Non-commutative cryptography

So imagine you and your friend are playing with some blocks. You have a red block and a blue block and your friend has a green block and a yellow block.

If you both follow the same rule that the red block always goes first, no matter what, then it's easy to predict what will happen. You'll put down the red block and then your friend will put down their green block. Then you'll put down the blue block and your friend will put down the yellow block.

But what if you and your friend don't follow the same rule? What if you decide that you'll always put down the red block first, but your friend decides that they'll always put down their yellow block first? Then things get tricky. You might put down your red block and your friend will put down their yellow block. Then you might put down your blue block and your friend might put down their green block. It becomes harder to predict what will happen because you and your friend aren't following the same rule.

Non-commutative cryptography is like that. It's a way of encrypting information so that it's hard to predict what will happen if two people are using different rules. In cryptography, we're often trying to keep information secret from other people who might want to steal it. Non-commutative cryptography helps us do that by making it harder to predict what will happen if someone tries to intercept our encrypted information.