IsogenyPoKviaCanonicalModPolys

Sage scripts for the paper "More Efficient Isogeny Proofs of Knowledge via Canonical Modular Polynomials" (ePrint: 2024/1738)

• The script constraints.sage expresses and verifies all arithmetizations; furthermore it automatically counts the number of constraints, variabls and non-zero entries.
• The script kernel_polynomials.sage verifies the computational claims in the proof of the Reconstruction Theorem.
• The script maximal_primes.sage verifies the computational claims needed to determine the maximal prime for which there exist at least three undirected edges between some pair of vertices in the supersingular isogeny graph (Proposition 22).
• The script splitting_special.sage verifies the claim of Proposition 11 in small prime characteristics, as excluded in the proof.
• The script additional_computations.sage verifies the computational claims of Corollary 5, Lemma 6, Lemma 7, Theorem 9 (excluding the claim relayed to Proposition 22) and Remark 5.