Private keys
In crypto, a private key is closer to a physical key than a password. It doesn't identify you nor ask for permission, it simply opens the door. If the key fits, then the door is unlocked.
In traditional software, access is checked against role-based access. There's always something in the middle of making a decision. In crypto, there is not necessarily a middle layer, the network simply checks whether the key matches.
Security hinges on how the key is generated, where it exists, and when it's allowed to be used. Once a system signs with it, the outcome is final.
Most of the complexity in crypto comes from trying to wrap traditional controls around that very simple rule.
Related
SciPHR