Journal Article10.1137/060670997
Zero-Knowledge against Quantum Attacks
TL;DR: This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks, and establishes for the first time that true zero- knowledge is indeed possible in the presence of quantum information and computation.
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Abstract: This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks. This includes the well-known Goldreich-Micali-Wigderson classical zero-knowledge protocols for graph isomorphism and graph 3-coloring (assuming the existence of quantum computationally concealing commitment schemes in the second case). Also included is a quantum interactive proof system for a complete problem for the complexity class of problems having honest verifier quantum statistical zero-knowledge proofs, which therefore establishes that honest verifier and general quantum statistical zero-knowledge are equal: $\mathrm{QSZK}= \mathrm{QSZK}_{\mathrm{HV}}$. Previously no nontrivial interactive proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.
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References
•Book
Quantum Computation and Quantum Information
Michael A. Nielsen,Isaac L. Chuang +1 more
- 01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Quantum Computation and Quantum Information
Michael A. Nielsen,Isaac L. Chuang +1 more
- 01 Dec 2010
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
19.6K
A method for obtaining digital signatures and public-key cryptosystems
TL;DR: An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key.
A Method for Obtaining Digital Signatures and Public Key Cryptosystems (Formerly on Digital Signatures and Public Key Cryptosystems)
Ronald L. Rivest,Adi Shamir,Len Adelman +2 more
- 01 Jan 1977
TL;DR: In this paper, a message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret prime numbers p and q.
8.2K
A fast quantum mechanical algorithm for database search
Lov K. Grover
- 01 Jul 1996
TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.
8.1K