Suppose that (n, e) is an RSA encryption key, with n = pq, where p and q are large 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 this decryption congruence also holds when gcd(M, pq) > 1.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.