辅助输入安全的损耗陷门函数的构造

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.

Construction of Auxiliary-Input Secure Lossy Trapdoor Functions

Analyzing the primitive of lossy trapdoor function, we know that all existing lossy trapdoor functions might not be provably secure when the adversary previously gets the related information on the trapdoor. This article presented a new lossy trapdoor function based on the d-linear assumption, and proved it to be auxiliary-input secure by using an extended version of the Goldreich-Levin theorem. It is verified that the slight variance of Peikert's learning with errors based lossy trapdoor function is auxiliary-input secure. Both lossy trapdoor functions in efficiency and security was analyzed.