SRP Protocol Design

SRP is the newest addition to a new class of strong authentication protocols that resist all the well-known passive and active attacks over the network. SRP borrows some elements from other key-exchange and identification protcols and adds some subtle modifications and refinements. The result is a protocol that preserves the strength and efficiency of the EKE family protocols while fixing some of their shortcomings.

The following is a description of SRP-6 and 6a, the latest versions of SRP:

 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

The host stores passwords using the following formula:

 x = H(s, p) (s is chosen randomly)
 v = g^x (computes password verifier)

The host then keeps {I, s, v} in its password database. The authentication protocol itself goes as follows:

User -> Host: I, A = g^a (identifies self, a = random number)
Host -> User: s, B = kv + g^b (sends salt, b = random number)
 Both: u = H(A, B)
 User: x = H(s, p) (user enters password)
 User: S = (B - kg^x) ^ (a + ux) (computes session key)
 User: K = H(S)
 Host: S = (Av^u) ^ b (computes session key)
 Host: K = H(S)

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

User -> Host: M = H(H(N) xor H(g), H(I), s, A, B, K)
Host -> User: H(A, 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.

A paper describing this protocol is also available, as well as a conference paper describing an older version of the protocol.

For historical interest, descriptions of the previous versions of SRP are available on this site:

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