Searchable encryption and IND$-$CPA security. As you have seen in the class, the

ciphertext of IND$-$CPA security of public key encryption does not leak any single bit of information.

Now consider encrypted database entries c$1$; c$2$; : : : ; c$`,$ where ci $=$ Enc$($pk;mi$)$ for a message mi$.$ The

database manager still wants to support basic database operations such as search, sort and more. Suppose

we design a special order preserving encryption which satises that Enc$($pk; x$)$ Enc$($pk; y$),$ i x y$.$

This naturally supports the sort operation on ciphertexts. Could you nd an issue with such kind

of order preserving encryption that everyone can easily crack the plaintext: i$.$e$.,$ given any ciphertext

c $=$ Enc$($pk;m$)$ for some unknown message m $($assuming the size of message is known, with $100-$bits$),$

anyone can easily gure out the value of m$.$