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**Authenticated Key Agreement Protocol (KAP) with RSA signature**

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.

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