Abstract
In this paper we present a new algorithm to construct the keys of the multivariate public key encryption scheme ZHFE. Constructing ZHFE’s trapdoor involves finding a low degree polynomial of q-Hamming-weight-three, as an aid to invert a pair of q-Hamming-weight-two polynomials of high degree and high rank. This is done by solving a large sparse linear system of equations. We unveil the combinatorial structure of the system in order to reveal the hidden structure of the matrix associated with it. When the system’s variables and equations are organized accordingly, an almost block diagonal shape emerges. We then exploit this shape to solve the system much faster than when ZHFE was first proposed. The paper presents the theoretical details explaining the structure of the matrix. We also present experimental data that confirms the notable improvement of the key generation complexity, which makes ZHFE more suitable for practical implementations.
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Acknowledgements
This work was partially supported by “Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación Francisco José de Caldas”, Colciencias (Colombia), Project No. 111865842333 and Contract No. 049-2015. We would like to thank Jintai Ding, Ludivic Perret, and Felipe Cabarcas for useful discussions. We would also like to thank the reviewers of PQCrypto 2016 for their constructive reviews and suggestions. And last but not least, we thank the Facultad de Ciencias of the Universidad Nacional de Colombia sede Medellín for granting us access to the Enlace server, where we ran most of the experiments of this paper.
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Baena, J.B., Cabarcas, D., Escudero, D.E., Porras-Barrera, J., Verbel, J.A. (2016). Efficient ZHFE Key Generation. In: Takagi, T. (eds) Post-Quantum Cryptography. PQCrypto 2016. Lecture Notes in Computer Science(), vol 9606. Springer, Cham. https://doi.org/10.1007/978-3-319-29360-8_14
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DOI: https://doi.org/10.1007/978-3-319-29360-8_14
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