Abstract
In this paper we deal with unconditionally secure commitment schemes based on pre-distributed data. We provide bounds for the amount of data which has to be pre-distributed to the participants of the commitment, thus solving an open problem stated in the literature. We also introduce the issue of homomorphism in unconditionally secure commitment schemes. We provide a definition and a construction based on modules of mappings over finite rings. As an application of our constructions, we provide a new pre-distributed primitive which yields non-interactive unconditionally secure zero knowledge proofs of any polynomial relation among commitments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
T. Matsumoto and H. Imai, On the Key Predistribution Systems: A Practical Solution to the Key Distribution Problem, Advances in Cryptology — CRYPTO’ 87, Santa Barbara, California, USA, 1987, LNCS 293 Springer 1988
B. Pfitzmann and M. Waidner. Information theoretic pseudosignatures and byzantine agreement for t >= n/3, Reserach Report IBM Reserach, Nov. 1996
R.L. Rivest, Unconditionally secure commitment and oblivious transfer schemes using concealing channels and a trusted initializer, pre-print available from http://theory.lcs.mit.edu/~{}rivest/Rivest-commitment.pdf.
C. Blundo, B. Masucci, D. R. Stinson, and R. Wei, Constructions and Bounds for Unconditionally Secure Non-Interactive Commitment Schemes, Designs, Codes, and Cryptography, (special issue in honour of Ron Mullin), Vol. 26, pp. 97–110, 2002.
G. Hanaoka, J. Shikata, Y. Zheng, H. Imai: Unconditionally Secure Digital Signature Schemes Admitting Transferability. Advances in Cryptology — ASIACRYPT 2000, Kyoto, Japan 2000, LNCS 1976, Springer 2000
U. Maurer, Authentication Theory and Hypothesis Testing, IEEE Transaction on Information Theory, vol. 46 No. 4, pp. 1350–1356, 2000.
J. Kilian, A Note on Efficient zero-knowledge Proofs and Arguments, 24th ACM Symposium on Theory of Computation, 1992, pp. 723–732
R. Blahut. Principles and Practice of Information Theory, Addison-Wesley Publishing Company, 1987.
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
Nascimento, A.C.A., Otsuka, A., Imai, H., Mueller-Quade, J. (2003). Unconditionally Secure Homomorphic Pre-distributed Commitments. In: Fossorier, M., Høholdt, T., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2003. Lecture Notes in Computer Science, vol 2643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44828-4_11
Download citation
DOI: https://doi.org/10.1007/3-540-44828-4_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40111-7
Online ISBN: 978-3-540-44828-0
eBook Packages: Springer Book Archive