A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Palladium-catalyzed oxidative cyclizations: synthesis of dihydropyranones and furanones

A boron-mediated syn- and anti-stereoselective aldol reaction giving rise to various beta-hydroxyenones was coupled to a Pd((II))-mediated oxidative cyclization to give 2,3,6-trisubstituted syn- and anti-dihydropyranones in good yields. The Pd((II))-mediated oxidative cyclization was expanded to alpha-hydroxyenones leading to furan-3(2H)-one derivatives, which include natural product bullatenone and a known precursor of geiparvarin. The sole product of the oxidative cyclization of alpha,beta-dihydroxyenone was a five-membered furan-3(2H)-one derivative, suggesting that the ring closure of these diols is both chemo- and regioselective.     

Eine neue Methode zur Bestimmung des spezifischen Kaliumpermanganatverbrauches von Humins?uren

Zusammenfassung Es wird eine indirekte Methode zur Bestimmung des spezifischen Kaliumpermanganatverbrauches von Huminsäuren beschrieben. Die Huminsäuren werden mit einer 0,01 m Blei(II)-nitratlösung gefällt und der gebildete Pb-Huminsäure-Niederschlag ausgewogen. Aus dem PbGehalt und dem Kaliumpermanganatverbrauch des Pb-HuminsäureKomplexes ergibt sich der Kaliumpermanganatverbrauch pro Milligramm Huminsäure. Im Gegensatz zu Eisen(III)-chlorid verändert Blei(II)nitrat die Oxydierbarkeit der Huminsäuren nicht, so daß indirekt und direkt bestimmter spezifischer Kaliumpermanganatverbrauch übereinstimmen.Es wurden die spezifischen Kaliumpermanganatverbrauchswerte von zwei Huminsäuren bekannter Oxydierbarkeit (Fluka-Humussäure und Moorwasser-Huminsäure) und von Huminsäuren aus 3 natürlichen Wässern bestimmt. Die Fehlerbereiche der Mittelwerte betragen bei den Modellsubstanzen (je 15 Analysenwerte) ±4% (Huminsäure Fluka) bzw. ±3% (Moorwasser-Huminsäure) und bei den praktischen Analysen ±4% ±11% bzw. ±7% des jeweiligen Mittelwertes.

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Summary An indirect method for the determination of the specific permanganate consumption of humic acids is described. The humic acids are precipitated by 0,01 M lead(II)nitrate and the precipitate of lead-humic acid is weighed. The permanganate consumption per mg humic acid results from the lead-content and the permanganate consumption of the lead-humic acid complex. As opposed to ferric chloride lead(II) nitrate does not change the oxidizability of humic acids; hence, indirectly and directly determined permanganate consumption equal each other. — The values of the specific permanganate consumption of two humic acids of known oxidizability and of three samples of humic acids isolated from natural water-sources are determined. The limit of error of the mean values is between ±3% and ±11%.

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Wir danken Frl. Roswitha Raspe und Frau Helga Boje für fleißige technische Mitarbeit.     

Synthesis of C-nor-heterocyclic steroid analogues

2-Substituted-amino-10H-thiazolo[5,4-b]benz[e]indene derivatives 5 representing a novel ring system were synthesized. Their acylation led to exo-acylated derivatives 9 that could be converted to the corresponding glycine analogues 12 .     

On triazoles. XXXIV. The correct structure of the ethoxycarboxylated 5-amino-1H-1,2,4-triazole and its product with hydrazine

The structure of the ethoxycarboxylated product of 5-amino-1H-1,2,4-triazole and its hydrazide was corrected using their ir, pmr, cmr and mass spectra.     

The coordinative properties of the ligands Ph2ECH2EPh2 (E = P,As, Sb) in carbonylvanadium complexes,and the molecular structure of η5-C5H5V(CO)3As2Ph4

Photo-reaction between the ligands Ph₂ECH₂EPh₂ (E = P: dppm, E = As: dpam, E = Sb: dpsm), L, and the vanadium complexes η⁵-C₅H₅V(CO)₄ and [Et₄N][V(CO)₆] yields monosubstituted mononuclear (dpsm) and dinuclear, ligand-bridged complexes (dpam, dpsm). With dppm, the final products are disubstituted chelate complexes, but monosubstituted mono- and dinuclear species are formed as intermediates.The shielding of the ⁵¹V nucleus decreases in the series dpsm > dppm > dpam and {M(CO)_n} > {M(CO)_n?1} L > {M(CO)_n?1}₂μ-L > {M(CO)_n?2}dppm ({M(CO)_n}[V(CO)₆]^?, η⁵-C₅H₅V(CO)₄). The half-widths of the NMR signals are greater for dinuclear than for mononuclear complexes.The crystal and molecular structures of η⁵-C₅H₅V(CO)₃As₂Ph₄ have been determined. The compound crystallizes in the space group P2₁/c with a = 1347.8, b = 1020.0, c = 2085.2 pm and β = 82.3°. Due to steric crowding, the ⁵¹V shielding is low composed to that of {η⁵-C₅H₅V(CO)₃}₂μ-dpam.     

On triazoles XLIX. Synthesis of 5,6‐dihydrothiazolo[3,2‐b]‐[1,2,4]triazol‐2‐yl‐, 6,7‐dihydro‐5H‐[1,2,4]triazolo[5,1‐b][1,3]thiazin‐2‐yl‐, and 5,6,7,8‐tetrahydro[1,2,4]triazolo[5,1‐b] [1,3]thiazepin‐2‐yl‐isoquinolinium salts

5′‐Mercapto‐1′H‐1,2,4‐triazol‐3′‐yl‐isoquinolinium salts (6) were synthesised by the reaction of ortho‐acyl phenylacetones (2) or the corresponding pyrylium salts (3) and 5‐amino‐2,3‐dihydro‐1H‐1,2,4‐triazole‐3‐thione (5) . Treatment of thioles 6 withα,ω‐dibromoalkanes led to type 15, 16 and 17 isoquinolinium salts condensed with thiazole, thiazine and thiazepine rings. When 6 are reacted with dibromomethane (10) 11 type dimeric structures are obtained.     

Interannular communication in the radical anions of bis-cyclooctatetraene systems

[reaction: see text] The room-temperature potassium reduction of 1,2-bis-cyclooctatetraeneoxypropane yields two different regio-spin isomer anion radicals in equilibrium (COT-O-C(Me)HCH(2)CH(2)-O-COT(*)(-) = (*)(-)COT-O-C(Me)HCH(2)CH(2)-O-COT) that is shifted far to the right. The presence of the unreduced ring perturbs the spin density on the reduced ring. Addition of more electrons generates the diradical dianion ((*)(-)COT-O-C(Me)HCH(2)CH(2)-O-COT(*)(-)), and the anion radical on the secondary side splits the degeneracy of the psuedo-ortho protons of the anion radical on the primary side.