@inproceedings{eed8294525fe42a997265ad38d7dd699,
title = "Hardness of k-LWE and applications in traitor tracing",
abstract = "We introduce the k-LWE problem, a Learning With Errors variant of the k-SIS problem. The Boneh-Freeman reduction from SIS to k-SIS suffers from an exponential loss in k. We improve and extend it to an LWE to k-LWE reduction with a polynomial loss in k, by relying on a new technique involving trapdoors for random integer kernel lattices. Based on this hardness result, we present the first algebraic construction of a traitor tracing scheme whose security relies on the worst-case hardness of standard lattice problems. The proposed LWE traitor tracing is almost as efficient as the LWE encryption. Further, it achieves public traceability, i.e., allows the authority to delegate the tracing capability to {"}untrusted{"} parties. To this aim, we introduce the notion of projective sampling family in which each sampling function is keyed and, with a projection of the key on a well chosen space, one can simulate the sampling function in a computationally indistinguishable way. The construction of a projective sampling family from k-LWE allows us to achieve public traceability, by publishing the projected keys of the users. We believe that the new lattice tools and the projective sampling family are quite general that they may have applications in other areas.",
keywords = "Lattice-based cryptography, LWE, Traitor tracing",
author = "San Ling and Phan, {Duong Hieu} and Damien Stehl{\'e} and Ron Steinfeld",
year = "2014",
doi = "10.1007/978-3-662-44371-2_18",
language = "English",
isbn = "9783662443705",
volume = "8616 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer, Springer Nature",
number = "PART 1",
pages = "315--334",
editor = "Garay, {Juan A.} and Rosario Gennaro",
booktitle = "Advances in Cryptology - CRYPTO 2014",
address = "United States",
edition = "PART 1",
note = "34rd Annual International Cryptology Conference, CRYPTO 2014 ; Conference date: 17-08-2014 Through 21-08-2014",
}