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Generalized Learning Problems and Applications to Non-commutative Cryptography

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Provable Security (ProvSec 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6980))

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Abstract

We propose a generalization of the learning parity with noise (LPN) and learning with errors (LWE) problems to an abstract class of group-theoretic learning problems that we term learning homomorphisms with noise (LHN). This class of problems contains LPN and LWE as special cases, but is much more general. It allows, for example, instantiations based on non-abelian groups, resulting in a new avenue for the application of combinatorial group theory to the development of cryptographic primitives. We then study a particular instantiation using relatively free groups and construct a symmetric cryptosystem based upon it.

Full version available at [7]. Supported in part by NSF grants CNS 1117675/1117679.

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Authors and Affiliations

  1. The City College of CUNY, USA

    Gilbert Baumslag, Nelly Fazio, Vladimir Shpilrain & William E. Skeith III

  2. Stevens Institute of Technology, USA

    Antonio R. Nicolosi

Authors
  1. Gilbert Baumslag
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  2. Nelly Fazio
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  3. Antonio R. Nicolosi
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  4. Vladimir Shpilrain
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  5. William E. Skeith III
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Editor information

Editors and Affiliations

  1. Palo Alto Research Center, 94304, Palo Alto, CA, USA

    Xavier Boyen

  2. School of Telecommunications Engineering, Xidian University, 710071, Xi’an, China

    Xiaofeng Chen

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Baumslag, G., Fazio, N., Nicolosi, A.R., Shpilrain, V., Skeith, W.E. (2011). Generalized Learning Problems and Applications to Non-commutative Cryptography. In: Boyen, X., Chen, X. (eds) Provable Security. ProvSec 2011. Lecture Notes in Computer Science, vol 6980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24316-5_23

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  • DOI: https://doi.org/10.1007/978-3-642-24316-5_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24315-8

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