Rivest, Shamir and Adleman (RSA) created one of the first practical public-key cryptosystems. In their scheme the encryption key is public and the decryption key is kept secret. Breaking RSA encryption is possible but success depends on the key length. The RSA Factoring Challenge led to the discovery of prime factors that can break RSA encryption. RSA-100 was cracked in a few days. RSA-768 fell on 12th December 2009 after a 2 year computation.
RSA has other weaknesses that can be mitigated but it is generally considered that a key length over 1024 bits is sufficient, and for good measure RSA-2048 and RSA-4096 are ideal, at least until quantum computers make further progress on factoring primes. However RSA-4096 has gained notoriety because it has been used by malware authors to encrypt data and demand payment for the decryption key. Ransomware, as it is known, can use other cipher suites as well but the choice of RSA-4096 is being used for dramatic effect.