NIST recommends the Advanced Encryption Standard (AES) with Galois/Counter Mode (GCM) as the most efficient technique for Authenticated Encryption with Associated Data (AEAD), outlined in FIPS 197 and SP 800-38D.
Additionally, for hashing purposes, SHA-256, defined in FIPS 180-4, is widely endorsed by NIST for its robustness and secure cryptographic properties.