Correlation Analysis of the Alternating Step Generator

The alternating step generator is a well-known keystream generator consisting of two stop/go clocked LFSRs, LFSR₁ and LFSR₂, whose clocks are controlled by another LFSR, LFSR₃, which is clocked regularly. A probabilistic analysis of this generator is conducted which shows that the posterior probabilites of individual bits of the first derivatives of the regularly clocked LFSR₁ and LFSR₂ sequences, when conditioned on a given segment of the first derivative of the keystream sequence, can be computed efficiently in a number of probabilistic models of interest. The expected values of these probabilities, for a random keystream sequence, are derived by an approximate theoretical analysis and are also verified by systematic computer experiments. It is pointed out that these posterior probabilities can be enhanced in a resynchronization scenario and thus used for a low-complexity fast correlation attack on the two LFSRs. More generally, it is argued that even without resynchronization these probabilities may be significantly different from one half for fast correlation attacks based on iterative decoding algorithms to be successful, although with incresead complexity. A related method for computing the posterior probabilities of individual bits of the LFSR₃ sequence, when conditioned on both the keystream sequence and the LFSR₁ and LFSR₂ sequences, is also developed. As these posterior probabilities are much more different from one half, they can be used for a low-complexity fast correlation attack on LFSR₃, provided that the initial states of LFSR₁ and LFSR₂ are previously reconstructed.     

Intramolecular general acid catalysis of phosphate transfer. nucleophilic attack by oxyanions on the PO3 2- group

Phosphate transfer from the 8-dimethylammonium-naphthyl-1-phosphate monoanion 4m to water and to a range of nucleophiles shows general acid catalysis by the neighboring NH(+) group, through the strong intramolecular hydrogen bond. Reactivity is insensitive to the charge on the nucleophile, so that fluoride and oxyanions displace dimethylaminonaphthol from the PO3(2-) group as effectively as do amines of the same basicity. Reactivity is (predictably) relatively insensitive to the basicity of the nucleophile and to the alpha-effect. A strong intramolecular hydrogen bond is present in the product, but also in the reactant, as evidenced by major perturbations in the pK(a)'s of the phosphate and dimethylamino groups, to 3.94 and 9.31, respectively, and by ab initio calculations. Rate accelerations are of the order of 10(6)-fold despite this stabilization: the strength of the hydrogen bond is evidently significantly enhanced in the transition state. The evidence suggests that it also depends remarkably strongly on the degree of ionization of the reacting phosphate group and will be significantly reduced for the neutral PO(OH)2 group. Thus, the hydrolysis of the substrate cation 4+ shows a correspondingly greater, >10(8)-fold acceleration.     

Nucleophilic attack by oxyanions on a phosphate monoester dianion: the positive effect of a cationic general Acid

The two negative charges on a phosphate monoester RO-PO32- at neutral pH provide a considerable electrostatic barrier toward reactions with nucleophilic reagents with a negative charge on the attacking atom. Electrostatic repulsion disappears when the hydrolysis of an aryl phosphate monoester is catalyzed by a neighboring cationic general acid. The hydrolysis of 8-dimethylammonium-1-phosphate (1) is catalyzed by oxyanions, fluoride anion, and hydroxylamines at similar rates.     

One-pot approach for the synthesis of trans-cyclopropyl compounds from aldehydes. Application to the synthesis of GPR40 receptor agonists

A novel multicatalytic one-pot process providing trans-cyclopropyl compounds from corresponding aldehydes has been developed and applied to the synthesis of GPR40 small molecule agonists.     

Versatility of the Biginelli reaction: Synthesis of new biphenyl dihydropyrimidin-2-thiones using different ketones as building blocks

A multi-component synthesis of biphenyl dihydropyrimidin-2-thiones from 1-phenylthiourea, aldehydes and ketones or di-ketones has been demonstrated. The reaction proceeded well for aldehydes with electron donor or acceptor substituents under mild conditions.