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114
Quantum algorithms for solvable groups
 In Proceedings of the 33rd ACM Symposium on Theory of Computing
, 2001
"... ABSTRACT In this paper we give a polynomialtime quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group, r ..."
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Cited by 45 (1 self)
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ABSTRACT In this paper we give a polynomialtime quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group
Succinct Quantum Proofs for Properties of Finite Groups
 In Proc. IEEE FOCS
, 2000
"... In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NPtype proof. Specifically, we consider quantum proofs for properties of blackbox groups, which are finite g ..."
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Cited by 83 (3 self)
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in polynomial time on a quantum computer. Classically this is impossibleit is proved that there exists a group oracle relative to which this problem does not have succinct proofs that can be checked classically with bounded error in polynomial time (i.e., the problem is not in MA relative to the group oracle
Parallelization, Amplification, and Exponential Time Simulation of Quantum Interactive Proof Systems
 In Proceedings of the 32nd ACM Symposium on Theory of Computing
, 2000
"... In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verier may perform quantum computations and exchange quantum information. We prove that any polynomialround quantum interactive proof system with twosided bounded error can be p ..."
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Cited by 77 (19 self)
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In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verier may perform quantum computations and exchange quantum information. We prove that any polynomialround quantum interactive proof system with twosided bounded error can
PSPACE has 2round quantum interactive proof systems
, 2008
"... In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive proof system that requires only two round ..."
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Cited by 1 (0 self)
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rounds of communication between the prover and verifier, while having exponentially small (onesided) probability of error. It follows that quantum interactive proof systems are strictly more powerful than classical interactive proof systems in the constantround case unless the polynomial time hierarchy
Probabilistically Checkable Proofs
"... Consider the problem of checking a proof for a mathematical theorem. Since proofs may be long and difficult to check in their entirety, the question is whether it would be possible to come up with a way of presenting a proof so that only a small part of it has to be checked in order to judge the va ..."
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, however, the prover is considered to be memoryless and thus cannot adjust his answers based on previous queries posed to him. A more appealing interpretation is to view PCP systems as a possible way of generalizing NP. Instead of conducting a polynomialtime computation upon receiving the entire proof (as
Epistemic Lessons from Computer Science: Interactive Proofs and Zero Knowledge
, 2007
"... This paper is situated at the junction of two youthful academic currents. The first current is a philosophical one, with a pioneering group of philosophers of science recently turning their attention to computer science in earnest, recognizing the Philosophy of Computer Science (PCS) as a new branch ..."
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computer science has to contribute to philosophy, rather than, say, economics or quantum physics. In particular, this paper will look at two related gems of computer science, the interactive proofs and zero knowledge protocols of Goldwasser, Micali and Rackoff (1985), and explore what these concepts have
Anonymous Hierarchical IdentityBased Encryption (Without Random Oracles). In: Dwork
 CRYPTO 2006. LNCS,
, 2006
"... Abstract We present an identitybased cryptosystem that features fully anonymous ciphertexts and hierarchical key delegation. We give a proof of security in the standard model, based on the mild Decision Linear complexity assumption in bilinear groups. The system is efficient and practical, with sm ..."
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Cited by 119 (10 self)
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was first used by Joux Decision Linear: The Linear assumption was first proposed by Boneh, Boyen, and Shacham for group signatures "Hard" means algorithmically nonsolvable with probability 1 /2 + Ω(poly(Σ) −1 ) in time O(poly(Σ)) for efficiently generated random "bilinear instances
On the fly authentication and signature schemes based on groups of unknown order
 Journal of Cryptology
"... Abstract. In response to the current need for fast, secure and cheap publickey cryptography, we propose an interactive zeroknowledge identification scheme and a derived signature scheme that combine provable security based on the problem of computing discrete logarithms in any group, short keys, ..."
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Cited by 26 (1 self)
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consequence, it can be used with most cryptographic group structures, including those of unknown order. Furthermore, the computation of the prover's response is done over the integers, hence can be done with very limited computational capabilities. This paper provides complete security proofs
Compositional Proofs of Concurrent Programs
"... This proposal concerns proving the correctness of programs expressed in the UNITY formalism. Under an existing EPSRC project, Paulson has already developed an environment for verifying UNITY programs. The environment is based on and distributed with Isabelle, a proof assistant developed at Cambridge ..."
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of the most important proof environments used today, namely HOL and Isabelle. Isabelle (originated by Paulson) is a generic theorem prover. It supports interactive proof in several formal systems, including firstorder logic, higherorder logic and ZermeloFrankel set theory. Derived logics can be supported
Results 1  10
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114