El-Gamal AA_β公钥密码体制--一种利用子集和问题设计非对称密码体制的新方法
The El-Gamal AA_β Public Key Cryptosystem - A new approach utilizing the subset sum problem in designing an asymmetric cryptosystem
摘要：
El-Gamal AA_β公钥密码体制是一种基于分段AA_β函数的新的非对称密码体制。AA_β-函数本质上是一个单向布尔函数，它是由Diffie Hellman密钥交换过程中计算g^a（mod p）以及RSA密码体制中计算C \equiv M^e（mod N）和M \equiv C^d（mod N）时的平方和乘法过程所激发的。它也是由椭圆曲线密码体制中的加法和倍点运算E=kG所激发的。围绕这个新设计的非对称密码系统的数学难题是NP完全问题，称为子集和问题。El-Gamal AA_β公钥密码体制通过向接收方发送双参数密文来模仿El-Gamal密码体制和椭圆曲线密码体制。
英文摘要：
The El-Gamal AA_β Public Key Cryptosystem is a new asymmetric cryptosystem based on the piecewise AA_β-function. The AA_β-function which is essentially a one way Boolean function was motivated by the squaring and multiplying process while computing g^a (mod p) in the Diffie Hellman key exchange procedure and also computing C \equiv M^e (mod N) and M \equiv C^d (mod N) in the RSA cryptosystem. It was also motivated by the add and double point operation E=kG in the elliptic curve cryptosystem. The hard mathematical problem surrounding this newly designed asymmetric cryptosystem is the NP-complete problem known as the subset sum problem. The El-Gamal AA_β Public Key Cryptosystem mimics the El-Gamal Cryptosystem and the Elliptic Curve Cryptosystem by sending a two parameter ciphertext to the recipient.
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