The message blinding method is the most efficient and secure countermeasure against first-order differential power analysis(DPA).Although cross correlation attacks(CCAs) were given for defeating message blinding metho...The message blinding method is the most efficient and secure countermeasure against first-order differential power analysis(DPA).Although cross correlation attacks(CCAs) were given for defeating message blinding methods,however searching for correlation points is difficult for noise,misalignment in practical environment.In this paper,we propose an optimized cross correlation power attack for message blinding exponentiation algorithms.The attack method can select the more correlative power points of share one operation in the modular multiplication by comparing variances between correlation coefficients.Further we demonstrate that the attack method is more efficient in experiments with hardware implementation of RSA on a crypto chip card.In addition to the proposed CCA method can recovery all 1024 bits secret key and recognition rate increases to 100%even when the recorded signals are noisy.展开更多
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep...In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.展开更多
基金supported in part by National Natural Science Foundation of China Project(Grant No.60873216) Scientific and Technological Research Priority Projects of Sichuan Province(Grant No. 2012GZ0017)
文摘The message blinding method is the most efficient and secure countermeasure against first-order differential power analysis(DPA).Although cross correlation attacks(CCAs) were given for defeating message blinding methods,however searching for correlation points is difficult for noise,misalignment in practical environment.In this paper,we propose an optimized cross correlation power attack for message blinding exponentiation algorithms.The attack method can select the more correlative power points of share one operation in the modular multiplication by comparing variances between correlation coefficients.Further we demonstrate that the attack method is more efficient in experiments with hardware implementation of RSA on a crypto chip card.In addition to the proposed CCA method can recovery all 1024 bits secret key and recognition rate increases to 100%even when the recorded signals are noisy.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)。
文摘In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.
