基于新分数阶算子的单向函数研究

In 1987, G. R. Blakley and William Rundel introduced "heat flow cryptosystem", which employs partial differential equations to construct cryptographic primitives. Compared with cryptographic algorithm based on discrete mathematical structures, the heat flow cryptosystem is continuous and lack of proof of security. As encryption and decryption of heat flow cryptosystem involving complex partial differential equation theory, the heat flow cryptosystem can resist brute force attack. We believe that: when the problem between discrete and continuous is solved and the heat flow cryptosystem has a proof of security, the heat flow cryptosystem can play a more positive role in future..This project aims to study a new fractional operator and a class of partial differential equations relating to this operator and its applications in Cryptography:.(1)this project employs a new fractional operator into the heat flow cryptosystem..(2)this project constructs a one-way functions based on the partial differential equations of the new fractional operators and demonstrate its security.

早在1987 年，G. R. Blakley 和William Rundel提出把偏微分方程及其反问题的理论应用到密码学，构造“热流密码体制”. 与基于离散数学结构的密码算法相比，热流密码体制是连续的，缺乏安全性的证明，但由于其加、解密过程涉及复杂的偏微分方程理论，因此具有很强的抗攻击能力．我们相信：一旦离散和连续的问题以及热流密码体制的可证明问题被解决，热流密码体制未来可以发挥更为积极的作用．. 本项目拟研究一个新分数阶算子及关于这个算子的一类偏微分方程在密码学中的应用. 特色与创新之处包括：.(1)本项目提出将一个新分数阶算子引入到热流密码体制中．.(2)本项目目提出构造基于新分数阶算子偏微分方程的单向函数，并论证其安全性．