Introduction to ciphers and substitution. Alice and Bob and Carl and Julius: terminology and Caesar Cipher ; The key to the matter: generalizing the Caesar Cipher ; Multiplicative ciphers ; Affine ...

Hard problems are usually not a welcome sight. But cryptographers love them. That’s because certain hard math problems underpin the security of modern encryption. Any clever trick for solving them ...

Apple says testing missed flaws in new encryption designed to protect against future attacks from quantum computers, so it turned to mathematical proofs to make sure the code works correctly before ...

The company has made public the mathematics behind its post-quantum encryption verification, setting a challenge to the entire industry to prove its own code is equally secure.

This article seeks to provide a practical understanding of the risks posed by quantum computing on modern day encryption standards. In assessing those risks, companies and individuals should consider ...