Multivariate Encryption Schemes Based on Polynomial Equations over Real Numbers
Multivariate Encryption Schemes Based on Polynomial Equations over Real Numbers
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DOI：
10.1007/978-3-030-44223-1_22
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
T. Yasuda;Yacheng Wang;T. Takagi
中科院分区：
文献类型：
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作者：
T. Yasuda;Yacheng Wang;T. Takagi
MQ问题是一个NP完全问题，与多元公钥密码学(MPKC)的安全性有关。它的变体，即约束 MQ 问题，首先在使用 ProvSec2018 提出的 pq 方法构建安全多元加密方案时被考虑。在本文中，我们提出了一种名为 PERN 的加密方案，其密钥空间完全包含 pq 方法的密钥空间。 PERN的解密采用求解实数上的非线性方程的方法，这与MPKC中现有加密方案的解密不同。 PERN的构造相当灵活，这使得我们能够构造一个多元加密方案，其公钥由2次、3次或更高次的多元多项式组成，同时将其公钥限制在合理的大小。
The MQ problem, an NP-complete problem, is related to the security of Multivariate Public Key Cryptography (MPKC). Its variant, the constrained MQ problem, was first considered in constructing secure multivariate encryption schemes using thepq-method proposed at ProvSec2018. In this paper, we propose an encryption scheme named PERN, whose key space completely includes that of thepq-method. The decryption of PERN uses methods of solving nonlinear equations over the real numbers, which is different from the decryption of the existing encryption schemes in MPKC. The construction of PERN is fairly flexible, which enables us to construct a multivariate encryption scheme, whose public key consists of multivariate polynomials of degree 2, 3 or higher degrees while constraining its public key to a reasonable size.