Engineering↗
Atkin-Morain Elliptic Curve Primality Proving
ECPP: using complex multiplication to construct curves of known order, avoiding point counting entirely.
Every page in the KEVOS library tagged certificate. 5 pages.
ECPP: using complex multiplication to construct curves of known order, avoiding point counting entirely.
What a primality certificate is, why verification is cheaper than production, and what a certificate does and does not guarantee.
Why proving compositeness is easy, proving primality is harder, and factoring is harder still — and what this asymmetry means in practice.
Primality proving by elliptic curves with known point counts, its recursive certificate, and the point-counting bottleneck.
Proving primality from a partial factorisation of one less than the candidate, and the certificate this produces.