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This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.
Schönhage-Strassen's algorithm is one of the best known algorithms for multiplying large integers. Implementing it ef?ciently is of utmost importance, since many other algorithms rely on it as a subroutine. We present here an improved implementation, based on the one distributed within the GMP library. The following ideas and techniques were used or… (More)
The role of several natural and synthetic carotenoids as scavengers of free radicals was studied in homogeneous solutions. A set of free radicals: *OH, *OOH, and *CH(3) were generated by using the Fenton reaction in dimethyl sulfoxide. It was shown that the spin trapping technique is more informative than optical methods for the experimental conditions… (More)
The Elliptic Curve Method (ECM) of factorization can be used in the relation collection phase of the Number Field Sieve (NFS) to help identify smooth integers. This requires rapidly nding small prime factors for a large number of composites, each of a few machine words in size. We present a software implementation of ECM that is optimized for high… (More)
The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we… (More)
1H NMR and CIDNP methods were used to demonstrate that triterpene glycoside (glycyrrhizic acid, GA) can substantially change the efficiency and direction of phototransformation of alkaloid lappaconitine (LA) due to both its solubilization in GA micelles and protonation of LA amine nitrogen in water-alcohol solutions. The LA solubilization in the GA micelle… (More)