Abstract
We study worst-case complexity assumptions that imply quantum bit-commitment schemes. First we show that QSZK \(\not\subseteq\) QMA implies a computationally hiding and statistically binding auxiliary-input quantum commitment scheme. We then extend our result to show that the much weaker assumption QIP \(\not\subseteq\) QMA (which is weaker than PSPACE \(\not\subseteq\) PP) implies the existence of auxiliary-input commitment schemes with quantum advice. Finally, to strengthen the plausibility of the separation QSZK \(\not\subseteq\) QMA we find a quantum oracle relative to which honest-verifier QSZK is not contained in QCMA.
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References
Aaronson, S.: Impossibility of succinct quantum proofs for collision-freeness. arxiv1101.0403 (2011)
Aaronson, S., Kuperberg, G.: Quantum versus classical proofs and advice. Theory of Computing 3(7), 129–157 (2007)
Ben-Or, M., Goldreich, O., Goldwasser, S., Håstad, J., Kilian, J., Micali, S., Rogaway, P.: Everything provable is provable in zero-knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 37–56. Springer, Heidelberg (1990)
Crépeau, C., Légaré, F., Salvail, L.: How to convert the flavor of a quantum bit commitment. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 60–77. Springer, Heidelberg (2001)
Fuchs, C.A., van de Graaf, J.: Cryptographic distinguishability measures for quantum-mechanical states. IEEE Trans. Inf. Theory 45(4), 1216–1227 (1999)
Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(3) (1991)
Haitner, I., Nguyen, M.H., Ong, S.J., Reingold, O., Vadhan, S.: Statistically hiding commitments and statistical zero-knowledge arguments from any one-way function. SIAM J. Comput. 39(3), 1153–1218 (2009)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)
Helstrom, C.W.: Detection theory and quantum mechanics. Inform. Control 10(3) (1967)
Impagliazzo, R., Luby, M.: One-way functions are essential for complexity based cryptography. In: IEEE Symp. Found. Comput. Sci. (FOCS), pp. 230–235 (1989)
Jain, R., Ji, Z., Upadhyay, S., Watrous, J.: QIP = PSPACE. In: ACM STOC (2010)
Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41(12), 2315–2323 (1994)
Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation. Graduate Studies in Mathematics, vol. 47. American Mathematical Society, Providence (2002)
Kitaev, A., Watrous, J.: Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. In: ACM STOC, pp. 608–617 (2000)
Lo, H.K., Chau, H.F.: Is quantum bit commitment really possible? Phys. Rev. Lett. 78, 3410 (1997)
Marriott, C., Watrous, J.: Quantum Arthur-Merlin games. Comput. Complex. 14(2) (2005)
Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett. 78, 3414 (1997)
Naor, M.: Bit commitment using pseudorandomness. J. of Cryptology 4(2), 151–158 (1991)
Nayak, A., Shor, P.: Bit-commitment-based quantum coin flipping. Phys. Rev. A 67(1), 012304 (2003)
Ostrovsky, R., Wigderson, A.: One-way functions are essential for non-trivial zero-knowledge. In: 2nd Israel Symposium on Theory and Computing Systems, pp. 3–17 (1993)
Rosgen, B., Watrous, J.: On the hardness of distinguishing mixed-state quantum computations. In: Conf. Comput. Compl. (CCC), pp. 344–354 (2005)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Spekkens, R.W., Rudolph, T.: Degrees of concealment and bindingness in quantum bit commitment protocols. Phys. Rev. A 65(1), 012310 (2001)
Vadhan, S.: An unconditional study of computational zero knowledge. SIAM J. Comput. 36(4), 1160–1214 (2006)
Watrous, J.: Succinct quantum proofs for properties of finite groups. In: FOCS 2000 (2000)
Watrous, J.: Limits on the power of quantum statistical zero-knowledge. In: FOCS 2002 (2002)
Watrous, J.: PSPACE has constant-round quantum interactive proof systems. Theor. Comput. Sci. 292(3), 575–588 (2003)
Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009)
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Chailloux, A., Kerenidis, I., Rosgen, B. (2011). Quantum Commitments from Complexity Assumptions. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_7
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