Combinatorial Rank Attacks Against the Rectangular Simple Matrix Encryption Scheme

Published

April 10, 2020

Author(s)

Dustin Moody, Ray A. Perlner, Daniel C. Smith-Tone, Daniel C. Apon, Javier Verbel

Abstract

In 2013, Tao et al. introduced the ABC Simple Matrix Scheme for Encryption, 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 setting 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.

Proceedings Title

Proceedings of PQCrypto 2020: The Eleventh International Conference on Post-Quantum Cryptography

Volume

12100

Conference Dates

April 15-17, 2020

Conference Location

Paris

Conference Title

PQCrypto 2020: The Eleventh International Conference on Post-Quantum Cryptography

Pub Type

Conferences

Download Paper

https://doi.org/10.1007/978-3-030-44223-1_17

Local Download

Keywords

Multivariate Cryptography, Simple Matrix, encryption, MinRank

Citation

Moody, D. , Perlner, R. , Smith-Tone, D. , Apon, D. and Verbel, J. (2020), Combinatorial Rank Attacks Against the Rectangular Simple Matrix Encryption Scheme, Proceedings of PQCrypto 2020: The Eleventh International Conference on Post-Quantum Cryptography, Paris, -1, [online], https://doi.org/10.1007/978-3-030-44223-1_17 (Accessed October 15, 2025)