As a software engineer, I'm trying to better understand the concepts behind things I work on daily. In my efforts to understand digital certificates, I started reading up on the specifics of the RSA system and it got me wondering how this is possible, and how the creators knew this would be possible.

I have a math background up to linear algebra/calculus but not much past that. When I look up online the specifics of RSA, I get the "how" but not the "why". I get statements about how the system hinges on the fact that factoring is a difficult problem, and how large prime numbers are used, but not how to actually understand the concept of the system.

From my understanding, it seems like symmetric encryption goes "backwards" when decrypting a message, where as asymmetric encryption goes "forwards" when decrypting, hence the modular arithmetic involved in the algorithm. Is this the concept behind RSA, going forwards to decrypt?