RSA

Rivest, Shamir and Adleman published it at MIT in 1977, a year after Diffie and Hellman had shown that asymmetric encryption was possible without showing how. The keys are built from two secret primes p and q; the public key carries their product n = pq. Multiplying is trivial, recovering p and q from n is something nobody knows how to do quickly. GCHQ's Clifford Cocks had found essentially the same scheme in 1973, but it stayed classified until 1997.

RSA is on its way out. Keys need 2048 or 3072 bits to match what a 256-bit elliptic curve gives, signing is slow, and naive implementations leak through padding errors — Bleichenbacher's 1998 attack still resurfaces in new products. TLS 1.3 dropped RSA key exchange entirely and keeps the algorithm only for signatures. A working quantum computer breaks it outright via Shor's algorithm, which is the whole motivation behind post-quantum cryptography.