Alice and Bob wish to create a secret key between them using

Alice and Bob wish to create a secret key between them using the Diffie-Hellman key exchange protocol. They select the prime p = 599 and the corresponding primitive root g = 7. Alice chooses her secret integer to be a = 288 and Bob chooses his to be b = 516. Compute the number A that Alice sends to Bob and the number B that Bob sends to Alice. Compute the shared secret Diffie-Hellman key as it would be done on Alice\'s end.

Solution

a=288 b=516 g=7 and p=599

A=g^a (mad p)

A= 7^288 (mod 599)

A=206

B=g^b (mod p)

B=7^516 (mod 599)

B=96

A\'=B^a (mod p)

A\'=96^288 (mod 599)

A\'=564

B\'=A^b (mod 599)

B\'=206^516 (mod 599)

B\'=564

I. alice sends bob the number 206 and bod sends alice the number 96

II. alice and bob\'s shared secret key is 546