Cryptology ePrint Archive: Report 2017/1254

Practical Applications of Improved Gaussian Sampling for Trapdoor Lattices

Kamil Doruk Gür and Yuriy Polyakov and Kurt Rohloff and Gerard W. Ryan and Hadi Sajjadpour and Erkay Savaş

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.

Category / Keywords: implementation / applications and digital signatures and implementation and lattice techniques and public-key cryptography and quantum cryptography

Original Publication (in the same form): IEEE Transactions on Computers

Date: received 28 Dec 2017, last revised 5 Mar 2019

Contact author: polyakov at njit edu

Available format(s): PDF | BibTeX Citation

Version: 20190306:034719 (All versions of this report)

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