A note on a Yao's theorem about pseudo-random generators.

Stéphane Ballet (1) , Robert Rolland (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: Complexity; Cryptography; Distinguishable; Prediction; Pseudo-randomness; Pseudo-random number generator; Yao’s theorem

Domaines: Théorie de l'information et codage [math.IT]

Stéphane Ballet, Robert Rolland. A note on a Yao's theorem about pseudo-random generators.. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2011, 3 (4), pp.189-206. ⟨hal-01079409⟩