Advances in quantum computers pose potential threats to the currently used public-key cryptographic algorithms such as RSA and ECC.As a promising candidate against attackers equipped with quantum computational power,M...Advances in quantum computers pose potential threats to the currently used public-key cryptographic algorithms such as RSA and ECC.As a promising candidate against attackers equipped with quantum computational power,Multivariate Public-Key Cryptosystems(MPKCs)has attracted increasing attention in recently years.Unfortunately,the existing MPKCs can only be used as multivariate signature schemes,and the way to construct an efficient MPKC enabling secure encryption remains unknown.By employing the basic MQ-trapdoors,this paper proposes a novel multivariate encryption scheme by combining MPKCs and code-based public-key encryption schemes.Our new construction gives a positive response to the challenges in multivariate public key cryptography.Thorough analysis shows that our scheme is secure and efficient,and its private key size is about 10 times smaller than that of McEliece-type cryptosystems.展开更多
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 ...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.展开更多
Multivariate Public Key Cryptography （MPKC） has intensively and rapidly developed during the past three decades. MPKC is a promising candidate for post-quantum cryptography. However, designing it is universally rega...Multivariate Public Key Cryptography （MPKC） has intensively and rapidly developed during the past three decades. MPKC is a promising candidate for post-quantum cryptography. However, designing it is universally regarded as a difficult task to design a secure MPKC foundation scheme, such as an encryption scheme and key exchange scheme. In this work, we investigate the security of a new public key cryptosystem that is based on the Morphism of Polynomials （MP）. The public key cryptosystem proposed by Wang et al. （Wuhan University, China） comprises a key exchange scheme and encryption scheme. Its security can be provably reduced to the hardness of solving a new difficult problem, namely, the Decisional Multivariate Diffie Hellman （DMDH） problem. This problem Js a variant of the MP problem, which is difficult to solve by random systems. We present a proposition that reduces the DMDH problem to an easy example of the MP problem. Then, we propose an efficient algorithm for the Key Recover Attack （KRA） on the schemes of the public key cryptosystem. In practice, we are able to entirely break the cryptosystem＇s claimed parameter of 96 security levels in less than 17.252 s. Furthermore, we show that finding parameters that yield a secure and practical scheme is impossible.展开更多
Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. Ho...Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.展开更多
基金National Natural Science Foundation of China under Grant No. 60970115,60970116,61003267, 61003268,61003214the Major Research Plan of the National Natural Science Foundation of China under Grant No. 91018008
文摘Advances in quantum computers pose potential threats to the currently used public-key cryptographic algorithms such as RSA and ECC.As a promising candidate against attackers equipped with quantum computational power,Multivariate Public-Key Cryptosystems(MPKCs)has attracted increasing attention in recently years.Unfortunately,the existing MPKCs can only be used as multivariate signature schemes,and the way to construct an efficient MPKC enabling secure encryption remains unknown.By employing the basic MQ-trapdoors,this paper proposes a novel multivariate encryption scheme by combining MPKCs and code-based public-key encryption schemes.Our new construction gives a positive response to the challenges in multivariate public key cryptography.Thorough analysis shows that our scheme is secure and efficient,and its private key size is about 10 times smaller than that of McEliece-type cryptosystems.
基金supported by the National Natural Science Foundation of China (Nos.61303212,61303024,61170080,61501333,61303024,and 61332019)the Foundation of Science and Technology on Information Assurance Laboratory (No.KJ-14-002)
文摘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.
文摘Multivariate Public Key Cryptography （MPKC） has intensively and rapidly developed during the past three decades. MPKC is a promising candidate for post-quantum cryptography. However, designing it is universally regarded as a difficult task to design a secure MPKC foundation scheme, such as an encryption scheme and key exchange scheme. In this work, we investigate the security of a new public key cryptosystem that is based on the Morphism of Polynomials （MP）. The public key cryptosystem proposed by Wang et al. （Wuhan University, China） comprises a key exchange scheme and encryption scheme. Its security can be provably reduced to the hardness of solving a new difficult problem, namely, the Decisional Multivariate Diffie Hellman （DMDH） problem. This problem Js a variant of the MP problem, which is difficult to solve by random systems. We present a proposition that reduces the DMDH problem to an easy example of the MP problem. Then, we propose an efficient algorithm for the Key Recover Attack （KRA） on the schemes of the public key cryptosystem. In practice, we are able to entirely break the cryptosystem＇s claimed parameter of 96 security levels in less than 17.252 s. Furthermore, we show that finding parameters that yield a secure and practical scheme is impossible.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60873249, 60973142)the National High-Tech Research & Development Program of China (Grant Nos. 2008AA10Z419, 2009AA011906)the Project Funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua University
文摘Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.
