基于Kummer曲面的RFID标签  

Design of RFID-tags on Kummer Surface

作　　者：林齐平 张方国[2,3] LIN Qi-Ping;ZHANG Fang-Guo(Xingtang Telecommunication Technology Co.Ltd.,Beijing 100191,China;School of Data and Computer Science,Sun Yat-Sen University,Guangzhou 510006,China;Guangdong Key Laboratory of Information Security,Guangzhou 510006,China)

机构地区：[1]兴唐通信科技有限公司,北京100191 [2]中山大学数据科学与计算机学院,广州510006 [3]广东省信息安全技术重点实验室,广州510006

出　　处：《密码学报》2020年第2期212-220,共9页Journal of Cryptologic Research

基　　金：国家重点研发计划(2017YFB0802500);国家自然科学基金(61672550)。

摘　　要：理论上使用公钥密码,包括椭圆曲线密码和超椭圆曲线密码来设计RFID标签已经比较成熟了.实验结果表明椭圆曲线密码或者超椭圆曲线密码用于RFID标签设计也很有效.与超椭圆曲线密码相比较,在亏格为2的曲线上使用Kummer曲面来计算标量乘会更快.但是,由于在Kummer曲面上没有简单的点加计算公式,这导致很难使用Kummer曲面来构造密码协议.在本文中,我们把Schnorr的鉴别协议扩展到Kummer曲面上.研究表明该协议可以只使用有限域Fq上的加法和乘法来计算,而且也不降低安全性.进一步地,我们用该协议来设计RFID标签.结果表明该协议在Kummer曲面上非常有效并很容易用于RFID标签设计中.在本文中,我们选取的是可转换为超椭圆曲线y^2+xy=x^5+f3x^3+εx^2+f0的Kummer曲面,其中ε∈{0,1}.我们方案的性能比其它使用公钥密码来设计RFID标签的方案都有效.Recently,RFID-tags have been constructed with public-key cryptography including ECC and HECC.Implementation results also showed that it is efficient to use ECC or HECC for RFID-tags.Compared with HECC,it is faster to compute scalar multiplication in genus 2 curves on Kummer surfaces.In particular,the scalar multiplication can be more efficient to be computed on Kummer surfaces than on elliptic curve when the characteristic of the finite field is 2.However,it is hard to construct cryptographic protocols on Kummer surfaces because of that it has no simple addition algorithm on Kummer surfaces.In this paper,we generalize Schnorr’s identification protocol to Kummer surfaces.We show that this protocol can be computed using only additions and multiplications in finite field Fq.And the security of it does not lose.Additionally,we describe how to use it on RFID-tags.It is showed that the protocol on Kummer surfaces are very cheap and can easily be implemented on an RFID-tag.In this paper,we choose the Kummer surface which links to a hyperelliptic curve y^2+xy=x^5+f3x^3+εx^2+f0 where ε∈{0,1}.The performance of our scheme is competitive in public key cryptography for RFID-tags.

关 键 词：鉴别协议 Kummer曲面 亏格2曲线 RFID标签 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]