Abstract
Yao’s theorem gives an equivalence between the indistinguishability of a pseudo-random generator and the unpredictability of the next bit from an asymptotic point of view. In this paper we present with detailed proofs, modified versions of Yao’s theorem which can be of interest for the study of practical cryptographic primitives. In particular we consider non-asymptotic versions. We study the case of one pseudo-random generator, then the case of a family of pseudo-random generators with the same fixed length and finally we consider the asymptotic case. We compute in each case the cost of the reduction (in the sense of complexity theory) between the two algorithms.
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Acknowledgements
We thank Marc Girault and the anonymous referees for their valuable remarks.
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Ballet, S., Rolland, R. A note on Yao’s theorem about pseudo-random generators. Cryptogr. Commun. 3, 189–206 (2011). https://doi.org/10.1007/s12095-011-0047-1
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DOI: https://doi.org/10.1007/s12095-011-0047-1
Keywords
- Complexity
- Cryptography
- Distinguishable
- Prediction
- Pseudo-randomness
- Pseudo-random number generator
- Yao’s theorem