Paper 2017/615

A Framework to Select Parameters for Lattice-Based Cryptography

Nabil Alkeilani Alkadri
Johannes Buchmann
Rachid El Bansarkhani
Juliane Krämer

Selecting parameters in lattice-based cryptography is a challenging task, which is essentially accomplished using one of two approaches. The first (very common) approach is to derive parameters assuming that the desired security level is equivalent to the bit hardness of the underlying lattice problem, ignoring the gap implied by available security reductions. The second (barely used) approach takes the gap and thus the security reduction into account. In this work, we investigate how efficient lattice-based schemes are if they respect existing security reductions. Thus, we present a framework to systematically select parameters for any lattice-based scheme using either approaches. We apply our methodology to the schemes by Lindner and Peikert (LP), by El Bansarkhani (LARA), and by Ducas et al. (BLISS). We analyze their security reductions and derive a gap of 2, 3, and 63 bits, respectively. We show how parameters impact the schemes' efficiency when involving these gaps.

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Published elsewhere. -
Lattice-Based Cryptography Ideal Lattices Parameter Selection Security Reduction Tightness Lattice-Based Assumptions
Contact author(s)
nalkeilani_alkadri @ cdc informatik tu-darmstadt de
2022-12-19: revised
2017-06-27: received
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      author = {Nabil Alkeilani Alkadri and Johannes Buchmann and Rachid El Bansarkhani and Juliane Krämer},
      title = {A Framework to Select Parameters for Lattice-Based Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2017/615},
      year = {2017},
      note = {\url{}},
      url = {}
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