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

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2 Suppose That Alice And Bob Decide To Communicate With Rsa Algorithm Given Bob S Public Key N Eb 7493 229 A 1 (145.74 KiB) Viewed 18 times

2. 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) c) Given Alice's private key dA = 1805, compute Alice's public key e 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) 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)