I’m no cryptographer, so take this with a good heap of salt.

Basically, all encryption multiplies some big prime numbers to get the key. Computers are pretty slow at division and finding the right components used to create the key takes a long time, it’s basically trial and error at the moment.
If you had an algorithm to solve for prime numbers, you could break any current encryption scheme and obviously cause a lot of damage in the wrong hands.

I haven’t seen that show, but it sounds like it has a basis in reality: there has been a real concern that quantum computers might be able to break much of current encryption because they are far quicker than classical computers at problems like finding the prime factors of a number, and widely used schemes like RSA encryption depend on that being hard to do. And that could be fairly catastrophic, not only for current communications and for data encrypted at rest, but because communications data can be collected now and decrypted later when the technology becomes available. As far as we know, no one has done it yet, but quantum computers are developing rapidly so the day may well come. So there’s a reason to move to encryption algorithms that are hard for quantum computers, even before such computers become a practical reality.