基于Kummer曲面的RFID标签

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.

Design of RFID-tags on Kummer Surface

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.