RSA is a public-key cryptosystem invented at MIT in 1977 by Ronald Rivest, Adi Shamir, and Leonard Adleman, whose surnames give the scheme its name. It was the first practical realization of the idea proposed in Diffie and Hellman’s “New Directions in Cryptography”: a method by which two parties can communicate securely without first sharing a secret key.
In RSA, each user holds a public key, which anyone may use to encrypt a message, and a private key, which only the owner can use to decrypt it. The two keys are mathematically linked through a pair of large prime numbers. The published RSA paper describes how to encrypt and decrypt messages and how to produce digital signatures using the same machinery.
The security of RSA rests on the practical difficulty of factoring: it is easy to multiply two large prime numbers together, but extremely hard to recover those primes from their product. As the RSA paper explains, an adversary who could factor the public modulus could break the system, but no efficient general factoring method is known for sufficiently large numbers.
Because the same key pair supports both confidential messaging and digital signatures, RSA became a foundational tool for secure communication and authentication on the internet, underpinning protocols and systems used far beyond its original academic context.