A Combinatorial Analysis of HC-128

We show that the knowledge of any one of the two internal state arrays of HC-128 along with the knowledge of 2048 keystream words is sufficient to construct the other state array completely in $2^{42}$ time complexity. Though our analysis does not lead to any attack on HC-128, it reveals a structural insight into the cipher. In the process, we theoretically establish certain combinatorial properties of HC-128 keystream generation algorithm. We also suggest a modification to HC-128 that takes care of the recently known cryptanalytic results with little reduction in speed

Large Components of Bipartite Random Mappings

A bipartite random mapping TK,L of a finite set V = V1 ∪ V2, |V1 | = K and |V2 | = L, into itself assigns independently to each i ∈ V1 its unique image j ∈ V2 with probability 1/L and to each i ∈ V2 its unique image j ∈ V1 with probability 1/K. We study the connected component structure of a random digraph G(TK,L),representingTK,L, asK→ ∞ and L →∞. We show that, no matter how K and L tend to infinity relative to each other, the joint distribution of the normalized order statistics for the component sizes converges in distribution to the Poisson-Dirichlet distribution on the simplex ∇ = {{xi} : � xi ≤ 1,xi≥xi+1 ≥ 0 for every i ≥ 1}