Following questions are based on RSA algorithm. (a) (5 points) Given n = 221 and e...

 

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Following questions are based on RSA algorithm. (a) (5 points) Given n = 221 and e = 5, find d? (b) (5 points) Given n = 3937 and e = 17, find d? (c) (5 points) Given p = 19, q = 23, and e = 3, find n, (n), and d? (d) (5 points) Bob chooses 7 and 11 as p and q prime numbers. Now he chooses two exponents e to be 13, then d is 37. Note e *d mod 60 = 1 i.e. they are inverse to each other. Now imagine that Alice wants to send the plaintext 5 to Bob. She uses RSA algorithm to encrypt the message (perform encryption). Also, show your work how Bob perform decryption operation in order to extract plaintext. (e) (10 points) Compute the two public keys and the common session key for the Diffie-Hellman key exchange schema with parameters p = 29 and a = 2. Choose two secret key Xa = 5 and Xb = 12. (f) (10 points) Alice and Bob want to exchange the session keys to each other using Diffie-Hellman key exchange algorithm. They agree on prime number q = 353 and a =3. Alice and Bob choose secret key Xa = 97 and Xb = 233 respectively. Compute respective public keys and shared session keys? Following questions are based on RSA algorithm. (a) (5 points) Given n = 221 and e = 5, find d? (b) (5 points) Given n = 3937 and e = 17, find d? (c) (5 points) Given p = 19, q = 23, and e = 3, find n, (n), and d? (d) (5 points) Bob chooses 7 and 11 as p and q prime numbers. Now he chooses two exponents e to be 13, then d is 37. Note e *d mod 60 = 1 i.e. they are inverse to each other. Now imagine that Alice wants to send the plaintext 5 to Bob. She uses RSA algorithm to encrypt the message (perform encryption). Also, show your work how Bob perform decryption operation in order to extract plaintext. (e) (10 points) Compute the two public keys and the common session key for the Diffie-Hellman key exchange schema with parameters p = 29 and a = 2. Choose two secret key Xa = 5 and Xb = 12. (f) (10 points) Alice and Bob want to exchange the session keys to each other using Diffie-Hellman key exchange algorithm. They agree on prime number q = 353 and a =3. Alice and Bob choose secret key Xa = 97 and Xb = 233 respectively. Compute respective public keys and shared session keys?