quantum's threat to crypto
yay? nay? math! 🧮
okay, travel time is over (for 2 weeks …), so time to lock back in. i’m gonna teach myself about quantum’s threat to crypto while i have a few hours to kill at the taipei airport. learn with me!
i’ve already briefly broken down what crypto even is, so i’m not going to do that again.
most crypto uses modular arithmetic, which behaves like a one-way function. this means that it’s easy to calculate a final “landing spot” after a set of mathematical jumps; however, as the numbers get significantly large, it is nearly impossible for computers to work in reverse and backtrack exactly how many jumps were taken to get there.
in crypto, the public key is that final landing spot (which anyone can see), while the private key is the specific number of steps (or the “jump count”) it took to reach there. since there are more possible counts than atoms in the universe, a standard computer would have to guess them one by one, which would take trillions of years.
we are not doing allat.
quantum cheats that system because it uses superposition. instead of checking one jump at a time, it creates a wave of all possible jump counts simultaneously. shor’s algorithm, specifically, leverages the fact that these math functions are periodic and it uses quantum interference to cancel out all the wrong keys and amplify the one that represents the function’s period.
once it finds that frequency, it uses a bit of classical math (continued fractions) to instantly calculate the private key.
so, what’s the crypto defense? lattice math!
in modular “clock math,” everything is a circle. quantum computers are built to find the patterns in circles (waves). lattice math is its nightmare: a 500-dimensional closet of junk. instead of a smooth curve or wave, we have a massive grid of points in a space so high-dimensional that we can’t even visualize it.
to crack it, we’d have to find the shortest distance between two points in this 500-dimensional space (shortest vector). quantum fails here because there’s no repeating wave in a lattice, so shor’s algorithm has no frequency to find.
you have to brute force lattice problems .. and that takes a long time.
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