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.***
