srp

Standalone apple SRP-6a implementation in go-lang

This is a standalone implementation of SRP in golang. It uses the go standard libraries and has no other external dependencies. This library can be used by SRP clients or servers.

SRP is a protocol to authenticate a user and derive safe session keys. It is the latest in the category of "strong authentication protocols".

SRP is documented here: http://srp.stanford.edu/doc.html. Briefly,

Design Overview

Conventions

N    A large safe prime (N = 2q+1, where q is prime)
   All arithmetic is done modulo N.
g    A generator modulo N
k    Multiplier parameter (k = H(N, g) in SRP-6a, k = 3 for legacy SRP-6)
s    User's salt
I    Username
p    Cleartext Password
H()  One-way hash function
^    (Modular) Exponentiation
u    Random scrambling parameter
a,b  Secret ephemeral values
A,B  Public ephemeral values
x    Private key (derived from p and s)
v    Password verifier

Differences from SRP-6a and RFC 5054

We differ from the SRP-6a spec and RFC 5054 in a couple of key ways:

• We hash the identity I; this provides some (minimal) protection against dictionary attacks on the username.
• We hash the user passphrase p; this expands shorter passphrase into longer ones and extends the alphabet used in the passphrase.
• We differ from RFC 5054 in our choice of hash function; we use Blake-2b. SHA-1 is getting long in the tooth, Blake2b is the current state-of-the art. Equivalently, one may use SHA3 (see below for using a user supplied hash function).

Generating and Storing the Password Verifier

The host calculates the password verifier using the following formula:

s = randomsalt()          (same length as N)
I = I
p = p                  (hash/expand I & p)
t = H(I, ":", p)
x = H(s, t)
v = g^x                   (computes password verifier)

The host then stores {I, s, v} in its password database - such that the triple can be retrieved by using I as the index/key.

Authentication Protocol

The authentication protocol itself goes as follows:

Client                       Server
--------------               ----------------
un, pw = < user input >
I = H(un)
p = H(pw)
a = random()
A = g^a % N
            I, A -->
                          s, v = lookup(I)
                          b = random()
                          B = (kv + g^b) % N
                          u = H(A, B)
                          S = ((A * v^u) ^ b) % N
                          K = H(S)
                          M' = H(K, A, B, I, s, N, g)
             <-- s, B
u = H(A, B)
x = H(s, p)
S = ((B - k (g^x)) ^ (a + ux)) % N
K = H(S)
M = H(K, A, B, I, s, N, g)

            M -->
                          M must be equal to M'
                          Z = H(M, K)
            <-- Z

Z' = H(M, K)
Z' must equal Z

When the server receives <I, A>, it can compute everything: shared key and proof-of-generation M'. The shared key is K.

To verify that the client has generated the same key K, the client sends M -- a hash of all the data it has and it received from the server. To validate that the server also has the same value, it requires the server to send its own proof. In the SRP paper, the authors use:

M = H(H(N) xor H(g), H(I), s, A, B, K)
M' = H(A, M, K)

We use a simpler construction:

M = H(K, A, B, I, s, N, g)
M' = H(M, K)

The two parties also employ the following safeguards:

1. The user will abort if he receives B == 0 (mod N) or u == 0.
2. The host will abort if it detects that A == 0 (mod N).
3. The user must show his proof of K first. If the server detects that the user's proof is incorrect, it must abort without showing its own proof of K.

Implementation Notes

In our implementation:

• The standard hash function is Blake2b-256; this can be changed by choosing an appropriate hash from crypto:

  
       s, err := srp.NewWithHash(crypto.SHA256, 4096)
  

Setting up the Verifiers on the Server

In order to authenticate and derive session keys, verifiers must be stored in a non-volatile medium on the server. The client provides the prime-field size, username and password when creating the verifier. The server stores the triple in a non-volatile medium. The verifiers are generated once when a user is created on the server.

The Client is the entity where the user enters their password and wishes to be authenticated with a SRP server. The communication between client and server can happen in clear text - SRP is immune to man in the middle attacks.

