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- Thorsten Kleinjung, Kazumaro Aoki, +10 authors Paul Zimmermann
- IACR Cryptology ePrint Archive
- 2010

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.

- Pierrick Gaudry, Alexander Kruppa, Paul Zimmermann
- ISSAC
- 2007

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)

- N E Polyakov, A I Kruppa, T V Leshina, T A Konovalova, L D Kispert
- Free radical biology & medicine
- 2001

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)

- Valeria S Kornievskaya, Alexander I Kruppa, Nicholas E Polyakov, Tatyana V Leshina
- The journal of physical chemistry. B
- 2007

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)

- A Kruppa, K Scharffetter-Kochanek, T Krieg, N Hunzelmann
- Dermatology
- 1998

Allergic reactions to macrolides appear to be very rare. Only a few cases of fixed drug eruption or urticaria due to the administration of erythromycin have been reported. Cross-reaction between the different macrolides have not yet been published. We report a case of a 31-year-old female patient who developed generalized urticaria and tachycardia shortly… (More)

- A Kruppa, B Korge, J Lasch, K Scharffetter-Kochanek, N Hunzelmann
- Acta dermato-venereologica
- 2000

1. Wade TR, Ackerman AB. Cornoid lamellation. A histologic reaction pattern. Am J Dermatopathol 1980; 2: 5 ± 15. 2. Schamroth JM, Zlotogorski A, Gilead L. Porokeratosis of MibelliÐoverview and review of the literature. Acta Derm Venerol 1997; 77: 207 ± 213. 3. Fields LL, White CR Jr, Maziarz RT. Rapid development of disseminated super®cial porokeratosis… (More)

- Alexander Kruppa
- 2009

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)

- Shi Bai, Cyril Bouvier, Alexander Kruppa, Paul Zimmermann
- Math. Comput.
- 2016

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)

- Peter L. Montgomery, Alexander Kruppa
- ANTS
- 2008

- Alexander Kruppa
- 2010