Suppose that Trudy obtains two RSA ciphertext messages, both of which were encrypted with Alice's public key, that is, C o = Mfi mod TV and C 1 = M\ mod TV. Trudy does not know Alice's private key or...

Suppose that Trudy obtains two RSA ciphertext messages, both of which were encrypted with Alice's public key, that is, C_o
= 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 (M_o
· 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 [67]. Discuss some significant potential uses for a practical fully homomorphic encryption scheme.