קולוקוויום וסמינרים

Differential Cryptanalysis is among the most popular types of attacks used to analyze and find vulnerabilities in modern block ciphers. To conduct a differential attack, one must first find a high-probability differential of the block cipher.

Existing search methods involve either intimate knowledge of the specific cipher that is being attacked, or use of search algorithms whose runtime rises exponentially with the number of rounds over which the search is conducted.

We present a quantum-based search method for high probability iterative differentials whose runtime scales linearly in the number of rounds over which the search is conducted and is completely agnostic of the implementation details of the cipher. 

Dominating Set is a fundamental problem in graph theory: given a graph, find a minimum-weight subset of vertices such that every vertex is either selected or shares an edge with a selected vertex.

In online settings where vertices arrive sequentially, comparing algorithms against an offline optimum with full knowledge of the input leads to extremely strong lower bounds, where even a simple star graph shows that any online algorithm must have competitive ratio Ω(n), with n being the number of vertices, matching the trivial strategy of selecting all vertices.

We study the incremental dominating set problem, where the optimal algorithm is constrained to the same choices available to online algorithms. This introduces a benchmark that enables a meaningful comparison between algorithms.

We present the first results for vertex-weighted graphs and randomized algorithms in this model. For incremental dominating set, we give an O(Δ)-competitive deterministic algorithm and an O(log²Δ)-competitive randomized algorithm, where Δ is the maximum degree in the graph.

We extend these results to the Connected Dominating Set problem, which requires the dominating set to be connected. When the neighborhood of each arriving vertex is known in advance, we can improve the competitive ratio of deterministic algorithms to be polylogarithmic.

Finally, we establish matching lower bounds, showing that all our results are optimal up to constant factors.