Suppose that Alice and Bob decide to communicate with RSA algorithm. Given Bob's public key (n, eB) = (7493, 229). a) If

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Suppose That Alice And Bob Decide To Communicate With Rsa Algorithm Given Bob S Public Key N Eb 7493 229 A If 1 (142.75 KiB) Viewed 13 times

Suppose that Alice and Bob decide to communicate with RSA algorithm. Given Bob's public key (n, eB) = (7493, 229). a) If Alice wishes to send Bob the message M = 125, compute the ciphertext. (1 mark) b) Perform the decryption process that would need to be done at Bob's end to decrypt Alice's ciphertext. (4 marks) Given Alice's private key dA = 1805, compute Alice's public key eA using the given modulus n above. (1 mark) d) If Alice were to apply her digital signature to the message M in (a), compute the signature using her private key dA in (c). (1 mark) e) Show how Bob would perform the corresponding authentication on Alice's signature produced in (d). (1 mark) f) = Suppose that Alice wants to send the message M in (a) to Bob and Charles, whose public keys are eв as given above and ec = 2209, respectively. Let gcd (eв, ec) 1, if Eve intercepts both of the ciphertexts C₁ and C₂ that were created using eв and ec respectively, show how she will be able to decrypt the message M. (Hint: Common Modulus Attack on RSA) (12 marks)