Security analysis of SHA-256 and sisters

TLDR: In this article, the security of SHA-256, SHA-384 and SHA-512 against collision attacks was studied. But the authors concluded that neither Chabaud and Joux's attack, nor Dobbertin-style attacks also don't apply on the underlying structure.

Abstract: This paper studies the security of SHA-256, SHA-384 and SHA-512 against collision attacks and provides some insight into the security properties of the basic building blocks of the structure. It is concluded that neither Chabaud and Joux's attack, nor Dobbertin-style attacks apply. Differential and linear attacks also don't apply on the underlying structure. However we show that slightly simplified versions of the hash functions are surprisingly weak : whenever symmetric constants and initialization values are used throughout the computations, and modular additions are replaced by exclusive or operations, symmetric messages hash to symmetric digests. Therefore the complexity of collision search on these modified hash functions potentially becomes as low as one wishes.