Version 1
: Received: 20 April 2020 / Approved: 22 April 2020 / Online: 22 April 2020 (06:09:50 CEST)
How to cite:
Diene, A.; Thabet, S.A.; Yusuf, Y. A Multivariate Signature Based On Block Matrix Multiplication. Preprints2020, 2020040392. https://doi.org/10.20944/preprints202004.0392.v1
Diene, A.; Thabet, S.A.; Yusuf, Y. A Multivariate Signature Based On Block Matrix Multiplication. Preprints 2020, 2020040392. https://doi.org/10.20944/preprints202004.0392.v1
Diene, A.; Thabet, S.A.; Yusuf, Y. A Multivariate Signature Based On Block Matrix Multiplication. Preprints2020, 2020040392. https://doi.org/10.20944/preprints202004.0392.v1
APA Style
Diene, A., Thabet, S.A., & Yusuf, Y. (2020). A Multivariate Signature Based On Block Matrix Multiplication. Preprints. https://doi.org/10.20944/preprints202004.0392.v1
Chicago/Turabian Style
Diene, A., Shaima Abdullah Thabet and Yahya Yusuf. 2020 "A Multivariate Signature Based On Block Matrix Multiplication" Preprints. https://doi.org/10.20944/preprints202004.0392.v1
Abstract
An oil and vinegar scheme is a signature scheme based on multivariate quadratic polynomials over finite fields. The system of polynomials contains $n$ variables, divided into two groups: $v$ vinegar variables and $o$ oil variables. The scheme is called balanced (OV) or unbalanced (UOV), depending on whether $v = 0$ or not, respectively. These schemes are very fast and require modest computational resources, which make them ideal for low-cost devices such as smart cards. However, the OV scheme has been already proven to be insecure and the UOV scheme has been proven to be very vulnerable for many parameter choices. In this paper, we propose a new multivariate public key signature whose central map consists of a set of polynomials obtained from the multiplication of block matrices. Our construction is motivated by the design of the Simple Matrix Scheme for Encryption and the UOV scheme. We show that it is secure against the Separation Method, which can be used to attack the UOV scheme, and against the Rank Attack, which is one of the deadliest attacks against multivariate public-key cryptosystems. Some theoretical results on matrices with polynomial entries are also given, to support the construction of the scheme.
Keywords
Multivariate Public Key Cryptosystem; Random polynomial; Oil Vinegar signature; Provable Security
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.