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. This connotation refers to the inherent abstractness of underlying mathematical concepts. But also to the capability of achieving seemingly paradox tasks, such as demonstrating knowledge of secret data without revealing the data itself.

In practice, a mathematical transformation converts data into an incomprehensible form which conceals the original data. In some scenarios, the transformation is reversible by any party possessing a certain secret, and practically by no other party. A typical example is keeping message or file 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.