Revisiting the Efficient Key Generation of ZHFE
Revisiting the Efficient Key Generation of ZHFE
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DOI：
10.1007/978-3-319-55589-8_13
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发表时间：
2017-04
期刊：
影响因子：
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通讯作者：
Yasuhiko Ikematsu;D. Duong;Albrecht Petzoldt;T. Takagi
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文献类型：
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作者：
Yasuhiko Ikematsu;D. Duong;Albrecht Petzoldt;T. Takagi
ZHFE是由Porras等人在PQCrypto'14上提出的，是现有的极少数多变量加密方案之一，也是后量子密码系统的一个非常有前途的候选方案。唯一的缺点是它的密钥生成速度慢。在PQCrypto'16上，Baena等人提出了一种构造ZHFE私钥的算法，该算法比原始算法快得多，但对于实际参数仍然效率低下。最近，Zhang和Tan提出了另一种私钥生成算法，该算法非常快，但不一定能够生成所有ZHFE私钥。在本文中，我们提出了一个新的有效的算法的私钥生成的ZHFE方案。我们的算法将Baena等人提出的算法的复杂度降低到，其中是变量个数，是线性代数常数。我们还估计了所有现有的私钥生成算法为ZHFE生成的可能密钥的数量。我们的算法生成的私有ZHFE密钥与原始算法和Baena等人的算法一样多。s的。这使得我们的算法是最适合的ZHFE计划。
ZHFE, proposed by Porras et al. at PQCrypto’14, is one of the very few existing multivariate encryption schemes and a very promising candidate for post-quantum cryptosystems. The only one drawback is its slow key generation. At PQCrypto’16, Baena et al. proposed an algorithm to construct the private ZHFE keys, which is much faster than the original algorithm, but still inefficient for practical parameters. Recently, Zhang and Tan proposed another private key generation algorithm, which is very fast but not necessarily able to generate all the private ZHFE keys. In this paper we propose a new efficient algorithm for the private key generation of the ZHFE scheme. Our algorithm reduces the complexity fromby Baena et al. to, wherenis the number of variables andis a linear algebra constant. We also estimate the number of possible keys generated by all existing private key generation algorithms for ZHFE. Our algorithm generates as many private ZHFE keys as the original and Baena et al.’s ones. This makes our algorithm be the best appropriate for the ZHFE scheme.