RSA cryptosystem

The RSA (Rivest–Shamir–Adleman) cryptosystem is a family of public-key cryptosystems (one of the oldest), widely used for secure data transmission. The initialism "RSA" comes from the last-names of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ), the British signals intelligence agency, by the English mathematician Clifford Cocks. That system was declassified in 1997. RSA is used in digital signature such as RSASSA-PSS or RSA-FDH, public-key encryption of very short messages (almost always a single-use symmetric key in a hybrid cryptosystem) such as RSAES-OAEP, and public-key key encapsulation. In RSA-based cryptography, a user's private key—which can be used to sign messages, or decrypt messages sent to that user—is a pair of large prime numbers chosen at random and kept secret. A user's public key—which can be used to verify messages from the user, or encrypt messages so that only that user can decrypt them—is the product of the prime numbers. The security of RSA is related to the difficulty of factoring the product of two large prime numbers, the "factoring problem". Breaking RSA encryption is known as the RSA problem. Whether it is as difficult as the factoring problem is an open question. There are no published methods to defeat the system if a large enough key is used.