Abstract
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.
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Kleinjung, T., Bos, J. W., & Lenstra, A. K. (2014). Mersenne factorization factory. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8873, pp. 358–377). Springer Verlag. https://doi.org/10.1007/978-3-662-45611-8_19
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