Depending on the resources available on a given client, it can choose a small or large prime-field; but once chosen it is recorded on the server until a new verifier is generated.

For example, a client will do:

    s, err := srp.New(n_bits)

    v, err := s.Verifier(username, password)
    id, verif := v.Encode()

    // Now, store 'id', 'verif' in non-volatile storage such that 'verif' can be
    // retrieved by providing 'id'.

Note that id is the hashed identity string for username. The server should store the encoded verifier string verif in a DB such that it can be looked up using id as the key.

Changing the default hash function

A client may wish to change the default hash function to something else. e.g.,::

    s, err := srp.NewWithHash(crypto.SHA256, n_bits)

    v, err := s.Verifier(username, password)
    id, verif := v.Encode()

Authentication attempt from the Client

The client performs the following sequence of steps to authenticate and derive session keys:

    s, err := srp.New(n_bits)

    c, err := s.NewClient(user, pass)
    creds := c.Credentials()

    // 1. send the credentials to the server. It is already in ASCII string form; this
    //    is essentially the encoded form of identity and a random public key.

    // 2. Receive the server credentials into 'server_creds'; this is the server
    //    public key and random salt generated when the verifier was created.

    // It is assumed that there is some network communication that happens
    // to get this string from the server.

    // Now, generate a mutual authenticator to be sent to the server
    auth, err := c.Generate(server_creds)

    // 3. Send the mutual authenticator to the server
    // 4. receive "proof" that the server too computed the same result.

    // Verify that the server actually did what it claims
    if !c.ServerOk(proof) {
        panic("authentication failed")
    }

    // Generate session key
    rawkey := c.RawKey()

Authenticating a Client on the Server

On the server, the authentication attempt begins after receiving the initial user credentials. This is used to lookup the stored verifier and other bits.:

    // Assume that we received the user credentials via the network into 'creds'


    // Parse the user info and authenticator from the 'creds' string
    id, A, err := srp.ServerBegin(creds)

    // Use 'id' to lookup the user in some non-volatile DB and obtain
    // previously stored *encoded* verifier 'v'.
    verifier := db.Lookup(id)


    // Create an SRP instance and Verifier instance from the stored data.
    s, v, err := srp.MakeSRPVerifier(verifier)

    // Begin a new client-server SRP session using the verifier and received
    // public key.
    srv, err := s.NewServer(v, A)

    // Generate server credentials to send to the user
    s_creds := srv.Credentials()

    // 1. send 's_creds' to the client
    // 2. receive 'm_auth' from the client

    // Authenticate user and generate mutual proof of authentication
    proof, ok := srv.ClientOk(m_auth)
    if ok != nil {
         panic("Authentication failed")
    }

    // 3. Send proof to client

    // Auth succeeded, derive session key
    rawkey := s.RawKey()

Generating new Safe Primes & Prime Field Generators

The SRP library uses a pre-calculated list of large safe prime for common widths along wit their field generators. But, this is not advisable for large scale production use. It is best that a separate background process be used to generate safe primes & the corresponding field generators - and store them in some cache. The function findPrimeField() can be modified to fetch from this cache. Depending on the security stance, the cache can decide on a "use once" policy or "use N times" policy.

The function srp.NewPrimeField() generates and returns a new large safe prime and its field generator.

Building SRP

There is an example program that shows you the API usage (documented above).:

    $ git clone https://github.com/arag0re/go-apple-srp6
    $ cd go-srp
    $ go test -v

Finally, build the example program:

    $ go build -o ex example/example.go
    $ ./ex

The example program outputs the raw-key from the client & server's perspective (they should be identical).

There is also a companion program in the example directory that generates prime fields of a given size:

    $ go build -o pf example/primefield.go
    $ ./pf 1024

The above program can be run to generate multiple fields on the command line:

    $ ./pf 1024 2048 4096 8192

The library uses go modules; so, it should be straight forward to import and use.