2014/01/01 by Thorsten Kleinjung, Joppe W. Bos, Arjen K. Lenstra · 1 citation
Computer Science · Engineering · #Cryptography and Data Security #Cryptography and Residue Arithmetic #graph theory and CDMA systems
paper · pdf · doi:10.1007/978-3-662-45611-8_19
openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present work in progress to completely factor seventeen Mersenne numbers using a variant of the special number field sieve where sieving on the algebraic side is shared among the numbers. It is expected that it reduces the overall factoring effort by more than 50%. As far as we know this is the first practical application of Coppersmith’s “factorization factory” idea. Most factorizations used a new double-product approach that led to additional savings in the matrix step.