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Finger vain encryption algorithm based on anerror-correcting code
WANG Kejun, CAO Yi, JIANG Bowei, XU Yibo, XING Xianglei
College of Automation, Harbin Engineering University, Harbin 150001, China
Abstract: This study presents an overall introduction of a finger vain encryption algorithm. A finger vain encryption algorithm with error correction is then designed by adding an error correction mechanism. This new finger vain encryption algorithm can produce a stochastic key in the form of a multinomial coefficient using a binary system sequencer, an encrypt finger vain, and the Lagrange interpolation value to restore the multinomial during authentication. The accuracy of this algorithm can be ensured using the cyclic redundancy check the code to determine the most accurate key. The experimental results indicate that the fuzzy vault algorithm with error correction can realize well the encryption and decryption of a vein template and meet the requirements of biological information security protection. In addition, the algorithm also indicates that the syste's safety performance can be enhanced by changing the keys' length.
Key words: finger vain encryption     error correcting code     finger vain minutiae     biometric encryption     random key     fuzzy vault algorithm

1 循环冗余校验码 (CRC) 算法及分析 1.1 CRC算法的定义

CRC利用n维实多项式线性空间进行编码[12-13]。任意要处理的二进制数据都可以写成一个n阶的实多项式：

 (1)

CRC校验可以检测出所有奇数个随机的错误和长度小于多项式阶数的错误。因此，为了降低误判的概率，可以采用更高阶次的生成多项式。例如，使用CRC-16算法，即采用16 bit的CRC校验可以保证1 014 bit的码元中仅有一个未被检测出错误。它的生成多项式为

 (2)
1.2 CRC校验码的算法分析

CRC校验码的编码过程为：首先将要发送的二进制数在多项式线性空间线性表示为g(x)，然后除以xyt(x) 生成多项式，最后取余数y(x) 作为CRC校验码。具体步骤如下：

2 基于纠错码的指纹加密算法模糊金库的实现 2.1 指静脉图像预处理

 图 1 指静脉图像预处理与特征点提取 Fig. 1 Finger vain image preprocessing and feature point extraction
2.2 基于纠错码的指静脉加密算法流程图 (如图 2)
 图 2 加密流程图 Fig. 2 The flow chart of encryption
2.3 基于纠错码的指静脉加密实现方法

 (3)

 (4)

ui转换成16 bit的二进制串作为加密单元，从而形成特征点集合，即

 (5)

m序列发生器产生192 bit的随机二进制数作为密钥，并在多项式线性空间中表示为[16]

 (6)

 (7)

 (8)

 (9)
 图 3 特征点和杂凑点的集合 Fig. 3 The formation of Fuzzy vault

2.4 密钥恢复

 (10)
 图 4 解密流程图 Fig. 4 The flow chart of decryption

 (11)

 (12)

3 实验结果分析与讨论

 多项式阶数 拒真率/% 误识率/% 8 11.6 1.5 10 11.0 0.5 12 10.8 0

 密钥位数/bit 拒真率/% 误识率/% 64 11.5 2.6 96 11.2 1.2 128 10.8 0

5 结束语

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DOI: . 10.11992/tis.201609028

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#### 文章信息

WANG Kejun, CAO Yi, JIANG Bowei, XU Yibo, XING Xianglei

Finger vain encryption algorithm based on anerror-correcting code

CAAI Transactions on Intelligent Systems, 2017, 12(1): 55-59
. http://dx.doi.org/10.11992/tis.201609028