AES

It came out of an open competition: NIST called for a replacement for the ageing DES in 1997, fifteen submissions were picked apart in public over three years, and the Belgian Rijndael by Joan Daemen and Vincent Rijmen won in 2000. That the process was transparent accounts for much of the trust in it — compare DES, whose design choices the NSA never explained. It was ratified as FIPS 197 in 2001.

The cipher runs 10 to 14 rounds of substitution, row shifts, column mixing and key addition. After 25 years there is no practical attack on full AES; what gets broken is implementations, not the mathematics — side-channel leakage through cache timing was a genuine problem until Intel added AES-NI instructions in 2010, which made it both faster and constant-time. AES on its own provides confidentiality but no authenticity, which is why real deployments always use a mode such as AES-GCM.