Abstract
In extension of the bit commitment task and following work initiated by Crépeau, we introduce and solve the problem of characterising the optimal rate at which a discrete memoryless channel can be used to for bit commitment. It turns out that the answer is very intuitive: it is the maximum equivocation of the channel (after removing trivial redundancy), even when unlimited noiseless bidirectional side communication is allowed. By a well–known reduction, this result provides a lower bound on the channel’s capacity for implementing coin tossing.
The method of proving this relates the problem to Wyner’s wire–tap channel in an amusing way. There is also an extension to quantum channels.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahlswede, R., Csiszár, I.: Common Randomness in Information Theory and Cryptography - Part I: Secret Sharing. IEEE Trans. Inf. Theory 39(4), 1121–1132 (1993)
Ahlswede, R., Winter, A.: Strong converse for identification via quantum channels. IEEE Trans. Inf. 48(3), 569–579 (2002); Addendum ibid 49(1), p. 346 (2003)
Beaver, D.: Commodity-Based Cryptography(Extended Abstract). In: Proc. 29thAnnual ACM Symposium on the Theory of Computing, El Paso, TX, May 4-6, pp. 446–455. ACM, New York (1997)
Bennett, C.H., Brassard, G.: Quantum Cryptography: Public Key Distribution and Coin Tossing. In: Proc. IEEE Int. Conf. on Computers Systems and Signal Processing, Bangalore (India), pp. 175–179 (1984)
Bennett, C.H., Brassard, G., Crépeau, C., Maurer, U.: Generalized Privacy Amplification. IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995)
Bennett, C.H., Shor, P.W.: Quantum Information Theory. IEEE Trans. Inf. Theory 44(6), 2724–2742 (1998)
Blum, M.: Coin fipping by telephone: a protocol for solving impossible problems. In: Proc. IEEE Computer Conference, pp. 133–137 (1982)
Brassard, G., Chaum, D., Crepeau, C.: Minimum disclosure proofs of knowledge. J. Computer Syst. Sci. 37, 156–189 (1988)
Brassard, G., Crepeau, C., Yung, M.: Constant-round perfect zero-knowledge computationally convincing protocols. Theoretical Computer Science 84, 23–52 (1991)
Cai, N., Yeung, R.W.: Quantum Privacy and Quanum Wiretap Channels (2003) (manuscript)
Chernoff, H.: A measure of asymptotic eciency for tests of a hypothesis based on the sum of observations. Ann. Math. Statistics 23, 493–507 (1952)
Crépeau, C.: Efficient Cryptographic Protocols Based on Noisy Channels. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 306–317. Springer, Heidelberg (1997)
Crépeau, C., Kilian, J.: Achieving oblivious transfer using weakened security assumptions. In: Proc. 29th FOCS, pp. 42–52. IEEE, Los Alamitos (1988)
Csiszár, I., Körner, J.: Information Theory: Coding Theorems for Discrete Memoryless Channels. Academic Press, New York (1981)
Damgård, I.B., Kilian, J., Salvail, L.: On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 56–73. Springer, Heidelberg (1999)
Halevi, S.: Efficient commitment schemes with bounded sender and unbounded receiver. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 84–96. Springer, Heidelberg (1995)
Halevi, S., Micali, S.: Practical and Provably-Secure Commitment Schemes from Collision Free Hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996)
Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum channel. Probl. Inf. Transm. 9(3), 177–183 (1973)
Maurer, U.: Protocols for Secret Key Agreement by Public Discussion Based on Common Information. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 461–470. Springer, Heidelberg (1993); Secret Key Agreement by Public Discussion. IEEE Trans. Inf. Theory 39(3),733-742 (1993)
Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Letters 78(17), 3414–3417 (1997)
Naor, M.: Bit commitment using pseudo-randomness. J. Cryptology 2(2), 151–158 (1991)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Ostrovsky, R., Venkatesan, R., Yung, M.: Secure commitments against a powerful adversary. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 439–448. Springer, Heidelberg (1992)
Rivest, R.L.: Unconditionally Secure Commitment and Oblivious Transfer Schemes Using Private Channels and a Trusted Initializer (1999) (unpublished manuscript)
Shannon, C.E.: A mathematical theory of communication, Bell System Tech. Journal 27, 379–423, 623-656 (1948)
Wyner, A.: The Wire Tap Channel. Bell System Tech. Journal 54, 1355–1387 (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Winter, A., Nascimento, A.C.A., Imai, H. (2003). Commitment Capacity of Discrete Memoryless Channels. In: Paterson, K.G. (eds) Cryptography and Coding. Cryptography and Coding 2003. Lecture Notes in Computer Science, vol 2898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40974-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-40974-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20663-7
Online ISBN: 978-3-540-40974-8
eBook Packages: Springer Book Archive