Cryptology ePrint Archive: Report 2017/506

Optimal Overcoming Weak Expectations

Maciej Skorski

Abstract: Barak et al. (CRYPTO'11) initiated the study of so called square-friendly applications which offer good security for keys with entropy deficiency (weak keys), for this reason being important for key derivation. The state of the art of security bounds was established by Dodis and Yu (TCC'13), by modeling "weak" keys as distributions of high collision entropy.

In this paper we answer the question what is the minimum requirement on weak keys to be "good" for these applications. The answer gives an elegant operational meaning to the notion of smooth collision entropy. Namely, smooth collision entropy is both sufficient and necessary (with essentially the same entropy parameters) to guarantee the security of square-friendly applications under weak keys. This characterization is a consequence of constrained optimization techniques.

Category / Keywords: foundations / key derivation, square-friendly applications, weak expectations, smooth entropy

Date: received 1 Jun 2017, withdrawn 12 Oct 2018

Contact author: maciej skorski at gmail com

Available format(s): (-- withdrawn --)

Note: this paper has an error in the proof. similar claims with correct proofs are part of another paper "Pseudorandomness Against Mean and Variance Bounded Attackers"

Version: 20181012:172953 (All versions of this report)

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