>>106160514I didn't actually answer anon
>>106157467, fug.
The simplest example comes from discrete logarithm: you take a special object "g" such that it is very efficient to compute it's powers: g^5, g^34, g^23423432, ...
As it turns out however, it is very hard to inverse this operation in some particular cases. If I show you h=g^345, you would have a hard time telling me that it's actually 345 in the exponent.
In this setting, your secret key would be 345 and your public key g^345. You cannot deduce the secret key from the public one.
Now this isn't unbreakable per se, it is simply believed that solving this problem is currently "hard". So when you read papers on cryptosystems build on this one particular problem, the discrete logarithm, you see theorems like "Assuming the hardness of the discrete logarithm, our encryption scheme is ... secure."