Differential and invertibility properties of BLAKE (full version)

Differential and Invertibility Properties of BLAKE

BLAKE is a hash function selected by NIST as one of the 14 second round candidates for the SHA-3 Competition. In this paper, we follow a bottom-up approach to exhibit properties of BLAKE and of its building blocks: based on differential properties of the internal function G, we show that a round of BLAKE is a permutation on the message space, and present an efficient inversion algorithm. For 1....

Analysis of BLAKE2

We present a thorough security analysis of the hash function family BLAKE2, a recently proposed and already in use tweaked version of the SHA-3 finalist BLAKE. We study how existing attacks on BLAKE apply to BLAKE2 and to what extent the modifications impact the attacks. We design and run two improved searches for (impossible) differential attacks — the outcomes suggest higher number of attacke...

A Survey of Invertibility and Spectrum Preserving Linear Maps

On Invertibility of Sobolev Mappings

We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.

Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.