Cryptology ePrint Archive: Report 2020/461

A Polynomial-Time Algorithm for Solving the Hidden Subset Sum Problem

Jean-Sébastien Coron and 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. While the Nguyen-Stern algorithm works quite well in practice for moderate values of n, we argue that its complexity is actually exponential in n; namely in the final step one must recover a very short basis of a n-dimensional lattice, which takes exponential-time in n, as one must apply BKZ reduction with increasingly large block-sizes. In this paper, we describe a variant of the Nguyen-Stern algorithm that works in polynomial-time. The first step is the same orthogonal lattice attack with LLL as in the original algorithm. In the second step, instead of applying BKZ, we use a multivariate technique that recovers the short lattice vectors and finally the hidden secrets in polynomial time. Our algorithm works quite well in practice, as we can reach n=250 in a few hours on a single PC.

Category / Keywords: public-key cryptography / Subset-sum problem, lattice cryptanalysis, LLL.

Original Publication (with minor differences): IACR-CRYPTO-2020

Date: received 21 Apr 2020, last revised 1 Jun 2020

Contact author: jscoron at gmail com,agnese gini@uni lu

Available format(s): PDF | BibTeX Citation

Version: 20200601:185853 (All versions of this report)

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