The study (or art, wisdom, science) of protecting (digital) data by mathematics. More literally, the study of writing in cipher.

Colloquially sometimes called (dark) magic, in the sense of mystery, wonder, marvel, beauty. But also in reference to the inherent abstractness of mathematical concepts.

In practice, a mathematical transformation converts plain data into an unreadable form which conceals the original data. In some scenarios, the transformation is reversible by any party possessing certain secret knowledge, and practically by no other party. A typical example is keeping message content confidential. In other scenarios, such as fingerprinting and thereby uniquely tagging data, the transformation is effectively irreversible.

As main tasks, cryptography secures, authenticates and validates (digital) data.