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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-22670-0_34
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