The Riemann hypothesis is part of Hilbert’s eighth problem in David Hilbert’s list of 23 unsolved problems. It is also one of the Clay Mathematics Institute’s Millennium Prize Problems. Some mathematicians consider...The Riemann hypothesis is part of Hilbert’s eighth problem in David Hilbert’s list of 23 unsolved problems. It is also one of the Clay Mathematics Institute’s Millennium Prize Problems. Some mathematicians consider it the most important unresolved problem in pure mathematics. Many mathematicians made a lot of efforts;they don’t have to prove the Riemann hypothesis. In this paper, I use the analytic methods to deny the Riemann Hypothesis;if there’s something wrong, please criticize and correct me.展开更多
Arbitrated quantum signature(AQS) is an important branch in quantum cryptography to authenticate quantum information, and cryptanalysis on AQS protocols helps to evaluate and improve security of AQS. Recently, it is d...Arbitrated quantum signature(AQS) is an important branch in quantum cryptography to authenticate quantum information, and cryptanalysis on AQS protocols helps to evaluate and improve security of AQS. Recently, it is discovered that an AQS protocol based on chained controlled-NOT(CNOT) algorithm is vulnerable to a novel attack because a transformation from binary keys into permutations and the chained CNOT algorithm have special properties, which enables a malicious receiver to forge signatures with probability 1/2. Moreover, a malicious signer can also deny his signatures with probability 1/4. Then, two possible improved methods are presented to resist these attacks: one is padding constants to reduce probability of the successful attacks, and the other is a circular chained CNOT algorithm to make the attack strategy invalid. And the security analysis shows that both the two improve methods could well resist these attacks.展开更多
文摘The Riemann hypothesis is part of Hilbert’s eighth problem in David Hilbert’s list of 23 unsolved problems. It is also one of the Clay Mathematics Institute’s Millennium Prize Problems. Some mathematicians consider it the most important unresolved problem in pure mathematics. Many mathematicians made a lot of efforts;they don’t have to prove the Riemann hypothesis. In this paper, I use the analytic methods to deny the Riemann Hypothesis;if there’s something wrong, please criticize and correct me.
基金supported by the National Natural Science Foundation of China (61502048)the National Science and Technology Major Project (2017YFB0803001)
文摘Arbitrated quantum signature(AQS) is an important branch in quantum cryptography to authenticate quantum information, and cryptanalysis on AQS protocols helps to evaluate and improve security of AQS. Recently, it is discovered that an AQS protocol based on chained controlled-NOT(CNOT) algorithm is vulnerable to a novel attack because a transformation from binary keys into permutations and the chained CNOT algorithm have special properties, which enables a malicious receiver to forge signatures with probability 1/2. Moreover, a malicious signer can also deny his signatures with probability 1/4. Then, two possible improved methods are presented to resist these attacks: one is padding constants to reduce probability of the successful attacks, and the other is a circular chained CNOT algorithm to make the attack strategy invalid. And the security analysis shows that both the two improve methods could well resist these attacks.
