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Cryptographic Functions from Worst-Case Complexity Assumptions

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Book cover The LLL Algorithm

Part of the book series: Information Security and Cryptography ((ISC))

Abstract

Lattice problems have been suggested as a potential source of computational hardness to be used in the construction of cryptographic functions that are provably hard to break. A remarkable feature of lattice-based cryptographic functions is that they can be proved secure (that is, hard to break on the average) based on the assumption that the underlying lattice problems are computationally hard in the worst-case. In this paper we give a survey of the constructions and proof techniques used in this area, explain the importance of basing cryptographic functions on the worst-case complexity of lattice problems, and discuss how this affects the traditional approach to cryptanalysis based on random challenges.

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Acknowledgements

This work was supported in part by NSF grant CCF-0634909. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of California at San Diego, La Jolla, CA, 92093, USA

    Daniele Micciancio

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  1. Daniele Micciancio
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Correspondence to Daniele Micciancio .

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  1. Dépt. Mathématiques et d'Informatique, Ecole Normale Supérieure, rue d'Ulm 45, Paris CX 05, 75230, France

    Phong Q. Nguyen

  2. Dept. Informatique, Université de Caen, Caen CX, 14032, France

    Brigitte Vallée

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Micciancio, D. (2009). Cryptographic Functions from Worst-Case Complexity Assumptions. In: Nguyen, P., Vallée, B. (eds) The LLL Algorithm. Information Security and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02295-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-02295-1_13

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