Answer following accordibg to RSA Cryptosystem

 

(a.) (2 points) Suppose that in addition to knowing the published modulo n = p. q and encryption exponent e, Eve also knows the sum p+q. Can Eve discover the decrypting factor? Explain how she can find d, or why it is impossible for her to do so. (b.) (6 points) Suppose Alice and Bob want to use RSA cryptosystem with modulus n = 11413 = 101 113 and the encryption factor e = 7467. i. If Alice's plaintext is m= 2. What is her corresponding ciphertext? ii. The ciphertext c= 5859 was obtained from this RSA algorithm. Decrypt it. (c.) (2 points) Explain why the exponents e = 1 and e= 2 should never be used as encryption factors in RSA.