### Cryptographic Extraction and Key Derivation: The HKDF Scheme

Hugo Krawczyk

##### Abstract

In spite of the central role of key derivation functions (KDF) in applied cryptography, there has been little formal work addressing the design and analysis of general multi-purpose KDFs. In practice, most KDFs (including those widely standardized) follow ad-hoc approaches that treat cryptographic hash functions as perfectly random functions. In this paper we close some gaps between theory and practice by contributing to the study and engineering of KDFs in several ways. We provide detailed rationale for the design of KDFs based on the extract-then-expand approach; we present the first general and rigorous definition of KDFs and their security which we base on the notion of computational extractors; we specify a concrete fully practical KDF based on the HMAC construction; and we provide an analysis of this construction based on the extraction and pseudorandom properties of HMAC. The resultant KDF design can support a large variety of KDF applications under suitable assumptions on the underlying hash function; particular attention and effort is devoted to minimizing these assumptions as much as possible for each usage scenario. Beyond the theoretical interest in modeling KDFs, this work is intended to address two important and timely needs of cryptographic applications: (i) providing a single hash-based KDF design that can be standardized for use in multiple and diverse applications, and (ii) providing a conservative, yet efficient, design that exercises much care in the way it utilizes a cryptographic hash function. (The HMAC-based scheme presented here, named HKDF, is being standardized by the IETF.)

Note: Corrects a typo in original version: The example at the top of page 12, using a function from {0,1}^{k+1} -> {0,1}^k, was mistakenly written before as {0,1}^{2k} -> {0,1}^k.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint. MINOR revision.Extended abstract to be published in Proceedings of Crypto'2010.
Contact author(s)
hugo @ ee technion ac il
History
2020-05-10: revised
See all versions
Short URL
https://ia.cr/2010/264

CC BY

BibTeX

@misc{cryptoeprint:2010/264,
author = {Hugo Krawczyk},
title = {Cryptographic Extraction and Key Derivation: The HKDF Scheme},
howpublished = {Cryptology ePrint Archive, Paper 2010/264},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/264}},
url = {https://eprint.iacr.org/2010/264}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.