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CM-based factorization

Complex multiplication based factorization. This repository contains proof of concept factorization code and scripts used in experiments.

Proof of concept script usage

Generating CM primes:

sage cm_factor.sage --action generate --prime-bits 64
16344322632527439553

CM factorization:

sage cm_factor.sage -N 158697752795669080171615843390068686677 -D 11
Factorization of N: 158697752795669080171615843390068686677 is: 
14793660019451035033 * 10727416514034371869

Advanced usage script

More complex script that was used to run experiments covered in the paper is experiments.sage. It covers distributed computation of the factorization, class number sampling, batch BCD computation, Hilbert polynomial generation, primorial D computation, benchmarking.

Dependencies

Sage 8 is required. Included packages coloredlogs, humanfriendly are optional.