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通过对损耗陷门函数的分析得知,在关于陷门的任意计算不可求逆的函数提前泄露的情况下,已有损耗陷门函数的可证明安全性将会受到较大的影响.如何保证损耗陷门函数在此应用场景下仍然是可证明安全的,是一个有意义的研究问题.为此,首先使用d线性假设,构造了一个新的损耗陷门函数,并利用扩展版的Goldreich-Levin定理,证明其是辅助输入安全的;其次通过对Peikert所构造的利用错误学习问题假设的损耗陷门函数进行适当的修改,也能证明其是辅助输入安全的;最后从效率和安全性角度出发,对2个损耗陷门函数进行了分析.
Based on the analysis of the traps, it is found that the demonstrable safety of the traps has a greater impact on the early leakage of any computationally irreversible trapdoor. The loss trapdoor function is still a valid research problem under this application scenario.Therefore, a new loss trapdoor function is first constructed using d-linear hypothesis and an Extended Goldreich- Levin’s theorem, it is proved that it is auxiliary input safe. Secondly, it can be proved that it is auxiliary input security by properly modifying the loss trapdoor function constructed by Peikert using the assumption of error learning problem. Finally, from the perspective of efficiency and security Departure, the two loss trapdoor functions were analyzed.