Homomorphic Encryption, Optical Computing, Silicon Photonics, Post Quantum Cryptography.
adding (3 + x) and (2+x) gives 5 + 2x (also a polynomial). Just as we did for the integers, we can also define a polynomial quotient ring. Particularly common quotient rings in RLWE are and Polynomial multiplication is fairly simple for small polynomials, but can get complicated very quickly. If