system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What is "lattice based asymmetric cryptography"?
gpt
Asymmetric cryptography is a kind of encryption where there are two keys, a public key and a private key. Generally, you keep the private key secret and publish the public key for anyone to see. A message encrypted using one key is decrypted using the other. Anyone can send you a secret message by encrypting it with your public key, so that only you can decrypt it using your private key. In addition, you can “sign” a message by encrypting it with your private key; then, anyone can decrypt it using your public key, and they can be sure that you wrote the message.

Asymmetric cryptography is very important to modern commerce. Secure websites (which these days are most commercial websites) use asymmetric cryptography to ensure that no one can impersonate them; that is, when you're talking to your bank, you're not really talking to a hacker's website instead.

The most common asymmetric cryptography system is RSA, which uses math involving factoring large numbers. It's hard to “break” RSA (decrypt a message without the appropriate key) because as far as we know it's hard to factor large numbers. However, we know that a sufficiently powerful quantum computer could easily factor large numbers and thus break RSA.

Certain mathematical problems involving structures called “lattices” are believed to be hard to solve, even on a quantum computer. New cryptographic systems have been devised that rely on lattice problems to ensure security instead of integer factorization. These systems, or systems like them, could someday supplant existing asymmetric systems like RSA if it looks like quantum computing will be a practical reality.