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
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
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 (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.
