First-degree prime ideals of composite extensions - Santilli, Giordano; Taufer, Daniele (Journal of mathematical cryptology, 2025)
Let and be linearly disjoint number fields and let be their compositum. We prove that the first-degree prime ideals (FDPIs) of may almost always be constructed in terms of the FDPIs of and , and . We identify the cases where this correspondence does not hold, and provide explicit counterexamples for each obstruction. We show that for every pair of coprime integers , such a correspondence almost always respects the divisibility of principal ideals of the form , with a few exceptions that we characterize. Finally, we establish the asymptotic computational improvement of such an approach, and we verify the reduction in time needed for computing such primes for certain concrete cases.