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See detailProvably Solving the Hidden Subset Sum Problem via Statistical Learning
Coron, Jean-Sébastien UL; Gini, Agnese UL

E-print/Working paper (2021)

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 ... [more ▼]

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(mod 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. [less ▲]

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See detailA Polynomial-Time Algorithm for Solving the Hidden Subset Sum Problem
Coron, Jean-Sébastien UL; Gini, Agnese UL

in Advances in Cryptology -- CRYPTO 2020 (2020, August 10)

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 ... [more ▼]

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. [less ▲]

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See detailSupersingular Isogeny-Based Designated Verifier Blind Signature
Sahu, Rajeev Anand UL; Gini, Agnese UL; Pal, Ankan

E-print/Working paper (2019)

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See detailImproved Cryptanalysis of the AJPS Mersenne Based Cryptosystem
Coron, Jean-Sébastien UL; Gini, Agnese UL

in Journal of Mathematical Cryptology (2019)

At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al ... [more ▼]

At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al. described an attack with complexity O(2^(2h)). In this paper, we describe an improvedattack with complexity O(2^(1.75h)) . [less ▲]

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