RSA is based on the practical difficulty of factoring the product of two large prime numbers, the factoring problem.

Note: A user of RSA creates and then publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers must be kept secret. Anyone can use the public key to encrypt a message, but with currently published methods, if the public key is large enough, only someone with knowledge of the prime numbers can feasibly decode the message.
References: https://en.wikipedia.org/wiki/RSA_(cryptosystem)