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中文摘要：
多变量公钥密码体制中存在多个私钥对应于同一个公钥的等价密钥问题.提出了Plus保形变换,并给出了其表达形式.用Plus保形变换和其他保形变换研究了几类多变量公钥密码体制的等价密钥问题.证明了只有用Big保形变换和Frobenius保形变换,才能得到Square体制的等价密钥.结果表明,任一公钥都有指数级个私钥与之对应,从而使私钥空间大量减少;多变量公钥密码体制要达到预定的安全强度,必须提高体制参数的大小.同时,使用私钥仿射结构具有稀疏性的标准形式,能有效地减少运算量,提高存储效率.
英文摘要：
The multivariate public key cryptosystem has the problem that multiple private keys correspond to a common public key.This paper defines the Plus sustaining transformation and presents its expression.The problem of equivalent keys in some multivariate public key cryptographic schemes is investigated with the Plus sustaining transformation and other sustaining transformations.It is proved that the equivalent keys of the Square scheme can be obtained only through the Big and the Frobenius sustaining transformation.The results show that the private key space can be significantly reduced due to the fact that any given public key corresponds to exponentially many private keys.Accordingly,to achieve the expected security,we must choose larger system parameters in the multivariate public key cryptosystems.Moreover,by utilizing the sparse normal form of affine transformations of private keys,we can effectively reduce the computational complexity and the storage requirements.
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