The Design and Research of Cubic Polynomial Public Key Cryptosystem and Genetic Cryptosystem Generator

• Main Authors: Chao-Ping Huang, 黃昭平
• Other Authors: Huey-Der Chu
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/06595669746730443443

碩士 === 國防管理學院 === 國防資訊研究所 === 88 === For the popular usage of Internets today, Electronic Commerce (EC) is the major trend of enterprise marketing. It makes the network shopping and e-business acceptable now. CA (Certificate Authority) is the most important function in the network marketing. The CA may sopports all trust functions in network environment. There are some problems in the operations of the CA: 1. How can the CA speed up enciphering/ deciphering secret messages in the increasing network transactions? 2. How to design a key recovery cryptosystem that the CA can execute the function of key recovery in certain necessary condition without storing user’s private key? 3. How to automatically generate new cryptosystem algorithms by computer? In this thesis, a Cubic Polynomial Cryptosystem (CPC) is proposed. The derivation of cipherments can be used by only polynomial computation. A theoretic derivation of CPC has been developed, the computations include only multiplication and addition, the computational complexity has been reduced from O(2n) to O(n), the efficiency is higher than RSA,ElGamal and ECC. The security of the proposed scheme is believed to be the hard of factorization problem; When transaction dissension occurred, CA or Trusted Key Recovery Center (TKRC) doesn’t store any user’s private key and could execute key recovery by government department’s digital signature or by secret sharing technology. The advantages are including omiting the space of the key storage and management problem. The applications of the proposed scheme include digital signature, certificate authentication, electronic vote or electronic biting. Due to the invention of public cryptography in 1976, most cryptosystem algorithms are developed by mathematical theory with human works. To overcome above the third problem, a Genetic Cryptosystem Generator (GCG) is proposed to use genetic algorithm (GA) to generate new cryptosystem algorithms. The proposed scheme is based on the concept of Darwinian’s theory that it develops to mimic natural evolution to find a better solution by using the biologic operations such as selection, crossover and mutation. In this thesis, GA is applied in cryptography, to try to find a reasonable solution that can meet the user’s requirement and find a more secure and more efficient cryptosystem algotithms automatically. We hope this research will provide a new direction for cryptosystem. With the proposed CPC and GCG, new ideas of polynomial computation and Genetic Algorithm are suggested to researches in the near future.