Authenticated KAP with RSA

This protocol is executed between Student Alice (You) and Mentor Bob.

Parameter values sent by Alice are included in brackets [ ] and must NOT be entered in the corresponding input fields.

The following functions are used in the protocol:

>>mod_exp(g,x,p)

>>randi(z)

>>genprime(nob)

>>genstrongprime(nob)

>>eeuklid(e,φ)

1. Generate two prime numbers p and q having length less than 20 bits using function genprime(). Send numbers [p,q] for verification to the Mentor.

2. Calculate value n=p*q and Euler's totient function's value φ=(p-1)*(q-1). Send [n,φ] for verification to the Mentor.

3. Choose RSA exponent e satisfying condition gcd(e, φ)=1 and private key d using extended Euclidean algorithm. Send [e,d] for verification to the Mentor.

4. Generate prime number p', private key x, where 1 < x < p' - 1 and find generator g. Send [p',g,x] for verification to the Mentor.

5. Find your public key PuK_A = g^x mod p' and sign it with RSA parameters. Send  [PuK_A,s_A] for verification to the Mentor.

6. Mentor sent his parameters (PuK_B,s_B,e_m,n_m). Verify signature and form key pair K_ab. Send [K_ab] for verification to the Mentor.