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RSA (Rivest-Shamir-Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission in such a cryptosystem the encryption key is public and differs from the decryption key which is kept secret (private).
In RSA, this asymmetry is based on the practical difficulty of factoring product of two large primes, "the problem of factoring", the abbreviation RSA is composed of the initial letters of the names of Rivest Ron, ADI Shamir and Leonard Adleman, who first publicly described the algorithm in 1978.
Clifford Cox, an English mathematician, working in the British intelligence Agency government communications (GCHQ), had developed equivalent system in 1973, but it wasn't declassified until 1997.
A user of RSA creates and then publishes a public key based on two large Prime numbers together with an additional value, primes must be kept secret.
Anyone can use the public key to encrypt the message, but published in the moment methods, and if the public key is large enough, only someone who knows the Prime numbers, can decrypt the message.
Violation of RSA encryption is known as the RSA problem, and the question remains as hard as the problem of factoring.
RSA is a slow algorithm, and because of this, he rarely used to directly encrypt the user data, but most often sends RSA encrypted shared key for encryption with a symmetric key, which in turn, can perform bulk operations encryption-decryption at much higher speed.