分布拟合技术及其在密码函数构造中的应用

Distribution Fitting and Its Applications in Construction of Cryptographic Functions

在计算平台上生成符合目标参数的分布样本是数值计算中的基本问题.通过优化形成高拟合度的分布参数,对探索新型密码函数的设计方法,尤其是安全的单向函数映射有着重要的意义.本文围绕密码学安全意义,讨论了通用情况下真实分布的参数与敌手的攻击优势之间满足的约束关系,提出了一种基于距离监督的分布拟合方法,用于生成与理想分布样本逼近的近似分布参数组合.使用分布隐含模型(DLM)构造真实分布的输出模型,采用复合距离测度优化参数组合,使DLM成为满足安全距离约束条件的目标分布样本生成器.构造了一类通用的单向陷门置换函数(OWTP),在计算上满足统计上的样本不可区分性,从理论上已经初步具备了用于直接构造部分密码算法的能力.

Generating samples being in compliance with desirable parameters is one of the fundamental problems on computing platforms.Optimizing the sampling method to generate ideal distribution is helpful in the design of new cryptographic functions,especially one-way functions in public key cryptography.This paper studies the constraints between parameters of real distributions and the advantages of adversaries,and presents a distribution approaching method based on distance supervision to generate the parameters of sub-optimal distribution.By constructing a latent distribution model(DLM)to generate real distribution,and optimizing the model using a compound distance measure,a sample generator compliance with the target distribution is designed.Based on the constructed DLM,a generic method is proposed to obtain one-way trapdoor permutation(OWTP)that satisfies computational indistinguishability,which proves the effectiveness of the construction ability of the DLM.