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apple account login srp-6a protocol

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)

Diff between standard and apple

 u = H(A,B)  ==> u = sha256(A+B) 
 k = H(N,g)  ==>  k = sha256(N+g)  N is 256byte big-endian order,  g is256 byte big-endian order bytes
 x = H(s,p)  ==> apple's s => H(":"+P) without username
 P password field P = hmac(pass, salt, iter) where pass = sha256(password_text)

Apple M1 field

i = H(g) xor H(N)
M1 = H(i) + H(I) + H(salt) + H(A) + H(B) + H(K) 
+  ==>  sha256_update

x-apple-i-md pairs

It's apple device time based token pairs. the token ticket is stored on akd-container-data//Library/adi.pb 
This file can store one or more  accounts device token ticket. when a device is newly active the akd process
exchange an apple signed binary blob. the ticket is based on adid process but the code is obfuscated by 
fairplay after-clang-obj compiler engine. it's hard to know what happened in the adid. Need this web-service?
contact me. 

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iOS/macOS login algorithm gsa

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