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An Algorithm for Judging and Generating Bilinear Multivariate Quadratic Quasigroups |
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PP: 2071-2076 |
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Author(s) |
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Ying Zhang,
Huisheng Zhang,
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Abstract |
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| Multivariate Quadratic Quasigroups (MQQs) as a suitable class of quasigroups for multivariate public key cryptography
recently have been an important mathematical tool in information security field. In this paper, we propose a necessary and sufficient
condition to verify whether a quasigroup given by its multiplication table is a bilinear MQQ, which shows that checking whether an
arbitrary quasigroup is a bilinear MQQ is equivalent to solving a simple matrix equation. Based on this condition, a deterministic
algorithm is proposed to judge whether a given quasigroup is a bilinear MQQ and then obtain the corresponding Boolean functions if
it is. An example is given to show the validity of our results. |
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