Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certain mathematical problems on non-commutative algebraic structures until now. In this background, Majid Khan et al.proposed two novel public-key encryption schemes based on large abelian subgroup of general linear group over a residue ring. In this paper we show that the two schemes are not secure. We present that they are vulnerable to a structural attack and that, it only requires polynomial time complexity to retrieve the message from associated public keys respectively. Then we conduct a detailed analysis on attack methods and show corresponding algorithmic description and efficiency analysis respectively. After that, we propose an improvement assisted to enhance Majid Khan's scheme. In addition, we discuss possible lines of future work.
The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.
MAO ShaowuZHANG HuanguoWU WanqingZHANG PeiSONG JunLIU Jinhui
Advances in quantum computation threaten to break public key cryptosystems that are based on the difficulty of factorization or the difficulty of discrete logariths, although, no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures up to now. The proposed new quasi-inverse based cryptography scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we illustrate that two of the quasi-inverse based cryptography are vulnerable to a structural attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. In addition, we conduct a detailed analysis on attack methods and provide some improved suggestions on these two schemes.
During the last two decades, there has been intensive and fast development in Multivariate Public Key Cryptography(MPKC), which is considered to be an important candidate for post-quantum cryptography. However,it is universally regarded as a difficult task, as in the Knapsack cryptosystems, to design a secure MPKC scheme(especially an encryption scheme) employing the existing trapdoor construction. In this paper, we propose a new key-exchange scheme and an MPKC scheme based on the Morphism of Polynomials(MP) problem. The security of the proposed schemes is provably reducible to the conjectured intractability of a new difficult problem,namely the Decisional Multivariate Diffie-Hellman(DMDH) problem derived from the MP problem. The proposed key agreement is one of several non-number-theory-based protocols, and is a candidate for use in the post-quantum era. More importantly, by slightly modifying the protocol, we offer an original approach to designing a secure MPKC scheme. Furthermore, the proposed encryption scheme achieves a good tradeoff between security and efficiency,and seems competitive with traditional MPKC schemes.
Advances in quantum computers threaten to break public-key cryptosystems(e.g., RSA, ECC, and EIGamal), based on the hardness of factoring or taking a discrete logarithm. However, no quantum algorithms have yet been found for solving certain mathematical problems in non-commutative algebraic structures. Recently,two novel public-key encryption schemes, BKT-B cryptosystem and BKT-FO cryptosystem, based on factorization problems have been proposed at Security and Communication Networks in 2013. In this paper we show that these two schemes are vulnerable to structural attacks and linearization equations attacks, and that they only require polynomial time complexity to obtain messages from associated public keys. We conduct a detailed analysis of the two attack methods and show corresponding algorithmic descriptions and efficiency analyses. In addition, we provide some improvement suggestions for the two public-key encryption schemes.
Jinhui LiuAiwan FanJianwei JiaHuanguo ZhangHouzhen WangShaowu Mao
The weight hierarchy of a [n; kI q] linear code C over Fq is the sequence(d1,… dr,… dk), where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new preconditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.
