The Grøstl hash function is one of the 5 final round candidates of the SHA-3 competition hosted by NIST. In this paper, we study the preimage resistance of the Grøstl hash function. We propose pseudo preimage attacks on Grøstl hash function for both 256-bit and 512-bit versions, i.e., we need to choose the initial value in order to invert the hash function. Pseudo preimage attack on 5(out of 10...

We consider multivariate pseudo-linear functions over finite fields of characteristic two. A pseudo-linear polynomial is a sum of guarded linear-terms, where a guarded linear-term is a product of one or more linear-guards and a single linear term, and each linear-guard is again a linear term but raised to the power q-1, where q is the field size. Pseudo-linear functions over GF(2) are given by ...

We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, s...

Kashihara[2] defined the Pseudo-Smarandache function Z by m(m+l) } Properties of this function have been studied in [1], [2] etc. 1. By answering a question by C. Ashbacher, Maohua Le proved that S(Z(n»-Z(S(n» changes signs infmitely often. Put d s,z (n) = I S(Z(n»-Z(S(s» I We will prove first that lim inf d s,z (n) ~ 1 (1) n-oo and (2) n-+oo p(p+l) Indeed, let n = , where p is an odd prime. Th...

We initiate the study of dynamic cooperative games—cooperative games where the characteristic function may change over time. We introduce two types of algorithmic problems for such games: computing a given solution concept at time t, and checking that a certain function of the game (e.g., the Shapley value of a given player or the value of the least core) remains within given bounds during time...

Given an undirected graph G = (V,E) with a weight function c ∈ R , and a positive integerK, the Kth Traveling Salesman Problem (KthTSP) is to findK Hamilton cyclesH1, H2, , ..., HK such that, for any Hamilton cycle H 6∈ {H1, H2, , ..., HK}, we have c(H) ≥ c(Hi), i = 1, 2, ...,K. This problem is NP-hard even for K fixed. We prove that KthTSP is pseudopolynomial when TSP is polynomial. 2010 Mathe...

Given a multiset S of n positive integers and a target integer t, the subset sum problem is to decide if there is a subset of S that sums up to t. We present a new divide-and-conquer algorithm that computes all the realizable subset sums up to an integer u in Õ ( min{√nu, u, σ} ) , where σ is the sum of all elements in S and Õ hides polylogarithmic factors. This result improves upon the standar...

Background: Synthetic dyes are serious pollutants and wide ranges of methods have been employed for their removal from aquatic systems. We studied the adsorption of "Nile blue A" (NBA), an anionic dye, from aqueous solution by oxidized multi-walled carbon nanotubes (MWCNTs). Methods: Scanning electron microscope and Fourier transform infrared spectroscopy were used to characterize ...

Previous research on automated mechanism design (proposed in UAI-02) assumed that the outcome space was flatly represented, which makes that work inapplicable if the outcome space is exponential, as it is, for example, in multi-item auctions. This paper introduces (to our knowledge) the first more concise representation for the problem, which relies on decomposing the outcome space into distinc...

This paper addresses the problem of optimally inserting idle time into a single-machine schedule when the sequence is fixed and the cost of each job is a convex function of its completion time. We propose a pseudo-polynomial time algorithm to find a solution within some tolerance of optimality in the solution space. The proposed algorithm generalises several previous works related to the subject.