Why is SRP not equivalent to plain text?

Question

About SRP: http://en.wikipedia.org/wiki/Secure_remote_password_protocol

I see that generating the session key (K) is completely safe, but in the last step the user sends a confirmation K (M). If the network is unsafe, and the attacker in the middle is counting M, will he be able to authenticate without the right?

Answer 1

A bit of background

Well-known values ​​(predefined):

  n    A large prime number. All computations are performed modulo n.
  g    A primitive root modulo n (often called a generator).

User password is set as:

x = H(s, P)
v = g^x 

  H()  One-way hash function
  s    A random string used as the user salt
  P    The user password
  x    A private key derived from the password and salt
  v    The host password verifier

Authentication:

+---+------------------------+--------------+----------------------+
|   | Alice                  | Public Wire  | Bob                  |
+---+------------------------+--------------+----------------------+
| 1 |                        |        C --> | (lookup s, v)        |
| 2 | x = H(s, P)            | <-- s        |                      |
| 3 | A = g^a                |        A --> |                      |
| 4 |                        | <-- B, u     | B = v + g^b          |
| 5 | S = (B - g^x)^(a + ux) |              | S = (A · v^u)^b      |
| 6 | K = H(S)               |              | K = H(S)             |
| 7 | M[1] = H(A, B, K)      |     M[1] --> | (verify M[1])        |
| 8 | (verify M[2])          | <-- M[2]     | M[2] = H(A, M[1], K) |
+---+------------------------+--------------+----------------------+

    u    Random scrambling parameter, publicly revealed
  a,b    Ephemeral private keys, generated randomly and not publicly revealed
  A,B    Corresponding public keys
  m,n    The two quantities (strings) m and n concatenated
    S    Calculated exponential value 
    K    Session key

The answer to your question:

, K (= ) , , .
P, 2, , v, S .

K, , , , . , , , .

Answer 2

K.

MITM:

Alice <-K-> Bob

K,

MITM:

Alice <-K1-> Eve <-K2-> Bob

K1, , , K2.