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

最近，一种新的威胁模型被发现，它可以用来破解许多现有的密码协议。 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。这种情况适用于防篡改设备，通过在极端物理环境中操作它们，可以使防篡改设备误算。 利用硬件故障攻击各种密码协议的可能性提出了许多有趣的开放问题。 首先，现在变得期望构造抵抗使用硬件故障的攻击的有效方案。 该项目将发展必要的理论，以证明某些方案的抗故障能力。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。 整数分解的困难性是一个标准的密码学假设。 将研究这一假设的各种数学含义。 前面的结果表明，因子分解的困难意味着多项式有许多根在低代数扩张的有理数是难以评估。 一般来说，多项式难以求值的标准在许多应用中是有用的。进一步的应用的硬度因子将被研究。具体来说，目标是构造新的多项式类，除非分解很容易，否则很难计算。 有几个这样的候选人，例如，某些多项式生成伽罗瓦扩展的有理数。 根据多项式生成的数域类型来估计计算某些多项式的难度是一个很有前途的研究领域。 这样的结果将有希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.***