有限域上二次型的密码学特性

Cryptography Property of Quadratic Forms over Finite Fields

该文给出有限域上二次型的紧致表示形式 ,讨论了它们的密码学特性 ;给出了特征等于 2的有限域上 ,二次型是平衡函数的充要条件 ,并指出特征不等于 2的有限域上 ,二次型都不是平衡函数 ;给出了二次函数是平衡函数的充要条件 .从该文结果可以看出Pieprzyk等用二次函数构造的方案是错误的 .

The compact form of quadratic forms over finite field is presented, the cryptography property is considered. The sufficient and necessary conditions that quadratic forms is balance over finite fields of characteristic 2 are presented. It is pointed that there are not balance quadratic forms over finite fields whose characteristic is not equal to 2. The sufficient and necessary conditions that quadratic function is balance are presented. Using the result obtained in the paper, authors point out the errors in the papers published by J. Pizprzyk in 2001, 2002.