Enhancing Goldreich, Goldwasser and Halevi's scheme with intersecting lattices

Authors

Arnaud Sipasseuth, University of WollongongFollow
Thomas Plantard, University of WollongongFollow
Willy Susilo, University of WollongongFollow

RIS ID

139915

Publication Details

Sipasseuth, A., Plantard, T. & Susilo, W. (2019). Enhancing Goldreich, Goldwasser and Halevi's scheme with intersecting lattices. Journal of Mathematical Cryptology, 13 (3-4), 169-196.

Abstract

We present a technique to enhance the security of the Goldreich, Goldwasser and Halevi (GGH) scheme. The security of GGH has practically been broken by lattice reduction techniques. Those attacks are successful due to the structure of the basis used in the secret key. In this work, we aim to present a new technique to alleviate this problem by modifying the public key which hides the structure of the corresponding private key. We intersect the initial lattice with a random one while keeping the initial lattice as our secret key and use the corresponding result of the intersection as the public key. We show sufficient evidence that this technique will make GGH implementations secure against the aforementioned attacks.