------------------------- m^phi(n) = 1 (mod n) ensure m and n are relative prime m^phi(p) = 1 (mod p) m^phi(q) = 1 (mod q) m^(p-1) = 1 (mod p) m^(q-1) = 1 (mod q) 1 = m^(p-1) (mod p) 1 = m^(q-1) (mod q) Chinese Remainder Theorem 1 = m^(p-1) * m^(q-1) (mod pq) ------------------------