Hardness of k-LWE and Applications in Traitor Tracing

San Ling, Duong Hieu Phan, Damien Stehlé, Ron Steinfeld

    Research output: Contribution to journalArticleResearchpeer-review

    1 Citation (Scopus)


    We introduce the k-(Formula presented.)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 (Formula presented.) traitor tracing is almost as efficient as the (Formula presented.) 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-(Formula presented.) 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.

    Original languageEnglish
    Pages (from-to)1318-1352
    Number of pages35
    Issue number4
    Publication statusPublished - Dec 2017


    • Lattice-based cryptography
    • LWE
    • Traitor tracing

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