Abstract
Many of the results in Modern Cryptography are actually transformations of a basic computational phenomenon (i.e., a basic primitive, tool or assumption) to a more complex phenomenon (i.e., a higher level primitive or application). The transformation is explicit and is always accompanied by an explicit reduction of the violation of the security of the complex phenomenon to the violation of the simpler one. A key aspect is the efficiency of the reduction. We discuss and slightly modify the hierarchy of reductions originally suggested by Leonid Levin.
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
Blum, M., Micali, S.: How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. SICOMP 13, 850–864 (1982); Preliminary version in 23rd FOCS (1982)
Goldreich, O.: Foundation of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)
Goldreich, O.: Foundation of Cryptography: Basic Applications. Cambridge University Press, Cambridge (2004)
Goldreich, O., Goldwasser, S., Micali, S.: How to Construct Random Functions. JACM 33(4), 792–807 (1986)
Goldreich, O., Impagliazzo, R., Levin, L.A., Venkatesan, R., Zuckerman, D.: Security Preserving Amplification of Hardness. In: 31st FOCS, pp. 318–326 (1990)
Goldreich, O., Levin, L.A.: Hard-core Predicates for any One-Way Function. In: 21st STOC, pp. 25–32 (1989)
Goldwasser, S., Micali, S.: Probabilistic Encryption. JCSS 28(2), 270–299 (1984); Preliminary version in 14th STOC (1982)
Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof Systems. SICOMP 18, 186–208 (1989); Preliminary version in 17th STOC (1985) Earlier versions date to 1982
Goldwasser, S., Micali, S., Rivest, R.L.: A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks. In: SICOMP, pp. 281–308 (April 1988)
Levin, L.A.: One-Way Function and Pseudorandom Generators. Combinatorica 7, 357–363 (1987)
Levin, L.A.: Randomness and Non-determinism. J. Symb. Logic 58(3), 1102–1103 (1993)
Luby, M.: Pseudorandomness and Cryptographic Applications. Princeton University Press, Princeton (1996)
Yao, A.C.: Theory and Application of Trapdoor Functions. In: 23rd FOCS, pp. 80–91 (1982)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Goldreich, O. (2011). On Security Preserving Reductions – Revised Terminology. 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_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-22670-0_34
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)