@inproceedings{costello2021sieving,
author = {Costello, Craig and Meyer, Michael and Naehrig, Michael},
title = {Sieving for Twin Smooth Integers with Solutions to the Prouhet-Tarry-Escott Problem},
booktitle = {EUROCRYPT 2021},
year = {2021},
month = {October},
abstract = {We give a sieving algorithm for finding pairs of consecutive smooth numbers that utilizes solutions to the Prouhet-Tarry-Escott (PTE) problem. Any such solution induces two degree-n polynomials, a(x) and b(x), that differ by a constant integer C and completely split into linear factors in \(\mathbb [Z][x]\). It follows that for any \(\ell \in \mathbb [Z]\) such that \(a(\ell ) \equiv b(\ell ) \equiv 0 \bmod [C]\), the two integers \(a(\ell )/C\) and \(b(\ell )/C\) differ by 1 and necessarily contain n factors of roughly the same size. For a fixed smoothness bound B, restricting the search to pairs of integers that are parameterized in this way increases the probability that they are B-smooth. Our algorithm combines a simple sieve with parametrizations given by a collection of solutions to the PTE problem.},
publisher = {Springer},
url = {http://approjects.co.za/?big=en-us/research/publication/sieving-for-twin-smooth-integers-with-solutions-to-the-prouhet-tarry-escott-problem-2/},
pages = {272-301},
}