纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Cor...纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Correction Code,ECC)改造基本HFE(Hidden Field Equations)密码算法,所得的新密码算法具有纠错和加密功能,而且因其具有概率密码特性以及建立在MQ困难问题之上,具有很高的安全强度。展开更多
The number of equivalent keys in multivariate cryptosystem is closely related to the scheme security. This study analyzes the structure of the private key space in some multivariate schemes. The result gives the lower...The number of equivalent keys in multivariate cryptosystem is closely related to the scheme security. This study analyzes the structure of the private key space in some multivariate schemes. The result gives the lower bounds on the number of equivalent keys of some variants of the hidden field equation （HFE） scheme including plus, minus-plus, embedding, and internal perturbation. This method estimates the number of invertible transformations which maintain the form of the central map invariant. Furthermore,a formal proof shows that the two modifications of fixing and embedding are equivalent in security analyses of multivariate schemes. Also this paper corrects previous proofs in Wolf’s work on the number of equivalent keys in HFEv,the unbalanced oil and vinegar （UOV） scheme, and the stepwise triangular systems （STS）.展开更多
文摘纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Correction Code,ECC)改造基本HFE(Hidden Field Equations)密码算法,所得的新密码算法具有纠错和加密功能,而且因其具有概率密码特性以及建立在MQ困难问题之上,具有很高的安全强度。
基金Supported by the National Key Basic Research and Development (973) Program of China (No.2007CB807902)the Tsinghua University Innovation Research Program (No.2009THZ01002)
文摘The number of equivalent keys in multivariate cryptosystem is closely related to the scheme security. This study analyzes the structure of the private key space in some multivariate schemes. The result gives the lower bounds on the number of equivalent keys of some variants of the hidden field equation （HFE） scheme including plus, minus-plus, embedding, and internal perturbation. This method estimates the number of invertible transformations which maintain the form of the central map invariant. Furthermore,a formal proof shows that the two modifications of fixing and embedding are equivalent in security analyses of multivariate schemes. Also this paper corrects previous proofs in Wolf’s work on the number of equivalent keys in HFEv,the unbalanced oil and vinegar （UOV） scheme, and the stepwise triangular systems （STS）.
