Graphs with Special Arcs and Cryptography

A combinatorial method of encryption with a similarity to the classical scheme of linear coding has been suggested by the author. The general idea is to treat vertices of a graph as messages and arcs of a certain length as encryption tools. We will study the quality of such an encryption in the case of graphs of high girth by comparing the probability to guess the message, (vertex) at random with the probability of breaking the key, i.e. guessing the encoding arc. In fact, the quality is good for graphs which are close to the Erdös bound, defined by the Even Cycle Theorem.In the case of parallelotopic graphs, there is a uniform way to match arcs with strings in a certain alphabet. Among parallelotopic graphs we distinguish linguistic graphs of affine type whose vertices (messages) and arcs (encoding tools) both could be naturally identified with vectors over the GF(q), and neighbors of the vertex defined by a system of linear equations. We will discuss families of linguistic and parallelotopic graphs of increasing girth as the source for assymmetric cryptographic functions and related open key algorithms.Several constructions of families of linguistic graphs of high girth with good quality, complexity and expansion coefficients will be considered. Some of those constructions have been obtained via group-theoretical and geometrical techniques.     

Synthesis of the ethyl ester of the mononitrile of malonic acid by the catalytic carbonylation of benzenesulfonyloxyacetonitrile

A new method has been developed for the synthesis of the ethyl ester of the mononitrile of malonic acid by the carbonylation of benzenesulfonyloxyacetonitrile in absolute ethanol in the presence of cobalt carbonyl. The yield of the desired product was 30% with 60–90% conversion of the starting compound. The effects of temperature, pressure, and reaction time were studied.N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. S. M. Kirov Urals Polytechnical Institute, Ekaterinburg. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 215–216, January, 1992.     

Formation of n-α-diazoacetylureas by the reaction of derivatives of 5-hydroxy-1,2,3-triazole-4-carboxamide with phenylisocyanate and phenyl isothiocyanate

The reaction of derivatives of 5-hydroxy-1,2,3-triazole-4-carboxamide with phenyl isocyanate and phenyl isothiocyanate proceeds at the 4-carboxamide fragment of the first, leading to the formation of derivatives of N-phenyl-N-(2-diazo-2-carbamoylacetyl)urea and -thiourea correspondingly.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1347–1350, October, 1992.     

A catalyst-free one-step synthesis of N-pyrimidinyl amidines from endocyclic enamines and 4-azidopyrimidines

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Heterocyclization of compounds containing diazo and cyano groups. 4. Reactions of 2-diazo-2-cyanoacetic acid amides with P4S10 and the lawesson reagent. Synthesis and recyclization of 5-amino-1,2,3-thiadiazole-4-carbothioamides

5-Amino-1,2,3-thiadiazole-4-carbothioamides were obtained in the reaction of carbonyl derivatives of diazoacetonitrile with P₄S₁₀ and the Lawesson reagent. A novel recyclization of 1,2,3-thiadiazole-4-carbothioamides was observed.See [1] for Communication 3.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 845–849, June, 1987.     

Synthesis of mesoionic[1,2,3]triazolo[5,1-d][1,2,5]triazepines

Intramolecular cyclization of 1-amino-3-phenacyl-4-carbohydrazido-1,2,3-triazolium-5-olates has been shown to take place via selective interaction of the carbonyl group with the terminal amino function of the hydrazido group to form a 1,2,5-triazepine ring. Minor products, resulting from the interaction of the α-nitrogen atom of the hydrazido group with the carbonyl function, having a N-amino-pyridazine structure were also detected and isolated. A general method for the synthesis of novel mesoionic 2-amino-7-aryl-4-oxo-2,4,5,8-tetrahydro[1,2,3]triazolo[5,1-d][1,2,5]triazepin-9-ium-3-olates was developed.     

Electronic spectroscopy and ionization potential of UO2 in the gas phase

The electronic spectroscopy of UO(2) has been examined using multiphoton ionization with mass-selected detection of the UO(2) (+) ions. Supersonic jet cooling was used to reduce the spectral congestion. Twenty-two vibronic bands of neutral UO(2) were observed in the range from 17,400 to 32,000 cm(-1). These bands originated from the U(5fphi(u)7ssigma(g))O(2) X (3)Phi(2u) and (3)Phi(3u) states. The stronger band systems are attributed to metal-centered 7p<--7s transitions. Threshold ionization measurements were used to determine the ionization potentials of UO and UO(2). These were found to be higher than the values obtained previously from electron impact measurements but in agreement with the results of recent theoretical calculations.     

Pericyclic and Heteroelectrocyclic Mechanisms for the Cyclization of 1,3,5-Hexatrien-1-one and Its 6-Aza Analog

The cyclization of 1,3,5-hexatrien-1-one, 1, and the Z- and E-isomers of 1-aza-1,3-butadienylketene 3 were studied using the semiempirical AM1 and PM3 methods. Cyclizations of compounds 1 and Z-3 are shown to occur via a mono-rotation mechanism with barriers of 15.49 and 32.85 kcal/mol respectively. The reactions proceed via non-planar transition states which result from rotation of the methylene group for compound 1 and the imino group for compound Z-3. Cyclization of E-3 proceeds via a non-rotatory mechanism through a planar transition state. The activation barrier is 4.83 kcal/mol (AM1). The electronic structures of the initial and final states, and of some intermediate structures, including the transition states for the cyclization of compounds 1 and 3, were analyzed by the natural orbital method using HF/6-31G*//AM1 calculations. Energetic, structural, and orbital criteria indicate the heteroelectric mechanism for the cyclization of compound E-3 and the pericyclic mechanism for the cyclization of compounds 1 and Z-3.