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14
Quantum algorithms for algebraic problems
, 2008
"... Quantum computers can execute algorithms that dramatically outperform classical computation. As the bestknown example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational pro ..."
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Cited by 23 (1 self)
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Quantum computers can execute algorithms that dramatically outperform classical computation. As the bestknown example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum
Quantum measurements for hidden subgroup problems with optimal sample
 Quantum Information and Computation
, 2008
"... One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versi ..."
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Cited by 16 (2 self)
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One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versions of the hidden subgroup problem. As a consequence of the bounds, we show that the sample complexity for both of the decision and identification versions isΘ(logH / log p) for a candidate setH of hidden subgroups in the case that the candidate subgroups have the same prime order p, which implies that the decision version is at least as hard as the identification version in this case. In particular, it does so for the important instances such as the dihedral and the symmetric hidden subgroup problems. Moreover, the upper bound of the identification is attained by the pretty good measurement, which shows that the pretty good measurements can identify any hidden subgroup of an arbitrary group with at most O(logH) samples. 1
Security notions for quantum publickey cryptography
 IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (Japanese Edition), J90A(5):367–375
, 2007
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On the Power of Quantum Encryption Keys
, 2008
"... The standard definition of quantum state randomization, which is the quantum analog of the classical onetime pad, consists in applying some transformation to the quantum message conditioned on a classical secret key k. We investigate encryption schemes in which this transformation is conditioned on ..."
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The standard definition of quantum state randomization, which is the quantum analog of the classical onetime pad, consists in applying some transformation to the quantum message conditioned on a classical secret key k. We investigate encryption schemes in which this transformation is conditioned on a quantum encryption key state ρk instead of a classical string, and extend this symmetrickey scheme to an asymmetrickey model in which copies of the same encryption key ρk may be held by several different people, but maintaining informationtheoretical security. We find bounds on the message size and the number of copies of the encryption key which can be safely created in these two models in terms of the entropy of the decryption key, and show that the optimal bound can be asymptotically reached by a scheme using classical encryption keys. This means that the use of quantum states as encryption keys does not allow more of these to be created and shared, nor encrypt larger messages, than if these keys are purely classical.
Quantum walks public key cryptographic system
"... Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quan ..."
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Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum publickey cryptographic system based on quantum walks. In particular, in the proposed protocol the public key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of publickey generation and encryption/decryption procedures.
1 SQIG—Instituto de Telecomunicações
"... Oblivious transfer based on quantum state ..."
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Quantum AsymmetricKey Cryptosystem Secure Against A Computationally Unbounded Adversary
, 2006
"... In this paper we propose a quantum asymmetrickey cryptosystem, which does not rely on a computationally hard problem for security, but on uncertainty principles of quantum mechanics, thus obtaining security against a computationally unbounded adversary. We first propose a universally composable sec ..."
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In this paper we propose a quantum asymmetrickey cryptosystem, which does not rely on a computationally hard problem for security, but on uncertainty principles of quantum mechanics, thus obtaining security against a computationally unbounded adversary. We first propose a universally composable security criteria for quantum asymmetrickey cryptosystems by adapting the universally composable security of quantum key distribution by Mayers et al. [4, 3] to the context of quantum asymmetrickey encryption. We then give a specific implementation using this security notion, which improves the quantum asymmetrickey cryptosystem of Kawachi et al. [15] in the sense of informationtheoretic security. We prove that the information leak on the decryption key from the multiple copies of the encryption keys released in our scheme is exponentially smaller than that in [15], which allows Alice to produce exponentially more encryption keys.
unknown title
, 903
"... Publickey cryptography based on bounded quantum reference frames ..."
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