Suppose that Trudy obtains two RSA ciphertext messages, both of which were encrypted with Alice’s public key, that is, Co = Mfi mod TV and C1 = M\ mod TV. Trudy does not know Alice’s private key or either plaintext message.
a. Show that Trudy can easily determine (Mo · M1)e mod TV.
b. Can Trudy also determine (M0 + M1)e mod TV?
c. Due to the property in part a, RSA is said to be homomorphic with respect to multiplication. Recently, a fully homomorphic encryption scheme has been demonstrated, that is, the multiplicative homomorphic property (part a) and the additive homomorphic property (part b) both hold . Discuss some significant potential uses for a practical fully homomorphic encryption scheme.
A digital signature or a MAC can be used to provide a cryptographic integrity check.
a. Suppose that Alice and Bob want to use a cryptographic integrity check. Which would you recommend that they use, a MAC or a digital signature? Why?
b. Suppose that Alice and Bob require a cryptographic integrity check and they also require non-repudiation. Which would you recommend that Alice and Bob use, a MAC or a digital signature? Why?
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