Hardness of k-LWE and applications in traitor tracing

San Ling, Duong Hieu Phan, Damien Noel Stehle, Ron Steinfeld

    Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

    20 Citations (Scopus)


    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.
    Original languageEnglish
    Title of host publicationAdvances in Cryptology - CRYPTO 2014: 34th Annual Cryptology Conference, Proceedings
    EditorsJuan A Garay, Rosario Gennaro
    Place of PublicationHeidelberg Germany
    Pages315 - 334
    Number of pages20
    ISBN (Electronic)9783662443712
    ISBN (Print)9783662443705
    Publication statusPublished - 2014
    EventAdvances in Cryptology 2014 - Santa Barbara, United States of America
    Duration: 17 Aug 201421 Aug 2014
    Conference number: 34

    Publication series

    NameLecture Notes in Computer Science
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349


    ConferenceAdvances in Cryptology 2014
    Abbreviated titleCRYPTO 2014
    CountryUnited States of America
    CitySanta Barbara

    Cite this

    Ling, S., Phan, D. H., Stehle, D. N., & Steinfeld, R. (2014). Hardness of k-LWE and applications in traitor tracing. In J. A. Garay, & R. Gennaro (Eds.), Advances in Cryptology - CRYPTO 2014: 34th Annual Cryptology Conference, Proceedings (pp. 315 - 334). (Lecture Notes in Computer Science; Vol. 8616). Springer. https://doi.org/10.1007/978-3-662-44371-2_18