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Cryptanalysis of the extension field cancellation cryptosystem

机译：延长现场取消密码系统的密码分析

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In this article, we present algebraic attacks against the Extension Field Cancellation (EFC) scheme, a multivariate public-key encryption scheme which was published at PQCRYPTO'2016. First, we present a successful Grobner basis message-recovery attack on the first and second proposed parameters of the scheme. For the first challenge parameter, a Grobner-based hybrid attack has a 265 bit complexity which beats the claimed 80 bit security level. We further show that the algebraic system arising from an EFC public-key is much easier to solve than a random system of the same size. Briefly, this is due to the apparition of many lower degree equations during the Grobner basis computation. We present a polynomial-time method to recover such lower-degree relations and also show their usefulness in improving the Grobner basis attack complexity on EFC. Thus, we show that there is an algebraic structural weakness in the system of equations coming from EFC and hence makes the scheme not suitable for encryption.
机译：在本文中，我们提出了针对扩展现场取消（EFC）方案的代数攻击，这是一个在PQCrypto'2016发表的多变量公钥加密方案。首先，我们在该方案的第一和第二建议参数上展示了成功的Grobner基础消息恢复攻击。对于第一个挑战参数，基于Grobner的混合攻击具有265位复杂性，该复杂性击败了所要求保护的80位安全级别。我们进一步表明，EFC公钥产生的代数系统比同一大小的随机系统更容易解决。简而言之，这是由于在Grobner基础计算期间许多较低度方程的幻影。我们提出了一种多项式方法来恢复这种较低程度的关系，并还表明了改善EFC对Grobner基础攻击复杂性的有用性。因此，我们表明，来自EFC的等式系统中存在代数结构弱点，因此使方案不适合加密。

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