The present thesis analyses the proposal of CubeHash with spe- cial emphasis on the following papers: "Inside the Hypercube" [1], "Sym- metric States and Their Improved Structure" [7] and "Linearisation Frame- work for Collision Attacks" [6]. The CubeHash algorithm is presented in a concise manner together with a proof that the CubeHash round function R : ({0, 1}32 )32 → ({0, 1}32 )32 is a permutation. The results of [1] and [7] con- cerning the CubeHash symmetric states are reviewed, corrected and substan- tiated by proofs. More precisely, working with a definition of D-symmetric state, based on [7], the thesis proves both that for V = Z4 2 and its linear subspace D, there are 22 |V | |D| D-symmetric states and an internal state x is D-symmetric if and only if the state R(x) is D-symmetric. In response to [1], the thesis presents a step-by-step computation of a lower bound for the num- ber of distinct symmetric states, explains why the improved preimage attack does not work as stated and gives a mathematical background for a search for fixed points in R. The thesis further points out that the linearisation method from [6] fails to consider the equation (A ⊕ α) + β = (A + β) ⊕ α (∗), present during the CubeHash iteration phase. Necessary and sufficient conditions for A being a solution to (∗) are...
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:326554 |
| Date | January 2013 |
| Creators | Stankovianska, Veronika |
| Contributors | Tůma, Jiří, Hojsík, Michal |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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