Welcome to the resource topic for 2021/1007
Title:
Provably Solving the Hidden Subset Sum Problem via Statistical Learning
Authors: Jean-Sebastien Coron, Agnese Gini
Abstract: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 n weights are also hidden. As an application, they showed how to break the Boyko et al. fast generator of random pairs (x,g^x \pmod{p}). The Nguyen-Stern algorithm works quite well in practice for moderate values of n, but its complexity is exponential in n. 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 n=250 in reasonable time.
ePrint: https://eprint.iacr.org/2021/1007
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