The Efficiency of Embedding-Based Attacks on the GGH Lattice-Based Cryptosystem-Reference-Cited by-同舟云学术

The Efficiency of Embedding-Based Attacks on the GGH Lattice-Based Cryptosystem

Published:2023-12-14 Issue:4 Volume:17 Page:673-690
ISSN:1823-8343
Container-title:Malaysian Journal of Mathematical Sciences
language:en
Short-container-title:MJMS

Author:

Mandangan, A.¹,Kamarulhaili, H.²,Asbullah, M. A.³

Affiliation:

1. Mathematics, Real-Time Graphics and Visualization Laboratory, Faculty of Sciences and Natural Resources, Universiti Malaysia Sabah, Sabah, Malaysia

2. School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia

3. Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, Selangor, Malaysia and Laboratory of Cryptography, Analysis and Structure, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia

Abstract

The Goldreich-Goldwasser-Halevi (GGH) cryptosystem is declared broken due to the modified versions of the embedding attacks, known as Nguyen's σ, Nguyen's 2σ and Lee-Hahn's attacks. Despite using the same approach as the original embedding attack, these attacks deployed different strategies and resulted in different performances for breaking the GGH cryptosystem. In this paper, we described those strategies in detail. Moreover, we investigated the mathematical factors behind these attacks' ability and performance discrepancies. Mathematical proof examines and discusses the factors that triggered those variances. As a result, the expected lattice gap and implemented lattice dimensions are mathematically proven as the factors that significantly influenced these attacks' performance. By demonstrating how the attacks manipulated these factors, any lattice-based cryptosystem that relies on the hardness of the CVP could avoid repeating the same slipup as the GGH. Hence, precautionary action could be proactively taken to prevent it from being threatened by embedding-based attacks.

Publisher

Universiti Putra Malaysia

Subject

General Mathematics

Reference15 articles.

1. Dadheech (2018). Preventing information leakage from encoded data in lattice-based cryptography. In 2018 International Conference on Advances in Computing, Communications and Informatics (ICACCI), pp. 1952–1955. IEEE. https://doi.org/10.1109/ICACCI.2018.8554942.

2. S. D. Galbraith (2012). Mathematics of Public Key Cryptography. Cambridge University Press, Cambridge.

3. N. Gama & P. Q. Nguyen (2008). Predicting lattice reduction. In Advances in Cryptology –EUROCRYPT 2008, pp. 31–51. Springer, Berlin, Heidelberg.

4. O. Goldreich, S. Goldwasser & S. Halevi (1997). The GGH cryptosystem challenges. In http://groups.csail.mit.edu/cis/lattice/challenge.html

5. O. Goldreich, S. Goldwasser & S. Halevi (1997). Public-key cryptosystems from lattice reduction problems. In Advances in Cryptology–CRYPTO ’97: 17th Annual International Cryptology Conference Santa Barbara, California, USA August 17–21, 1997 Proceedings 17, pp. 112–131. Springer, Berlin, Heidelberg.