In a Post Quantum Computing World: For Robust Cooking — You Need a Bit of Oil and Vinegar

I’m going to try and explain the Unbalanced Oil and Vinegar (UOV) scheme for a quantum robust cryptography method with asymmetric encryption (and where we create a public key and a private key). It is defined as a multivariate polynomial method. So let’s start nice and simple …

“Okay”, your teacher says, solve “x² + 2 x = 8”, and you quickly say “I think that x is equal to 2”.

Now the teacher says, “Solve: 2x + y = 1 and 3x + y = 7”,

And you quickly do a calculation and put up your hand … “I think x is 2 and y is 1”. “Well done”, says the teacher, “And now solve…

5 x+ 4y + 10 w + 9 z = 99
6 x + 3 y + 2 w + 3 z =38
8 x + 2 y + 7 w + z = 51
x + 9 y + 4 w + 6 z =57

[The answer is below]

Things now get a bit difficult for you, as this is an NP-hard mathematical problem, where we would require significant computing power to solve large equations with many variables.

If we just have one variable, we can use the least mean squares method to compute the values. For example if we have:

x² + 2 x - 8 = 0