The theory of quadratic residues plays an important role in cryptography.In 2001,Cocks developed an identity-based encryption(IBE)scheme based on quadratic residues,resolving Shamir’s 17-year-old open problem.However...The theory of quadratic residues plays an important role in cryptography.In 2001,Cocks developed an identity-based encryption(IBE)scheme based on quadratic residues,resolving Shamir’s 17-year-old open problem.However,a notable drawback of Cocks’scheme is the significant expansion of the ciphertext,and some of its limitations have been addressed in subsequent research.Recently,Cotan and Teşeleanu highlighted that previous studies on Cocks’scheme relied on a trial-and-error method based on Jacobi symbols to generate the necessary parameters for the encryption process.They enhanced the encryption speed of Cocks’scheme by eliminating this trialand-error method.Based on security analysis,this study concludes that the security of Cotan-Teşeleanu’s proposal cannot be directly derived from the security of the original Cocks’scheme.Furthermore,by adopting the Cotan-Teşeleanu method and introducing an additional variable as a public element,this study develops a similar enhancement scheme that not only accelerates the encryption speed but also provides security equivalent to the original Cocks’scheme.展开更多
采用透射电镜(TEM)和扫描电镜(SEM)分析了不同时效热处理制度下镍基GH99高温合金中γ'相的尺寸、形貌变化,采用维氏硬度计测试不同时效热处理制度下的合金硬度。结果表明:γ'相随着时效温度的升高和保温时间的延长而明显粗化,...采用透射电镜(TEM)和扫描电镜(SEM)分析了不同时效热处理制度下镍基GH99高温合金中γ'相的尺寸、形貌变化,采用维氏硬度计测试不同时效热处理制度下的合金硬度。结果表明:γ'相随着时效温度的升高和保温时间的延长而明显粗化,其粗化符合沉淀相粗化理论(LSW理论);随着γ'相的不断长大,部分γ'相的形貌由球形转变为立方形。经计算得到γ'相长大激活能约为248.8 k J/mol。此外发现硬度随γ'相尺寸的增大而逐渐增大,但当γ'相尺寸超过37.2 nm时,硬度随γ'相长大呈下降趋势,在750℃时得到合金的最大硬度为395.16 HV。展开更多
基金Rising-Star Program of Shanghai 2023 Science and Technology Innovation Action Plan(Yangfan Special Project),China(No.23YF1401000)Fundamental Research Funds for the Central Universities,China(No.2232022D-25)。
文摘The theory of quadratic residues plays an important role in cryptography.In 2001,Cocks developed an identity-based encryption(IBE)scheme based on quadratic residues,resolving Shamir’s 17-year-old open problem.However,a notable drawback of Cocks’scheme is the significant expansion of the ciphertext,and some of its limitations have been addressed in subsequent research.Recently,Cotan and Teşeleanu highlighted that previous studies on Cocks’scheme relied on a trial-and-error method based on Jacobi symbols to generate the necessary parameters for the encryption process.They enhanced the encryption speed of Cocks’scheme by eliminating this trialand-error method.Based on security analysis,this study concludes that the security of Cotan-Teşeleanu’s proposal cannot be directly derived from the security of the original Cocks’scheme.Furthermore,by adopting the Cotan-Teşeleanu method and introducing an additional variable as a public element,this study develops a similar enhancement scheme that not only accelerates the encryption speed but also provides security equivalent to the original Cocks’scheme.
文摘采用透射电镜(TEM)和扫描电镜(SEM)分析了不同时效热处理制度下镍基GH99高温合金中γ'相的尺寸、形貌变化,采用维氏硬度计测试不同时效热处理制度下的合金硬度。结果表明:γ'相随着时效温度的升高和保温时间的延长而明显粗化,其粗化符合沉淀相粗化理论(LSW理论);随着γ'相的不断长大,部分γ'相的形貌由球形转变为立方形。经计算得到γ'相长大激活能约为248.8 k J/mol。此外发现硬度随γ'相尺寸的增大而逐渐增大,但当γ'相尺寸超过37.2 nm时,硬度随γ'相长大呈下降趋势,在750℃时得到合金的最大硬度为395.16 HV。
