Hello, This question been confusing me i been trying to work it on all day but no luck. Provide a clear explanation and please make it clear to understand and read.

Thank you

Rose wants to break a version of the RSA algorithm des1gned by Alice, Bob, and Joey. Alice, Bob, and Joey have chosen a number n, and two public keys 6; and eg that are relatively prime. There are also two private keys (2}, d2, corresponding to the public keys e; and 82, respectively. Alice, Bob, and Joey agree that every message sent to them needs to be encrypted twice, each time with a diHerent public key. That, is, if Tom wants to send a message m to Alice, Bob, and Joey, then he should send ciphertexts c1 and c2 computed as follows: E51 c1 E m [mod 10.), c2 E me2 (mod 71). After receiving Tom '8 ciphertexts, Alice, Bob, and Joey m ade public 73, 61, eg, c1, c2. (a) Rose has announced that she has broken the algorithm of Alice, Bob, and Joey without knowing the private keys (2'; and d2. Gully has seen the workings of Rose and has conrmed that Rose is right. Please explain how Rose broke the algorithm. Your solution cannot be based on factoring 73; solutions that are based on the factorisa tion on 72 won 't be accepted. (b) For the tuple 72 = 11021, e; : 5, 632 = 19, c1 = 3302, and c2 = .9049, Use Rose 's idea to nd the message m that Tom sent. Part (a) Receives 8 marks for a correct general analysis that will work for every tuple n, 61, 82, c1, c2, with each step well justied. For different levels of correctness, the student receives between 7 and 0 marks. Part (b) Receive 10 marks for correctly computing the message m. This includes 5 marks for applications of the Euclidean algorithm followed by the extended Euclidean algorithm, and 2 marks for the computation of a relevant inverse, and 2 marks for giving m. For different levels of correctness, receives between 9 and 0 marks