Practical Applications of Improved Gaussian Sampling for Trapdoor Lattices

Kamil D. Gur, Yuriy Polyakov, Kurt Rohloff, Gerard W. Ryan, Hadi Sajjadpour, Erkay Savas

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Lattice trapdoors are an important primitive used in a wide range of cryptographic protocols, such as identity-based encryption (IBE), attribute-based encryption, functional encryption, and program obfuscation. In this paper, we present software implementations of the Gentry-Peikert-Vaikuntanathan (GPV) digital signature, IBE and ciphertext-policy attribute-based encryption (CP-ABE) schemes based on an efficient Gaussian sampling algorithm for trapdoor lattices, and demonstrate that these three important cryptographic protocols are practical. One important aspect of our implementation is that it supports prime moduli, which are required in many cryptographic schemes. Also, our implementation uses bases larger than two for the gadget matrix whereas most previous implementations use the binary base. We show that the use of higher bases significantly decreases execution times and storage requirements. We adapt IBE and CP-ABE schemes originally based on learning with errors (LWE) hardness assumptions to a more efficient Ring LWE (RLWE) construction. To the best of our knowledge, ours are the first implementations employing the Gaussian sampling for non-binary bases of the gadget matrix. The experimental results demonstrate that our lattice-based signature, IBE and CP-ABE implementations, which are based on standard assumptions with post-quantum security, provide a performance comparable to the recent state-of-The-Art implementation works based on stronger/non-post-quantum assumptions.

Original languageEnglish (US)
Article number8493319
Pages (from-to)570-584
Number of pages15
JournalIEEE Transactions on Computers
Volume68
Issue number4
DOIs
StatePublished - Apr 1 2019

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics

Keywords

  • GPV digital signature
  • Gaussian sampler
  • Lattice-based cryptography
  • RLWE
  • attribute-based encryption
  • identity-based encryption

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