Question: Diffie-Hellman and El Gamal Please note: In task b), c), and d), use the square-and-multiply algorithm for the exponentiation of concrete values. State all intermediate
Diffie-Hellman and El Gamal Please note: In task b), c), and d), use the square-and-multiply algorithm for the exponentiation of concrete values. State all intermediate steps. (a) Show concisely that 5 Z17 is an element of maximum order. What is the order? (b) The secret parameters a = 17 and b = 49 are used in the multiplicative group Z73 with the generator = 5. Calculate the public keys A and B and the shared key kAB resulting from the DiffieHellman key exchange. The value x = 36 shall be signed using the El Gamal signature scheme. The system uses the following parameters: Prime number p = 137 and generator = 3. (c) State the public key of the sender. Assume d = 19 is chosen as secret key. (d) kE = 29 is chosen as an ephemeral key. Determine the signature (r, s) for the message x
7. Diffie-Hellman and El Gamal Please note: In task b), c), and d), use the square-and-multiply algorithm for the exponentiation of concrete values. State all intermediate steps. (a) Show concisely that 5Z17 is an element of maximum order. What is the order? (b) The secret parameters a=17 and b=49 are used in the multiplicative group Z73 with the generator =5. Calculate the public keys A and B and the shared key kAB resulting from the DiffieHellman key exchange. The value x=36 shall be signed using the El Gamal signature scheme. The system uses the following parameters: Prime number p=137 and generator =3. (c) State the public key of the sender. Assume d=19 is chosen as secret key. (d) kE=29 is chosen as an ephemeral key. Determine the signature (r,s) for the message x
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