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,
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
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).
The host calculates the password verifier using the following formula:
s = randomsalt() (same length as N)
I = H(I)
p = H(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.
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:
- The user will abort if he receives
B == 0 (mod N) or u == 0. - The host will abort if it detects that
A == 0 (mod N). - 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.
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)
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.
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()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()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()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.
There is an example program that shows you the API usage (documented above).:
$ git clone https://github.com/ooozws/go-srp
$ cd go-srp
$ go test -vFinally, build the example program:
$ go build -o ex example/example.go
$ ./exThe 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 1024The above program can be run to generate multiple fields on the command line:
$ ./pf 1024 2048 4096 8192The library uses go modules; so, it should be straight forward to import and use.
The client and server both derive the same value for RawKey(). This is the crux of the SRP protocol. Treat this as a "master key". It is not advisable to use the RawKey() for encryption purposes. It is better to derive a separate key for each direction (client->server and server->client). e.g.,:
c2s_k = KDF(rawkey, counter, "C2S")
s2s_k = KDF(rawkey, counter, "S2C")KDF above can be a reputable key derivation function such as PBKDF2 or Scrypt. The "counter" is incremented every time you derive a new key.
I am not a cryptographer. Please consult your favorite crypto book for deriving encryption keys from a master key.
Here is a example KDF using scrypt:
import "golang.org/x/crypto/scrypt"
// Safe values for Scrypt() parameters
const _N int = 65536
const _r int = 1024
const _p int = 64
// Kdf derives a 'sz' byte key for use 'usage'
func Kdf(key []byte, salt []byte, usage string, sz int) []byte {
u0 := []byte(usage)
pw := append(key, u0...)
k, _ := scrypt.Key(pw, salt, _N, _r, _p, sz)
return k
}Argon is
the new state of the art (2018) key derivation algorithm. The
Argon2id variant is resistant to timing, side-channel and
Time-memory tradeoff attacks. Here is an example using the Argon2id
variant:
import (
"runtime"
"golang.org/x/crypto/argon2"
)
// safe values for IDKey() borrowed from libsodium
const _Time uint32 = 3
const _Mem uint32 = 256 * 1048576 // 256 MB
// Kdf derives a 'sz' byte key for use 'usage'
func Kdf(key, salt []byte, usage string, sz int) []byte {
u0 := []byte(usage)
pw := append(key, u0...)
return argon2.IDKey(pw, salt, _Time, _Mem, runtime.NumCPU(), uint32(sz))
}