# Key derivation without entropy waste

Dodis Y, Pietrzak KZ, Wichs D. 2014. Key derivation without entropy waste. EUROCRYPT: Theory and Applications of Cryptographic Techniques, LNCS, vol. 8441, 93–110.

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*Conference Paper*|

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**Scopus indexed**

Author

Dodis, Yevgeniy;
Pietrzak, Krzysztof Z

^{ISTA}^{}; Wichs, DanielEditor

Nguyen, Phong;
Oswald, Elisabeth

Department

Series Title

LNCS

Abstract

We revisit the classical problem of converting an imperfect source of randomness into a usable cryptographic key. Assume that we have some cryptographic application P that expects a uniformly random m-bit key R and ensures that the best attack (in some complexity class) against P(R) has success probability at most δ. Our goal is to design a key-derivation function (KDF) h that converts any random source X of min-entropy k into a sufficiently "good" key h(X), guaranteeing that P(h(X)) has comparable security δ′ which is 'close' to δ. Seeded randomness extractors provide a generic way to solve this problem for all applications P, with resulting security δ′ = O(δ), provided that we start with entropy k ≥ m + 2 log (1/δ) - O(1). By a result of Radhakrishnan and Ta-Shma, this bound on k (called the "RT-bound") is also known to be tight in general. Unfortunately, in many situations the loss of 2 log (1/δ) bits of entropy is unacceptable. This motivates the study KDFs with less entropy waste by placing some restrictions on the source X or the application P. In this work we obtain the following new positive and negative results in this regard: - Efficient samplability of the source X does not help beat the RT-bound for general applications. This resolves the SRT (samplable RT) conjecture of Dachman-Soled et al. [DGKM12] in the affirmative, and also shows that the existence of computationally-secure extractors beating the RT-bound implies the existence of one-way functions. - We continue in the line of work initiated by Barak et al. [BDK+11] and construct new information-theoretic KDFs which beat the RT-bound for large but restricted classes of applications. Specifically, we design efficient KDFs that work for all unpredictability applications P (e.g., signatures, MACs, one-way functions, etc.) and can either: (1) extract all of the entropy k = m with a very modest security loss δ′ = O(δ·log (1/δ)), or alternatively, (2) achieve essentially optimal security δ′ = O(δ) with a very modest entropy loss k ≥ m + loglog (1/δ). In comparison, the best prior results from [BDK+11] for this class of applications would only guarantee δ′ = O(√δ) when k = m, and would need k ≥ m + log (1/δ) to get δ′ = O(δ). - The weaker bounds of [BDK+11] hold for a larger class of so-called "square- friendly" applications (which includes all unpredictability, but also some important indistinguishability, applications). Unfortunately, we show that these weaker bounds are tight for the larger class of applications. - We abstract out a clean, information-theoretic notion of (k,δ,δ′)- unpredictability extractors, which guarantee "induced" security δ′ for any δ-secure unpredictability application P, and characterize the parameters achievable for such unpredictability extractors. Of independent interest, we also relate this notion to the previously-known notion of (min-entropy) condensers, and improve the state-of-the-art parameters for such condensers.

Publishing Year

Date Published

2014-04-01

Volume

8441

Page

93 - 110

Conference

EUROCRYPT: Theory and Applications of Cryptographic Techniques

Conference Location

Copenhagen, Denmark

Conference Date

2014-05-11 – 2014-05-15

IST-REx-ID

### Cite this

Dodis Y, Pietrzak KZ, Wichs D. Key derivation without entropy waste. In: Nguyen P, Oswald E, eds. Vol 8441. Springer; 2014:93-110. doi:10.1007/978-3-642-55220-5_6

Dodis, Y., Pietrzak, K. Z., & Wichs, D. (2014). Key derivation without entropy waste. In P. Nguyen & E. Oswald (Eds.) (Vol. 8441, pp. 93–110). Presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark: Springer. https://doi.org/10.1007/978-3-642-55220-5_6

Dodis, Yevgeniy, Krzysztof Z Pietrzak, and Daniel Wichs. “Key Derivation without Entropy Waste.” edited by Phong Nguyen and Elisabeth Oswald, 8441:93–110. Springer, 2014. https://doi.org/10.1007/978-3-642-55220-5_6.

Y. Dodis, K. Z. Pietrzak, and D. Wichs, “Key derivation without entropy waste,” presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Copenhagen, Denmark, 2014, vol. 8441, pp. 93–110.

Dodis, Yevgeniy, et al.

*Key Derivation without Entropy Waste*. Edited by Phong Nguyen and Elisabeth Oswald, vol. 8441, Springer, 2014, pp. 93–110, doi:10.1007/978-3-642-55220-5_6.**All files available under the following license(s):**

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