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In this paper, we present two explicit inva-lid-curve attacks on the genus 2 hyperelliptic curve o-ver a finite field. First, we propose two explicit attack models by injecting a one-bit fault in a given divisor. Then, we discuss the construction of an invalid curve based on the faulted divisor. Our attacks are based on the fact that the Hyperelliptic Curve Scalar Multiplica-tion (HECSM) algorithm does not utilize the curve parameters and We consider three hyperelliptic curves as the attack targets. For curve with security level 186 (in bits), our attack method can get the weakest inva-lid curve with security level 42 (in bits); there are 93 invalid curves with security level less than 50. We al-so estimate the theoretical probability of getting a weak hyperelliptic curve whose cardinality is a smooth integer. Finally, we show that the complexity of the fault attack is subexponential if the attacker can freely inject a fault in the input divisor. Cryptosystems based on the genus 2 hyperelliptic curves cannot work against our attack algorithm in practice. 相似文献
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采用电磁搅拌结合定向凝固技术将过共晶铝硅合金中的初晶硅和铝硅合金分离,并研究不同的杂质元素在铝硅体系中的分布特点。结果表明:杂质元素主要分布在铝硅合金以及铝硅合金和初晶硅的晶界中。同时,根据初晶硅富集区域不同位置硅含量的不同,初晶硅的形貌由鱼骨状变成板状和球状,并且随着样品中不同位置硅含量的增多,初晶硅中的杂质含量降低。样品底部杂质的含量约为10×10^-6,与原料冶金级硅中的杂质含量1248.47×10^-6相比,杂质的去除效果很好。 相似文献
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本文介绍了我国饮用水源存在的供水现状,并对水源地污染来源进行了分析,最后提出了饮用水源的保护对策。 相似文献
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电磁法分离高硅铝硅合金[ω(硅)≥24%~25%]中初晶硅相富集,同时获得低硅铝硅合金,是一种低能耗、短流程且对环境友好的技术。文章对比真空电阻炉与电磁感应炉高硅铝合金分离效果,分析了初晶硅的富集情况,并通过建立定量评估分离效率η表达式计算不同实验条件对分离效率的影响。 相似文献
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