Alice and Bob decide to use RSA public key cryptosystem to share secret message. Alice publishes...

 

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Alice and Bob decide to use RSA public key cryptosystem to share secret message. Alice publishes her RSA public key: modulus N = 55 and exponent e = 7. . . If Bob wants to send Alice the message m = 27. What ciphertext does Bob send to Alice? If Alice receives another ciphertext c = 2 from Bob, what is the corresponding plaintext? Remark: this problem tests your understanding of the RSA public key cryptosystem. 1. For n=pq, where p and q are distinct odd primes, define (n)= (p-1)(q-1) gcd(p-1,q-1) Suppose that we modify the RSA cryptosystem by requiring that ed=1 mod (n). a. Prove that encryption and decryption are still inverse operations in this modified cryptosystem. b. If p=37, q=79, and e-7, compute d in this modified cryptosystem, as well as in the original RSA cryptosystem. Alice and Bob decide to use RSA public key cryptosystem to share secret message. Alice publishes her RSA public key: modulus N = 55 and exponent e = 7. . . If Bob wants to send Alice the message m = 27. What ciphertext does Bob send to Alice? If Alice receives another ciphertext c = 2 from Bob, what is the corresponding plaintext? Remark: this problem tests your understanding of the RSA public key cryptosystem. 1. For n=pq, where p and q are distinct odd primes, define (n)= (p-1)(q-1) gcd(p-1,q-1) Suppose that we modify the RSA cryptosystem by requiring that ed=1 mod (n). a. Prove that encryption and decryption are still inverse operations in this modified cryptosystem. b. If p=37, q=79, and e-7, compute d in this modified cryptosystem, as well as in the original RSA cryptosystem.