Ghash
In cryptography, Galois/Counter Mode (GCM) is a mode of operation for symmetric-key cryptographic block ciphers that provides both encryption and message authentication in a single pass. It belongs to the class of authenticated encryption with associated data (AEAD) algorithms. In practice, GCM gives a recipient two guarantees at once: the message content was hidden from anyone without the key, and the data arrived exactly as sent. Encrypted web connections, Wi-Fi security, and virtual private networks rely on this property through protocols such as TLS and WPA3. GCM was designed by David A. McGrew and John Viega, first published in 2005, and standardized by NIST in Special Publication 800-38D in November 2007. Galois Message Authentication Code (GMAC) is an authentication-only variant that can form an incremental message authentication code.
GCM uses a 128-bit block cipher (commonly AES) run in counter mode for encryption, and uses arithmetic in the Galois field GF(2128) to compute the authentication tag, hence its name. Because successive ciphertext blocks are produced independently, encryption and decryption can be fully parallelized, in contrast to chaining modes such as cipher block chaining (CBC). GCM was designed to be patent-free.
GCM is widely deployed in network security protocols. It is used in TLS 1.2 and TLS 1.3, IEEE 802.1AE (MACsec) Ethernet security, IPsec, SSH, and other protocols. AES-GCM is included in the NSA's Commercial National Security Algorithm Suite.
Security depends on choosing a unique initialization vector (IV) for every encryption under the same key; reuse of an initialization vector can expose the encryption key and allow forgery. For any given key and initialization vector, GCM is limited to encrypting 239−256 bits of plaintext. The authentication strength of the mode decreases with shorter tag lengths; NIST SP 800-38D recommends tag lengths of at least 96 bits.
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