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Suppose 2 parties A and B wish to setup a common secret key among themselves using DH key exchange technique .
They agree on 619 as the modulus and 3 as primitive root . Party A chooses 16 and party B chooses 15 as their respective
secrets . what is DH key ?

 

A)  21

B) 24

C)  242

D) 223

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The Diffie–Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure channel. This key can then be used to encrypt subsequent communications using a symmetric key cipher.

1. A and B agree to use a modulus p = 619 and base g = 3(primitive root)

2. A chooses a secret integer a = 16, then sends B  H = ga mod p = $3^{16}$ mod $619$ = $223$

3. B chooses a secret integer b = 15, then sends A Ggb mod p = $3^{15}$ mod $619$ = $487$

4. A computes s = Ga mod p = $487^{16}$ mod $619$ = $24$

5. B computes s = Hb mod p = $223^{15}$ mod $619$ = $24$

6. A and B now share a secret i.e $24$ 

                        $OR$

simply The D-H key is $g^{ab}$ mod $p$ = $3^{16*15}$ mod $619$ = $24$

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