TY - JOUR
AU - Coron, Jean-Sébastien
AU - Gini, Agnese
PY - 2022/03/23
Y2 - 2024/05/20
TI - Provably Solving the Hidden Subset Sum Problem via Statistical Learning
JF - Mathematical Cryptology
JA - mathcryptology
VL - 1
IS - 2
SE - Articles
DO -
UR - https://journals.flvc.org/mathcryptology/article/view/130558
SP - 70-84
AB - <p>At Crypto ’99, Nguyen and Stern described a lattice based algorithm for solving the hidden subset sum problem, a variant of the classical subset sum problem where the <em>n</em> weights are also hidden. As an application, they showed how to break the Boyko et al. fast generator of random pairs (<em>x</em>, <em>g<sup>x</sup></em> (mod <em>p</em>)). The Nguyen-Stern algorithm works quite well in practice for moderate values of <em>n</em>, but its complexity is exponential in <em>n</em>. A polynomial-time variant was recently described at Crypto 2020, based on a multivariate technique, but the approach is heuristic only. In this paper, we describe a proven polynomial-time algorithm for solving the hidden subset-sum problem, based on statistical learning. In addition, we show that the statistical approach is also quite efficient in practice: using the FastICA algorithm, we can reach <em>n</em> = 250 in reasonable time.</p>
ER -