I will rate the answer asap as the answer seems correct. Thx

This exercise illustrates another example of a protocol failure (due to Simmons) in volving the RSA Cryptosystem; it is called the "common modulus protocol failure." Suppose Bob has an RSA Cryptosystem with modulus n and encryption exponent b , and Charlie has an RSA Cryptosystem with (the same) modulus n and encryp- tion exponent b2. Suppose also that gcd(bi,b2) - 1. Now, consider the situation that arises if Alice encrypts the same plaintext x to send to both Bob and Charlie Thus, she computes yi- r1 mod n and y2 -x yl to Bob and y2 to Charlie. Suppose Oscar intercepts yl and y2, and performs the computations indicated in Algorithm 5.16. r*2 mod n, and then she sends Algorithm 5.16: RSA coMMON MoDuLUS DECRYPTION(n, bi, b2, yi, y2) return () (a) Prove that the value xi computed in Algorithm 5.16 is in fact Alice's plain- text, x. Thus, Oscar can decrypt the message Alice sent, even though the cryptosystem may be "secure.'" (b) Illustrate the attack by computing x by this method if n - 18721, b - 43, b2-7717, yi-12677 and y2 :-14702. This exercise illustrates another example of a protocol failure (due to Simmons) in volving the RSA Cryptosystem; it is called the "common modulus protocol failure." Suppose Bob has an RSA Cryptosystem with modulus n and encryption exponent b , and Charlie has an RSA Cryptosystem with (the same) modulus n and encryp- tion exponent b2. Suppose also that gcd(bi,b2) - 1. Now, consider the situation that arises if Alice encrypts the same plaintext x to send to both Bob and Charlie Thus, she computes yi- r1 mod n and y2 -x yl to Bob and y2 to Charlie. Suppose Oscar intercepts yl and y2, and performs the computations indicated in Algorithm 5.16. r*2 mod n, and then she sends Algorithm 5.16: RSA coMMON MoDuLUS DECRYPTION(n, bi, b2, yi, y2) return () (a) Prove that the value xi computed in Algorithm 5.16 is in fact Alice's plain- text, x. Thus, Oscar can decrypt the message Alice sent, even though the cryptosystem may be "secure.'" (b) Illustrate the attack by computing x by this method if n - 18721, b - 43, b2-7717, yi-12677 and y2 :-14702