One of the most difficult problems in cryptographic key management is keeping a secret key safe from both compromise and loss. If you don't make enough backups, the key might be destroyed in a hardware failure or natural disaster. But if any backup is compromised, the key is compromised. Rather...

Number theory is, roughly speaking, the study of properties of integers. Often a problem which is easy for real numbers, such as factoring or linear programming, seems to be considerably more difficult when restricted to integers (in fact, integer programming is NP-hard). Much of the focus of modern...