Suppose that (n,e) is an RSA encryption key, with n = pq

Chapter 4, Problem 28E

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Suppose that (n,e) is an RSA encryption key, with n = pq are larging primes and gcd(e,(p – 1)(q – 1)) =1. Furthermore, suppose that d is an inverse of e modulo (p – 1)(q – 1).Suppose that C ? Me(mod pq). In the text we showed that RSA decryption, that is the congruence Cd ? M (mod pq) holds when gcd(M,pq) = 1. Show that is decryption congruence also holds when gcd(M,pq) > 1. [Hint : Use congruences modulo p and modulo q and apply the Chinese remainder theorem]

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