Practical Cryptanalysis of a Public-key Encryption Scheme Based on New Multivariate Quadratic Assumptions

Martin Roland Albrecht, Jean-Charles Faugére, Robert Fitzpatrick, Ludovic Perret, Yosuke Todo, Keita Xagawa

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

In this paper, we investigate the security of a public-key encryption scheme introduced by Huang, Liu and Yang (HLY) at PKC’12. This new scheme can be provably reduced to the hardness of solving a set of quadratic equations whose coefficients of highest degree are chosen according to a discrete Gaussian distributions. The other terms being chosen uniformly at random. Such a problem is a variant of the classical problem of solving a system of non-linear equations (PoSSo), which is known to be hard for random systems. The main hypothesis of Huang, Liu and Yang is that their variant is not easier than solving PoSSo for random instances. In this paper, we disprove this hypothesis. To this end, we exploit the fact that the new problem proposed by Huang, Liu and Yang reduces to an easy instance of the Learning With Errors (LWE) problem. The main contribution of this paper is to show that security and efficiency are essentially incompatible for the HLY proposal. That is, one cannot find parameters which yield a secure and a practical scheme. For instance, we estimate that a public-key of at least 1.03 GB is required to achieve 80-bit security against the simplest of our attacks. As a proof of concept, we present 3 practical attacks against all the parameters proposed by Huang, Liu and Yang. With the most efficient attack, we have been able to recover the private-key in roughly 5 minutes for the first challenge (i.e. Case 1) proposed by HLY and less than 30 minutes for the second challenge (i.e. Case 2).
Original languageEnglish
Title of host publicationPublic-Key Cryptography – PKC 2014 : 17th International Conference on Practice and Theory in Public-Key Cryptography, Buenos Aires, Argentina, March 26-28, 2014. Proceedings
PublisherSpringer
Publication date2014
Pages446-464
ISBN (Print)978-3-642-54630-3
ISBN (Electronic)978-3-642-54631-0
DOIs
Publication statusPublished - 2014
Event17th International Conference on Practice and Theory in Public-Key Cryptography - Buenos Aires, Argentina
Duration: 26 Mar 201428 Mar 2014
Conference number: 17

Conference

Conference17th International Conference on Practice and Theory in Public-Key Cryptography
Number17
CountryArgentina
CityBuenos Aires
Period26/03/201428/03/2014
SeriesLecture Notes in Computer Science
Volume8383
ISSN0302-9743

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