Estimates of the mean size of the subset image under composition of random mappings

Let XN be a set of N elements and F1, F2,… be a sequence of random independent equiprobable mappings XN → N. For a subset S0 ⊂ XN, |S0|=m, we consider a sequence of its images St=Ft(…F2(F1(S0))…), t=1,2… An approach to the exact recurrent computation of distribution of |St| is described. Two-sided inequalities forM{|St|||S0|=m} such that the difference between the upper and lower bounds is o(m)for m, t, N → ∞, mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

Analysis of the Perfect Table Fuzzy Rainbow Tradeoff

Cryptanalytic time memory tradeoff algorithms are tools for inverting one-way functions, and they are used in practice to recover passwords that restrict access to digital documents. This work provides an accurate complexity analysis of the perfect table fuzzy rainbow tradeoff algorithm. Based on the analysis results, we show that the lesser known fuzzy rainbow tradeoff performs better than the original rainbow tradeoff, which is widely believed to be the best tradeoff algorithm. The fuzzy rainbow tradeoff can attain higher online efficiency than the rainbow tradeoff and do so at a lower precomputation cost.

Password Recovery Research and its Future Direction

As users become increasingly aware of the need to adopt strong password, it brings challenges to digital forensics investigators due to the password protection of potential evidentiary data. On the other hand, due to human nature and their tendency to select memorable passwords, which compromises security for convenience, users may select strong passwords by considering a permutation of dictionary words. In this chapter, the authors discuss the existing password recovery methods and identify promising password recovery approaches. They also present their previous work on the design of a time-memory tradeoff pre-computed table coupled with a new sorting algorithm, and its two new storage mechanisms. The results on the evaluation of its password recovery performance are also presented. In this chapter, the authors propose the design of a new password recovery table by integrating the construction of common passwords within the enhanced rainbow table to incorporate the two promising password recovery approaches. They then present the theoretical proof of the feasibility of this technique.