This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success probability.The runtime complexity of the algorit...This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success probability.The runtime complexity of the algorithm is polynomial in the size of F and the condition number of certain Macaulay matrix associated with F.As a consequence,the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of F.The authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum,the block cipher AES,the hash function SHA-3/Keccak,the multivariate public key cryptosystems,and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are large.This leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.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
基金supported by the National Natural Science Foundation of China under Grant No.11688101and NKRDP 2018YFA0704705。
文摘This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success probability.The runtime complexity of the algorithm is polynomial in the size of F and the condition number of certain Macaulay matrix associated with F.As a consequence,the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of F.The authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum,the block cipher AES,the hash function SHA-3/Keccak,the multivariate public key cryptosystems,and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are large.This leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.
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.
