I am currently learning about lattices and came across a Mr.Bill Buchanan video that explains the Ring-LWE problem. I understand how modulo works and quite understand the math behind it.
However, I got stuck by the system of equations that are used in the video!
A = (4 + x + 11x^2 + 10x^3)
S = (6 + 9x + 11x^2 + 11x^3)
e = (0 - x + x^2 + x^3)
what is the result of B = A*S + e over the ring Z13[x]/[x^4+1]
He got the answer: 10 + 5x + 10x^2 + 7x^3
How did he get to the final answer using the provided quotient ring?
Can someone please explain in step-by-step solution?
Thank you in advance for helping me understand.
Here is a screenshot from the actual video: the actual equation system
By @coffeemath "To begin, multiply and add the polynomials in the usual way. Then you will have a sixth degree result. Two things are involved to get the result in Z13[x]. First, the degree 4,5,6 terms can be combined with lower degree since x^4=-1, x^5=-x, and x^6=-x^2. second, coefficients may be reduced mod 13."
Thank you very much for your help. Your comment solved the issue