Paper 2018/265

Compact, Scalable, and Efficient Discrete Gaussian Samplers for Lattice-Based Cryptography

Ayesha Khalid, James Howe, Ciara Rafferty, Francesco Regazzoni, and Maire O’Neill


Lattice-based cryptography, one of the leading candidates for post-quantum security, relies heavily on discrete Gaussian samplers to provide necessary uncertainty, obfuscating computations on secret information. For reconfigurable hardware, the cumulative distribution table (CDT) scheme has previously been shown to achieve the highest throughput and the smallest resource utilisation, easily outperforming other existing samplers. However, the CDT sampler does not scale well. In fact, for large parameters, the lookup tables required are far too large to be practically implemented. This research proposes a hierarchy of multiple smaller samplers, extending the Gaussian convolution lemma to compute optimal parameters, where the individual samplers require much smaller lookup tables. A large range of parameter sets, covering encryption, signatures, and key exchange are evaluated. Hardware-optimised parameters are formulated and a practical implementation on Xilinx Artix- 7 FPGA device is realised. The proposed sampling designs demonstrate promising performance on reconfigurable hardware, even for large parameters, that were otherwise thought infeasible.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. IEEE ISCAS 2018
lattice-based cryptographypost-quantum cryptographyGaussian samplershardware securityFPGA.
Contact author(s)
james howe @ bristol ac uk
2018-03-13: received
Short URL
Creative Commons Attribution


      author = {Ayesha Khalid and James Howe and Ciara Rafferty and Francesco Regazzoni and Maire O’Neill},
      title = {Compact, Scalable, and Efficient Discrete Gaussian Samplers for Lattice-Based Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2018/265},
      year = {2018},
      note = {\url{}},
      url = {}
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