Abstract
In 1995, Ajtai described a construction of one-way functions whose security is equivalent to the difficulty of some well known approximation problems in lattices. We show that essentially the same construction can also be used to obtain collision-free hashing. This paper contains a self-contained proof sketch of Ajtai’s result.
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.
Similar content being viewed by others
References
Ajtai, M.: Generating Hard Instances of Lattice Problems. In: 28th ACM Symposium on Theory of Computing, Philadelphia, pp. 99–108 (1996)
Carter, L., Wegman, M.: Universal Classes of Hash Functions. J. Computer and System Sciences 18, 143–154 (1979)
Goldreich, O., Krawczyk, H., Luby, M.: On the existence of pseudorandom generators. SIAM J. on Computing 22(6), 1163–1175 (1993)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A Pseudorandom Generator from any One-way Function. SIAM J. on Computing 28(4), 1364–1396 (1990); Combines papers of Impagliazzo et al. (21st STOC, 1989) and Håstad (22nd STOC, 1990)
Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring Polynomials with Rational Coefficients. Mathematische Annalen 261, 515–534 (1982)
Schnorr, C.P.: A more efficient algorithm for a lattice basis reduction. Journal of Algorithms 9, 47–62 (1988)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Goldreich, O., Goldwasser, S., Halevi, S. (2011). Collision-Free Hashing from Lattice Problems. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-22670-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22669-4
Online ISBN: 978-3-642-22670-0
eBook Packages: Computer ScienceComputer Science (R0)