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About RSA, please answer the following questions.

(a) Suppose p=11 and q=7. What is ? (n), where n=p?q?

(b) If the public key e is 11, find the private key d.

(c) If the ciphertext is 4, what is the plaintext?

(d) For encryption, i.e., M11 (mod n), what is the number of multiplications to calculate M11 by using direct multiplication?

(e) Repeat (d) but using square and multiply algorithm.

(f) Please show two reasons why we need Hash function in RSA signature algorithm.

(g) Please explain why we can reduce the exponential computation by half when using Chinese Remainder Theorem

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