Definition
Cryptography is the practice and study of techniques for secure communication in the presence of an adversary. Its goals are usually summarized as the CIA triad: Confidentiality (only authorized parties can read the message), Integrity (the message has not been altered in transit), and Authenticity (the message is from who it claims to be from). Modern cryptography is grounded in mathematics — particularly number theory, algebra, and probability theory — rather than the obscurity of the algorithm.
Branches Relevant to VPNs
Symmetric cryptography (AES, ChaCha20) handles bulk data encryption. Asymmetric cryptography (RSA, ECC) handles key exchange and digital signatures. Hash functions (SHA-256, SHA-3, BLAKE2) provide integrity and are used to derive keys. Authenticated encryption (AES-GCM, ChaCha20-Poly1305) combines confidentiality and integrity in a single primitive. A VPN protocol composes all of these into a coherent system.
Cryptographic Maturity
Good cryptography depends on more than choosing strong algorithms. Implementation matters enormously — a side-channel attack can leak the key from an otherwise unbroken cipher. Random number generation must be high-quality. Key management — generation, storage, rotation, revocation — is often the weakest link in deployed systems. The history of broken VPNs (PPTP, early WEP, FREAK, Logjam) is a history of correct algorithms paired with weak implementations or weak parameters.