Generalization of Isomorphism of Polynomials with Two Secrets and Its Application to Public Key Encryption
Generalization of Isomorphism of Polynomials with Two Secrets and Its Application to Public Key Encryption
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DOI：
10.1007/978-3-030-44223-1_19
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发表时间：
2020-04
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影响因子：
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通讯作者：
Bagus Santoso
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作者：
Bagus Santoso
基于多元二次多项式的公钥加密方案大多依赖于隐场方程（HFE）范式。然而，大多数基于HFE的计划在推出后仅几年就被打破了。在本文中，我们提出了一种替代的范式，用于构建基于多元二次多项式的PKE。在我们的建议的核心是一个新的家庭的计算问题的基础上推广的同构多项式与两个秘密（IP 2S）的问题。新家族中的主要计算问题被证明与原始IP 2S问题一样困难，并且更鲁棒，在这个意义上，我们可以将其与循环矩阵作为解决方案相关联，而不会降低其计算难度太多，与原始IP 2S问题相反，一旦与循环矩阵相关联，它就立即变得容易。通过将其与循环矩阵相关联，我们得到了一个Diffie-Hellman结构，它允许我们有一个El-Gamal一样的PKE计划。
Most of the public key encryption (PKE) schemes based on multivariate quadratic polynomials rely on Hidden Field Equation (HFE) paradigm. However, most of HFE based schemes have been broken in only several years just after their introduction. In this paper, we propose an alternative paradigm for constructing PKE based on multivariate quadratic polynomials. At the heart of our proposal is a new family of computational problems based on the generalization of Isomorphism of Polynomials with Two Secrets (IP2S) problem. The main computational problem in the new family is proven as hard as the original IP2S problem and is more robust, in the sense that we can associate it with circulant matrices as solutions without degrading its computational hardness too much, in contrast to the original IP2S problem which immediately becomes easy as soon as it is associated with circulant matrices. By associating it to circulant matrices, we obtain a Diffie-Hellman like structure which allows us to have an El-Gamal like PKE scheme.