Cryptology ePrint Archive: Report 2020/1086

Combinatorial Rank Attacks Against the Rectangular Simple Matrix Encryption Scheme

Daniel Apon and Dustin Moody and Ray Perlner and Daniel Smith-Tone and Javier Verbel

Abstract: In 2013, Tao et al. introduced the ABC Simple Matrix Encryption Scheme, a multivariate public key encryption scheme. The scheme boasts great efficiency in encryption and decryption, though it suffers from very large public keys. It was quickly noted that the original proposal, utilizing square matrices, suffered from a very bad decryption failure rate. As a consequence, the designers later published updated parameters, replacing the square matrices with rectangular matrices and altering other parameters to avoid the cryptanalysis of the original scheme presented in 2014 by Moody et al.

In this work, we show that making the matrices rectangular, while decreasing the decryption failure rate, actually, and ironically, diminishes security. We show that the combinatorial rank methods employed in the original attack of Moody et al. can be enhanced by the same added degrees of freedom that reduce the decryption failure rate. Moreover, and quite interestingly, if the decryption failure rate is still reasonably high, as exhibited by the proposed parameters, we are able to mount a reaction attack to further enhance the combinatorial rank methods. To our knowledge this is the first instance of a reaction attack creating a significant advantage in this context.

Category / Keywords: Multivariate Cryptography, Simple Matrix, encryption, Min-Rank

Original Publication (in the same form): PQCrypto 2020

Date: received 9 Sep 2020

Contact author: daniel apon at nist gov,dustin moody@nist gov,ray perlner@nist gov,daniel smith@nist gov,javerbel@unal edu co

Available format(s): PDF | BibTeX Citation

Version: 20200910:063828 (All versions of this report)

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