On non-negligible bias of the first output byte of RC4 towards the first three bytes of the secret key

In this paper, we show that the first byte of the keystream output of RC4 has non-negligible bias towards the sum of the first three bytes of the secret key. This result is based on our observation that the index, where the first byte of the keystream output is chosen from, is approximately twice more likely to be 2 than any other value. Our technique is further used to theoretically prove Roos’s experimental observation (A class of weak keys in the RC4 stream cipher, 1995) related to weak keys.     

On the pH-dependent quenching of quantum dot photoluminescence by redox active dopamine

We investigated the charge transfer interactions between luminescent quantum dots (QDs) and redox active dopamine. For this, we used pH-insensitive ZnS-overcoated CdSe QDs rendered water-compatible using poly (ethylene glycol)-appended dihydrolipoic acid (DHLA-PEG), where a fraction of the ligands was amine-terminated to allow for controlled coupling of dopamine-isothiocyanate onto the nanocrystal. Using this sample configuration, we probed the effects of changing the density of dopamine and the buffer pH on the fluorescence properties of these conjugates. Using steady-state and time-resolved fluorescence, we measured a pronounced pH-dependent photoluminescence (PL) quenching for all QD-dopamine assemblies. Several parameters affect the PL loss. First, the quenching efficiency strongly depends on the number of dopamines per QD-conjugate. Second, the quenching efficiency is substantially increased in alkaline buffers. Third, this pH-dependent PL loss can be completely eliminated when oxygen-depleted buffers are used, indicating that oxygen plays a crucial role in the redox activity of dopamine. We attribute these findings to charge transfer interactions between QDs and mainly two forms of dopamine: the reduced catechol and oxidized quinone. As the pH of the dispersions is changed from acidic to basic, oxygen-catalyzed transformation progressively reduces the dopamine potential for oxidation and shifts the equilibrium toward increased concentration of quinones. Thus, in a conjugate, a QD can simultaneously interact with quinones (electron acceptors) and catechols (electron donors), producing pH-dependent PL quenching combined with shortening of the exciton lifetime. This also alters the recombination kinetics of the electron and hole of photoexcited QDs. Transient absorption measurements that probed intraband transitions supported those findings where a simultaneous pronounced change in the electron and hole relaxation rates was measured when the pH was changed from acidic to alkaline.     

A New Route to the Synthesis of 7-Functionalised Bicyclo[2.2.1]Heptane Derivatives

A new route to the synthesis of 7-functionalised bicyclo[2.2.1]heptane derivatives having a bridgehead alkoxy group is described involving Wolff rearrangement of α-diazo ketone in a bicyclo[2.2.2]octane derivative.     

Integers without large prime factors in short intervals: Conditional results

Under the Riemann hypothesis and the conjecture that the order of growth of the argument of ζ(1/2 + it) is bounded by $\left( {\log t} \right)^{\frac{1} {2} + o\left( 1 \right)}$\left( {\log t} \right)^{\frac{1} {2} + o\left( 1 \right)} , we show that for any given α > 0 the interval $(X,X + \sqrt X (\log X)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + o\left( 1 \right)} ]$(X,X + \sqrt X (\log X)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + o\left( 1 \right)} ] contains an integer having no prime factor exceeding X ^α for all X sufficiently large.     

Amphiphilic drug persuaded collapse of polyvinylpyrrolidone and poly(ethylene glycol) chains: A dynamic light scattering study

Light scattering has proved to be useful in characterizing colloidal systems. We have studied the interaction between an amphiphilic drug, amitriptyline hydrochloride (AMT), and neutral polymers, polyvinylpyrrolidone (PVP) and poly(ethylene glycol) (PEG), using the dynamic light scattering (DLS) technique. AMT was found to interact with PVP more strongly than PEG. A large decrease of the size of aggregates upon increase of AMT concentration indicates a successive collapse of the polymer conformation. The partial negatively charged oxygen atoms, present in the amide group of PVP, were believed to be responsible for the collapse while interacting with the cationic head group of AMT. Presence of NaBr in the solution enhanced the effect markedly and made the AMT–PVP aggregates more compact. The PEG aggregates also showed a similar behavior, although less pronounced than the PVP. The results obtained in the present investigations may be helpful to design the drug delivery systems for the antidepressant drugs as the higher concentration of these drugs is harmful for the human body. Likewise, as the results have shown that on increasing the temperature there is a decrease in the extent of interaction; this may be helpful for the controlled release formulations.