Cryptography serves dual purposes: it protects your cities from enemy Spies and enables your Spies to carry out offensive missions more successfully. It's a good go-to policy in the late game, especially if you have a substantial scientific, cultural, or economic advantage over your opponents and they're trying to use their Spies to close the gap.
Civilopedia entry Edit
Cryptography prior to the modern age was primarily a matter of encryption, often simple transposition or substitution cyphers, making a message nonsense without a key. Like a game for bright children. By World War II, however, cryptography was mostly a matter of mathematical theory and computer science … hardly child’s play. Cryptographic algorithms were designed around computational assumptions and integer factorization. At England’s Bletchley Park facility during World War II, research culminated in Colossus – civilization’s first electronic, digital, programmable computer – built to decrypt the Lorenz cipher. Now nations, corporations, and hackers devote immense blocks of computing time and analysis to cryptosystems … creating them and breaking them.