一种基于演化密码和HMM改进的Koblitz安全曲线产生新方法  

Evolutionary cryptography theory based generating method for a secure Koblitz elliptic curve and its improvement by a hidden Markov models

作　　者：王潮[1] 张焕国[2,3] 刘礼黎 

机构地区：[1]上海大学通信与信息工程学院,上海200072 [2]武汉大学计算机学院,武汉430072 [3]空天信息安全与可信计算教育部重点实验室,武汉430072 [4]华为公司,上海201206

出　　处：《中国科学：信息科学》2013年第3期322-334,共13页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:60970006;60970115;61272096;91018008);空天信息安全与可信计算教育部重点实验室开放基金(批准号:AISTC2009 04);上海市重点学科和科委重点实验室项目(批准号:S30108;08DZ2231100)资助

摘　　要：考虑未来云计算攻击和量子计算机攻击，需要储备安全强度更高的ECC安全曲线．利用隐Markov模型（HMM）预测迹向量解决基点计算难题，完善基于演化密码思想提出的Koblitz安全曲线产生新算法，完成了F（2 2000）以内Koblitz安全曲线的搜索实验，产生的安全曲线基域的覆盖范围、曲线的规模和产生效率均超过美国NIST的公开报道参数．可提供的安全曲线的基域和基点最高超过1900bit，远超过美国NIST公布的571bit．在NIST公布的F（2163）-F（2571）范围之间还有新的安全曲线发现．对产生的安全曲线进行了详细的安全分析，表明与NIST推荐的安全曲线具有相同的安全准则．Considering potential attacks from cloud-computing and quantum-computing, it is becoming nec- essary to provide higher security elliptic curves. The hidden Markov models are introduced for designing the trace-vector computation algorithm to accelerate the search for elliptic curve （EC） base-points. We present a new algorithm for secure Koblitz EC generation based on evolutionary cryptography theory. The algorithm is tested by selecting a secure Koblitz EC over the field F（22~~~）, with experiments showing that both the base field and base point of the secure curve generated exceed the parameter range for Koblitz curves recommended by NIST. The base fields generated go beyond 1900 bits, which is higher than the 571 bits recommended by NIST. We also find new secure curves in the range F（2163）-F（2571） recommended by NIST. We perform a detailed security analysis of those secure curves, showing that those we propose satisfy the same security criteria as NIST.

关 键 词：安全曲线选择 演化密码 蚁群算法 Koblitz曲线HMM 

分 类 号：TN918.1[电子电信—通信与信息系统]