obtain the users password except by way of a computationally infeasible dictionary attack. A compromized key would, however, allow an attacker to impersonate the server side of an SRP authenticated connection. Consequently, care should be taken to prevent unauthorized access to verification keys for applications in which the client side relies on the server being genuine.

## Usage

SRP usage begins with create_salted_verification_key(). This function creates a salted verification key from the user’s password. The resulting salt and key are stored by the server application and will be used during the authentication process.

The authentication process occurs as an exchange of messages between the clent and the server. The Example below provides a simple demonstration of the protocol. A comprehensive description of the SRP protocol is contained in the SRP 6a Protocol Description section.

The User & Verifier constructors, as well as the create_salted_verification_key() function, accept optional arguments to specify which hashing algorithm and prime number arguments should be used during the authentication process. These options may be used to tune the security/performance tradeoff for an application. Generally speaking, specifying arguments with a higher number of bits will result in a greater level of security. However, it will come at the cost of increased computation time. The default values of SHA1 hashes and 2048 bit prime numbers strike a good balance between performance and security. These values should be sufficient for most applications. Regardless of which values are used, the parameters passed to the User and Verifier constructors must exactly match those passed to create_salted_verification_key()

## Constants

Hashing Algorithm Constants
Hash Algorithm | Number of Bits
--- | ---
SHA1 | 160
SHA224 | 224
SHA256 | 256
SHA384 | 384
SHA512 | 512

Note

Larger hashing algorithms will result in larger session keys.

Prime Number Constants
Prime Number Size | Number of Bits
--- | ---
NG_1024 | 1024
NG_2048 | 2048
NG_4096 | 4096
NG_8192 | 8192
NG_CUSTOM | User Supplied

Note

If NG_CUSTOM is used, the ‘n_hex’ and ‘g_hex’ parameters are required. These parameters must be ASCII text containing hexidecimal notation of the prime number ‘n_hex’ and the corresponding generator number ‘g_hex’. Appendix A of RFC 5054 contains several large prime number, generator pairs that may be used with NG_CUSTOM.

## Functions

`srp.``create_salted_verification_key`(username, password[, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None])

  username Name of the user

  password Plaintext user password

  hash_alg, ng_type, n_hex, g_hex Refer to the Constants section.

  Generate a salted verification key for the given username and password and return the tuple: (salt_bytes, verification_key_bytes)

## `Verifier` Objects

A `Verifier` object is used to verify the identity of a remote user.

Note

The standard SRP 6 protocol allows only one password attempt per connection.

class `srp.``Verifier`(username, bytes_s, bytes_v, bytes_A[, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None])

  username Name of the remote user being authenticated.

  bytes_s Salt generated by `create_salted_verification_key()`.

  bytes_v Verification Key generated by `create_salted_verification_key()`.

  bytes_A Challenge from the remote user. Generated by `User.start_authentication()`

  hash_alg, ng_type, n_hex, g_hex Refer to the Constants section.

  `authenticated`()

    Return True if the authentication succeeded. False otherwise.

  `get_username`()

    Return the name of the user this `Verifier` object is for.

  `get_session_key`()

    Return the session key for an authenticated user or None if the authentication failed or has not yet completed.

  `get_challenge`()

    Return (bytes_s, bytes_B) on success or (None, None) if authentication has failed.

  `verify_session`(user_M)

    Complete the `Verifier` side of the authentication process. If the authentication succeded the return result, bytes_H_AMK should be returned to the remote user. On failure, this method returns None.

## `User` Objects

A `User` object is used to prove a user’s identity to a remote `Verifier` and verifiy that the remote `Verifier` knows the verification key associated with the user’s password.

class `srp.``User`(username, password[, hash_alg=SHA1, ng_type=NG_2048, n_hex=None, g_hex=None])

  username Name of the user being authenticated.

  password Password for the user.

  hash_alg, ng_type, n_hex, g_hex Refer to the Constants section.

  `authenticated`()

    Return True if authentication succeeded. False otherwise.

  `get_username`()

    Return the username passed to the constructor.

  `get_session_key`()

    Return the session key if authentication succeeded or None if the authentication failed or has not yet completed.

