Search results for: M. K. Schnorr

Authors: Wenjie Qin, Kewei Lv

Abstract:

In 1996, Boneh and Venkatesan proposed the Hidden Number Problem (HNP) and proved the most significant bits (MSB) of computational Diffie-Hellman key exchange scheme and related schemes are unpredictable bits. They also gave a method which is a lattice rounding technique to solve HNP in non-uniform model. In this paper, we put forward a new concept that is Schnorr-MSB-HNP. We also reduce the problem of solving Schnorr signature private key with a few consecutive most significant bits of random nonce (used at each signature generation) to Schnorr-MSB-HNP, then we use the rounding technique to solve the Schnorr-MSB-HNP. We have come to the conclusion that if there is a ‘miraculous box’ which inputs the random nonce and outputs 2loglogq (q is a prime number) most significant bits of nonce, the signature private key will be obtained by choosing 2logq signature messages randomly. Thus we get an attack on the Schnorr signature private key.

Keywords: rounding technique, most significant bits, Schnorr signature algorithm, nonce, Schnorr-MSB-HNP

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Authors: A. Jéglot, F. Plauborg, M. K. Schnorr, R. S. Sørensen, L. Elsgaard

Abstract:

Artificial wetlands such as woodchip bioreactors are efficient tools to remove nitrate from agricultural wastewater with a minimized environmental impact. However, the temperature dependence of the microbiological nitrate removal prevents the woodchip bioreactors from being an efficient system when the water temperature drops below 8℃. To quantify and describe the temperature effects on nitrate removal efficiency, we studied nitrate-reducing enrichments from a woodchip bioreactor in Denmark based on samples collected in Spring and Fall. Growth was quantified as optical density, and nitrate and nitrous oxide concentrations were measured in time-course experiments to compare the growth of the microbial population and the nitrate conversion efficiencies at different temperatures. Ammonia was measured to indicate the importance of dissimilatory nitrate reduction to ammonia (DNRA) in nitrate conversion for the given denitrifying community. The temperature responses observed followed the increasing trend proposed by the Arrhenius equation, indicating higher nitrate removal efficiencies at higher temperatures. However, the growth and the nitrous oxide production observed at low temperature provided evidence of the psychrotolerance of the microbial community under study. The assays conducted showed higher nitrate removal from the microbial community extracted from the woodchip bioreactor at the cold season compared to the ones extracted during the warmer season. This indicated the ability of the bacterial populations in the bioreactor to evolve and adapt to different seasonal temperatures.

Keywords: agricultural waste water treatment, artificial wetland, denitrification, psychrophilic conditions

Procedia PDF Downloads 99