If quantum computers were ever invented, they would decimate the infrastructure used to protect online information. Researchers have had to come up with new, post-quantum, encryption schemes to save as much information as possible from quantum hackers.
The National Institute of Standards and Technology has been searching for a post-quantum standard. Three of them use a scheme that is inspired by lattices.
Post-quantum possibilities are different from current standards. They all rely on the same type of math. It could take centuries for a computer to factor a large number into its prime constituents, which is the basis for the security of current cryptography systems. It's hard to decode secrets because of the asymmetric nature of the information.
A quirk of factor makes it vulnerable to be attacked by quantum computers. Stange is a mathematician at the University of Colorado, Boulder. Cryptographers had a new job after Shor, which was to find a novel set of mathematical operations that are easy to do but difficult to reverse.
One of the most successful attempts to date is lattice cryptography. It is based on the difficulty of reverse engineering sums of points.
A lattice is a bunch of points in a regular pattern all over the plane. A friend wants you to name 10 points. He won't draw the entire lattice because he's being difficult. The first point has an x-value of 101 and a y-value of 19 and the second point has coordinates.
When you subtract two points from a lattice, you get a third point in the same lattice. All you have to do is add up the points your friend gave you and then add them up or combine them. You can answer your friend's question if you do this eight different ways.
Your friend isn't happy. He asks you if the point is on the same lattice after giving you the same two points. You will probably end up just guessing and checking to get the answer because this problem is harder than the first one.
You would do the following if you wanted to use lattice cryptography. A friend wants to send you a message. There is a grid of numbers. It has two rows and two columns.
You came up with a secret key that only you know about. 3 and 2 are the secret numbers of your private key. The numbers in the first and second columns are added up. If you add up the results in each row, you can get a third column.
The column should be on the end of the grid. Your public key is in this new three column grid. Don't be afraid to share it!
A real-world scenario won't be easy to understand. Adding noise to your final column is needed to keep hackers from decoding your private key. We are ignoring that step for simplicity.
The public key will be used by your friend to send you a message. She thinks of her own numbers. She adds up the numbers in the first and second rows. She added up the results in each column to get a third row.
The new row is attached to the grid and sent back to you. She would need to make noise to her row.
You will read it now. If your friend's last row is correct, you need to do this. Your private key can be applied to the first two entries. The result should be in line with the last one.
A row with a wrong number can be sent to you by your friend. She knows that the number won't work out for you.
If your friend sends a row where the last number is correct, you will interpret it as a zero. You will interpret a row as a 1 if it is incorrect. The row contains a single bit.
An attacker won't be able to access your private key or your friend's. The attacker won't know if the final number is correct or not without those.
You would like to send a message that is longer than a few words. 100 new columns will be generated if people receive a 100 bit message. The sender of the message will modify the last 100 entries to either a 0 or a 1 for each entry.
lattice cryptography will have many nuances that are not covered in this scenario. It is not worth using the matrix if you want the message to be safe from the eyes. Researchers use matrices to cut down on the number of parameters. There is a whole suite of changes that can be applied to the problem itself.
It is possible that someone will find a fatal flaw in lattice cryptography. There is no guarantee that a particular scheme will work. Until it's cracked, cryptanalysis works. A post-quantum cryptography scheme was cracked using an ordinary laptop. To Stange, the entire project creates an uncomfortable contradiction: "What I find so amazing is that we've built this infrastructure for the human race on the belief that our ability as humans is limited." "It is so backwards."
If you're interested, the answer is 7 [101, 19] - 3 [235, 44].
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