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Number-theoretic constructions of efficient pseudo-random functions
Abstract
We describe efficient constructions for various cryptographic primitives (both in private-key and in public-key cryptography). We show these constructions to be at least as secure as the decisional version of the Diffie-Hellman assumption or as the assumption that factoring is hard. Our major result is a new construction of pseudo-random functions such that computing their value at any given point involves two multiple products. This is much more efficient than previous proposals. Furthermore, these functions have the advantage of being in TC/sup 0/ (the class of functions computable by constant depth circuits consisting of a polynomial number of threshold gates) which has several interesting applications. The simple algebraic structure of the functions implies additional features. In particular, we show a zero-knowledge proof for statements of the form "y=f/sub s/(x)" and "y/spl ne/f(x)" given a commitment to a key s of a pseudo-random function f/sub s/.
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Cites
A public key cryptosystem and a signature scheme based on discrete logarithms
Elgamal, T. (1985) · IEEE Transactions on Information Theory · doi:10.1109/tit.1985.1057074 · Cited by 8,059
Valiant, L. G. (1984) · Communications of the ACM · doi:10.1145/1968.1972 · Cited by 3,279
Cited by
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Practical Threshold Signatures
Shoup, V. (2000) · Lecture Notes in Computer Science · doi:10.1007/3-540-45539-6_15 · Cited by 874
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Steiner, M., Tsudik, G., & Waidner, M. (2000) · IEEE Transactions on Parallel and Distributed Systems · doi:10.1109/71.877936 · Cited by 601
Keyword Search and Oblivious Pseudorandom Functions
Freedman, M. J., Ishai, Y., Pinkas, B., & Reingold, O. (2005) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-30576-7_17 · Cited by 441
Self-citationMiMC: Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity
Albrecht, M., Grassi, L., Rechberger, C., Roy, A., & Tiessen, T. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-662-53887-6_7 · Cited by 258
Metadata
- Authors
- Naor, M., & Reingold, O.
- Venue
- Proceedings 38th Annual Symposium on Foundations of Computer Science
- Publisher
- IEEE Comput. Soc
- Published
- 2002-11-22
- Pages
- 458-467
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2144560442
- Cited by
- 353
- References
- 2
- FWCI
- 12.78
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Naor, M., & Reingold, O. (2002). Number-theoretic constructions of efficient pseudo-random functions. Proceedings 38th Annual Symposium on Foundations of Computer Science. https://doi.org/10.1109/sfcs.1997.646134
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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