From Convolution to Negacyclic Ring Arithmetic

Every code listing from this chapter of Applied Post-Quantum Cryptography — 2 in total, 2 runnable here. Edit any cell and press Run.

The book's snippets build on each other down the chapter, but a Sage Cell kernel runs one cell and keeps no state afterwards, so each cell replays the earlier listings with apqc_book. That call is the only thing added to the book's own code.

← the playground

Listing 1 — A reproducible Sage experiment

The following experiment uses one field, one input vector, and the negacyclic matrix on both sides of the comparison.

Listing 2 — A cyclic comparison

It is useful to see the conventional circulant case too, provided it is labelled correctly. This version changes both the matrix and the quotient modulus to x⁴-1: