Skye: An Expanding PRF based Fast KDF and its Applications

Abstract

A Key Derivation Function (KDF) generates a uniform and highly random key-stream from weakly random key material. KDFs are broadly used in various security protocols such as digital signatures and key exchange protocols. HKDF, the most deployed KDF in practice, is based on the extract-then-expand paradigm. It is presently used, among others, in the Signal Protocol for end-to-end encrypted messaging. HKDF is a generic KDF for general input sources and thus is not optimized for source-specific use cases such as key derivation from Diffie-Hellman (DH) sources (i.e. DH shared secrets as key material). Furthermore, the sequential HKDF design is unnecessarily slow on some general-purpose platforms that can benefit from parallelization. In this work, we propose a novel, efficient and secure KDF called Skye. Skye follows the extract-then-expand paradigm and consists of two algorithms: efficient deterministic randomness extractor and expander functions. Instantiating our extractor for dedicated source-specific (e.g. DH sources) inputs leads to a significant efficiency gain over HKDF while maintaining its security level. We provide concrete security analysis of Skye and both its underlying algorithms in the standard model. We provide a software performance comparison of Skye with the AES-based expanding PRF ButterKnife and HKDF with SHA-256 (as used in practice). Our results show that in isolation Skye performs from 4x to 47x faster than HKDF, depending on the availability of AES or SHA instruction support. We further demonstrate that with such a performance gain, when Skye is integrated within the current Signal implementation, we can achieve significant overall improvements ranging from 38% to 64% relative speedup in unidirectional messaging. Even in bidirectional messaging, that includes DH computation with dominating computational cost, Skye still contributes to 12-36% relative speedup when just 10 messages are sent and received at once.