  `start_authentication`()

    Return (username, bytes_A). These should be passed to the constructor of the remote `Verifer`

  `process_challenge`(bytes_s, bytes_B)

    Processe the challenge returned by `Verifier.get_challenge()` on success this method returns bytes_M that should be sent to `Verifier.verify_session()` if authentication failed, it returns None.

  `verify_session`(bytes_H_AMK)

    Complete the `User` side of the authentication process. By verifying the bytes_H_AMK value returned by `Verifier.verify_session()`. If the authentication succeded `authenticated()` will return True

## Example

Simple Usage Example:

    import srp

    # The salt and verifier returned from srp.create_salted_verification_key() should be
    # stored on the server.
    salt, vkey = srp.create_salted_verification_key( 'testuser', 'testpassword' )

    class AuthenticationFailed (Exception):
        pass

    # ~~~ Begin Authentication ~~~

    usr      = srp.User( 'testuser', 'testpassword' )
    uname, A = usr.start_authentication()

    # The authentication process can fail at each step from this
    # point on. To comply with the SRP protocol, the authentication
    # process should be aborted on the first failure.

    # Client => Server: username, A
    svr      = srp.Verifier( uname, salt, vkey, A )
    s,B      = svr.get_challenge()

    if s is None or B is None:
        raise AuthenticationFailed()

    # Server => Client: s, B
    M        = usr.process_challenge( s, B )

    if M is None:
        raise AuthenticationFailed()

    # Client => Server: M
    HAMK     = svr.verify_session( M )

    if HAMK is None:
        raise AuthenticationFailed()

    # Server => Client: HAMK
    usr.verify_session( HAMK )

    # At this point the authentication process is complete.

    assert usr.authenticated()
    assert svr.authenticated()

## Implementation Notes

This implementation of SRP consists of both a pure-python module and a C-based implementation that is approximately 10x faster. By default, the C-implementation will be used if it is available. An additional benefit of the C implementation is that it can take advantage of of multiple CPUs. For cases in which the number of connections per second is an issue, using a small pool of threads to perform the authentication steps on multi-core systems will yield a substantial performance increase.

## SRP 6a Protocol Description

The original SRP protocol, known as SRP-3, is defined in RFC 2945. This implementation, however, uses SRP-6a which is a slight improvement over SRP-3. The authoritative definition for the SRP-6a protocol is available at http://srp.stanford.edu. An additional resource is RFC 5054 which covers the integration of SRP into TLS. This RFC is the source of hashing strategy and the predefined N and g constants used in this implementation.

The following is a complete description of the SRP-6a protocol as implemented by this library. Note that the ^ symbol indicates exponentiaion and the | symbol indicates concatenation.

Primary Variables used in SRP 6a

Variables | Description
--- | ---
N | A large, safe prime (N = 2q+1, where q is a Sophie Germain prime) All arithmetic is performed in the field of integers modulo N
g | A generator modulo N
s | Small salt for the verification key
I | Username
p | Cleartext password
H() | One-way hash function
a,b | Secret, random values
K | Session key

Derived Values used in SRP 6a

Derived Values | Description
--- | ---
k = H(N,g) | Multiplier Parameter
A = g^a | Public ephemeral value
B = kv + g^b | Public ephemeral value
x = H(s, H( I | ‘:’ | p )) | Private key (as defined by RFC 5054)
v = g^x | Password verifier
u = H(A,B) | Random scrambling parameter
M = H(H(N) xor H(g), H(I), s, A, B, K) | Session key verifier

Protocol Description

The server stores the password verifier v. Authentication begins with a message from the client:

    client -> server: I, A = g^a

The server replies with the verifier salt and challenge:

    server -> client: s, B = kv + g^b

At this point, both the client and server calculate the shared session key:

    client & server: u = H(A,B)

    server: K = H( (Av^u) ^ b )

    client: x = H( s, H( I + ':' + p ) )
    client: K = H( (B - kg^x) ^ (a + ux) )

Now both parties have a shared, strong session key K. To complete authentication they need to prove to each other that their keys match:

    client -> server: M = H(H(N) xor H(g), H(I), s, A, B, K)
    server -> client: H(A, M, K)

SRP 6a requires the two parties to use the following safeguards:

1. The client will abort if it recieves B == 0 (mod N) or u == 0
2. The server will abort if it detects A == 0 (mod N)
3. The client must show its proof of K first. If the server detects that this proof is incorrect it must abort without showing its own proof of K