Riddhipratim Basu

A complete characterization of the evolution of RC4 pseudo random generation algorithm

Abstract In this paper, we provide a complete characterization of the RC4 Pseudo Random Generation Algorithm (PRGA) for one step: i = i + 1; j = j + S[i]; swap(S[i], S[j]); z = S[S[i] + S[j]]. This is the first time such an involved description is presented to get a concise view of how RC4 PRGA evolves. Considering all the permutations (we also keep in mind the Finney states), we find that the distribution of z is not uniform given i, j. A corollary of this result shows that information about j is always leaked from z. Next, studying two consecutive steps of RC4 PRGA, we prove that the index j is not produced uniformly at random given the value of j two steps ago. We also provide additional evidence of z leaking information on j. Further, we present a novel distinguisher for RC4 which shows that under certain conditions the equality of two consecutive bytes is more probable than by random association. Our analysis holds regardless of the amount of initial keystream bytes thrown away during the RC4 PRGA.

On Some Sequences of the Secret Pseudo-random Index j in RC4 Key Scheduling

RC4 Key Scheduling Algorithm (KSA) uses a secret pseudo-random index j which is dependent on the secret key. Let S N be the permutation after the complete KSA of RC4. It is known that the value of j in round y + 1 can be predicted with high probability from S N [y ] for the initial values of y and from

Evolving voter model on dense random graphs

S^{-1}_N[y]

Characterization of cutoff for reversible Markov chains

for the final values of y . This fact has been exploited in several recent works on secret key recovery from S N . In this paper, we perform extensive analysis of some special sequences of indices corresponding to the j values that leak useful information for key recovery. We present new theoretical results on the probability and the number of such sequences. As an application, we explain a new secret key recovery algorithm that can recover a 16 bytes secret key with a success probability of 0.1409. Our strategy has high time complexity at this point and requires further improvement to be feasible in practice.

Limit Theorems for Longest Monotone Subsequences in Random Mallows Permutations

In this paper we examine a variant of the voter model on a dynamically changing network where agents have the option of changing their friends rather than changing their opinions. We analyse, in the context of dense random graphs, two models considered in Durrett et. al.(Proc. Natl. Acad. Sci. 109: 3682-3687, 2012). When an edge with two agents holding different opinion is updated, with probability

SPECTRAL PROPERTIES OF RANDOM TRIANGULAR MATRICES

\frac{\beta}{n}

Trapping games on random boards

, one agent performs a voter model step and changes its opinion to copy the other, and with probability

Non-fixation for Conservative Stochastic Dynamics on the Line

1-\frac{\beta}{n}

Last Passage Percolation with a Defect Line and the Solution of the Slow Bond Problem

, the edge between them is broken and reconnected to a new agent chosen randomly from (i) the whole network (rewire-to-random model) or, (ii) the agents having the same opinion (rewire-to-same model). We rigorously establish in both the models, the time for this dynamics to terminate exhibits a phase transition in the model parameter

Lipschitz embeddings of random sequences

\beta