Proposal for Research on Fault Resistant Cryptography and the Hardness of Factoring

最近，人们发现了一种新的威胁模型，可以用来破坏许多现有的加密协议。这种威胁是基于这样一个事实，即某些硬件可能会被诱导执行错误计算。此场景适用于在极端物理环境中操作可能导致误算的防篡改设备。利用硬件故障攻击各种加密协议的可能性引发了许多有趣的开放问题。首先，现在需要构建有效的方案，以抵抗使用硬件故障的攻击。该项目将发展必要的理论，以证明某些方案的故障抗力。其他加密方案将被分析，以确定它们是否容易受到新的攻击。分解整数的难度是一个标准的密码学假设。我们将研究这一假设的各种数学含义。先前的结果表明，因式分解的困难意味着在有理的低代数扩展中具有多根的多项式很难求值。一般来说，判定多项式何时难以求值的准则在许多应用中都是有用的。将进一步研究保理硬度的应用。具体地说，目标是构造难以求值的新多项式类，除非分解很容易。有几个这样的候选者，例如，某些多项式在有理上产生伽罗瓦扩展。根据多项式产生的数域类型来估计多项式的难度是一个很有前途的研究领域。这样的结果有望阐明计算多项式的复杂性

Recently, a new threat model has been discovered which can be used to break many existing cryptographic protocols. The threat is based on the fact that certain hardware may be induced to perform miscalculations. This scenario is applicable to tamper proof devices which can be made to miscalculate by operating them in an extreme physical environment. The possibility of attacking various cryptographic protocols using hardware faults raises many interesting open problems. First, it now becomes desirable to construct efficient schemes which are resistant to attacks using hardware faults. The project will develop the theory necessary to prove the fault resistance of certain schemes. Other cryptographic schemes will be analyzed to determine whether they are susceptible to the new attack. The hardness of factoring integers is a standard cryptographic assumption. Various mathematical implications of this assumption will be studied. The previous results show that the hardness of factoring implies that polynomials having many roots in low algebraic extensions of the rationals are hard to evaluate. Generally speaking, criteria for when polynomials are hard to evaluate are useful in many applications. Further applications of the hardness of factoring will be studied. Specifically, the goal is to construct new classes of polynomials which are hard to evaluate, unless factoring is easy. There are several such candidates, for example, certain polynomials which generate Galois extensions over the rationals. Estimating the difficulty of evaluating certain polynomials based on the type of number fields they generate is a promising area of research. Such results will hopefully shed light on the complexity of evaluating polynomials.***