Category
7 articles in this category.
The Merkle-Hellman knapsack cryptosystem hides an easy subset sum problem behind modular multiplication. Learn how its keys, encryption, and decryption work, and watch a lattice reduction attack with the LLL algorithm recover messages from the public key alone.
22 min read
The Rabin cryptosystem encrypts by squaring a number modulo n = pq. Learn how decryption finds four square roots with the Chinese remainder theorem, why redundancy is needed, why breaking it is as hard as factoring, and why a chosen-ciphertext attack still defeats the plain version.
18 min read
DSA was the U.S. government's answer to a simple question: how do you prove a message came from you, without RSA's patent? Learn how the Digital Signature Algorithm works, and why a single reused number sank Sony's PS3 security.
9 min read
What if you could add two numbers together without ever decrypting them? Paillier encryption makes that possible. It's the mathematical trick behind private vote tallying and secure multi-party computation.
8 min read
RSA made public-key cryptography practical for the world. Here's how it works, why it's secure, and where it's headed as quantum computing looms.
18 min read
Schnorr signatures are what DSA might have been if a 20-year patent hadn't gotten in the way. Simpler, provably secure, and now at the heart of Bitcoin's Taproot upgrade: here's how they work.
8 min read
Diffie-Hellman solved cryptography's oldest problem: sharing a secret over a channel anyone can watch. Here's the math, and how it still secures the web.
14 min read
