On the Concrete Security of Goldreich’s Pseudorandom Generator

Abstract : Local pseudorandom generators allow to expand a short random string into a long pseudo-random string, such that each output bit depends on a constant number d of input bits. Due to its extreme efficiency features, this intriguing primitive enjoys a wide variety of applications in cryptography and complexity. In the polynomial regime, where the seed is of size n and the output of size n s for s > 1, the only known solution, commonly known as Goldreich's PRG, proceeds by applying a simple d-ary predicate to public random sized subsets of the bits of the seed. While the security of Goldreich's PRG has been thoroughly investigated, with a variety of results deriving provable security guarantees against class of attacks in some parameter regimes and necessary criteria to be satisfied by the underlying predicate, little is known about its concrete security and efficiency. Motivated by its numerous theoretical applications and the hope of getting practical instantiations for some of them, we initiate a study of the concrete security of Goldreich's PRG, and evaluate its resistance to cryptanalytic attacks. Along the way, we develop a new guess-and-determine-style attack, and identify new criteria which refine existing criteria and capture the security guarantees of candidate local PRGs in a more fine-grained way.
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Submitted on : Monday, December 10, 2018 - 4:06:31 PM
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Geoffroy Couteau, Aurélien Dupin, Pierrick Méaux, Mélissa Rossi, Yann Rotella. On the Concrete Security of Goldreich’s Pseudorandom Generator. ASIACRYPT 2018 - 24th Annual International Conference on the Theory and Application of Cryptology and Information Security, Dec 2018, Brisbane, Australia. pp.96-124, ⟨10.1007/978-3-030-03329-3_4⟩. ⟨hal-01944772⟩

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