# A New Design for Alignment-Free Chaffed Cancelable Iris Key Binding Scheme

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## Abstract

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## 1. Introduction

- Unlinkability: The protected biometric templates from the same subject should not be differentiable to prevent cross-matching across various applications.
- Revocability: It should be computationally infeasible to derive its original data from multiple protected templates.
- Non-invertibility: It should be computationally infeasible to derive its original biometric data from the protected template and/or the helper data.
- Performance: The accuracy of the cancelable template in recognition performance must be approximately preserved with respect to its original counterparts without the template protection scheme.

## 2. Related Work

#### 2.1. Fuzzy Commitment

#### 2.2. Fuzzy Vault

#### 2.3. Cancelable Biometrics

#### 2.4. Motivation and Contribution

## 3. Methodology

#### 3.1. Key Binding

- Cryptographic key generation: A random binary cryptographic key $\mathit{K}={\left\{{k}_{j}\right\}}_{j=1}^{n}$ is generated where ${k}_{j}\in \left\{0,1\right\}$ and $n$ is the input parameter determining the cryptographic key length.
- Genuine and synthetic template generation: IrisCode $\mathit{I}$ goes through feature transformation to generate a genuine iris template (Bloom filtered IrisCode) ${\mathit{B}}_{g}$ while a synthetic iris template can be generated through permutation as ${\mathit{B}}_{s}\leftarrow \mathrm{Perm}\text{}\left({\mathit{B}}_{g}\right)$.
- Key binding: Given a key, $\mathit{K}\in {\left\{0,1\right\}}^{n}$, we can define $n$ number of IFO hash groups $\left\{{H}_{1},\dots ,{H}_{n}\right\}.$ Each hash group ${H}_{j}$ (for $j=1:n$) is used to generate the $j$-th IFO hashed code ${\mathit{C}}_{j}$ based on the input matrix of either genuine or synthetic Bloom filtered IrisCode. For example, if ${k}_{j}=1$, the j-th hashed code can be described as ${\mathit{C}}_{j}\leftarrow {H}_{j}\left({\mathit{B}}_{g}\right)$, where ${H}_{j}\left({\mathit{B}}_{g}\right)=\left\{{h}_{i\left(j\right)}\left({\mathit{B}}_{g}\right)|i=1,\dots ,mhashfunctions\right\}$; otherwise (if ${k}_{j}=0$), the $j$-th hashed code is described as ${\mathit{C}}_{j}\leftarrow {H}_{j}\left({\mathit{B}}_{s}\right)$.
- Hashed code generation: $n$ number of hashed codes are constructed $\left[{\mathit{C}}_{1},{\mathit{C}}_{2},\dots ,{\mathit{C}}_{n}\right]$ and stored in the database instead of the corresponding cryptographic key $\mathit{K}$.
- Storage: The collection of output IFO hashed codes $\left[{\mathit{C}}_{1},{\mathit{C}}_{2},\dots ,{\mathit{C}}_{n}\right]$ are then stored together with the collection of IFO hash groups $\left\{{H}_{1},\dots ,{H}_{n}\right\}$ used in the process of key binding.

#### 3.2. Key Retrieval

- Genuine template generation: ${\mathit{I}}^{\prime}$ has to go through a similar transformation to first generate a query Bloom filtered IrisCode matrix, which can then be described as ${\mathit{B}}^{\prime}\leftarrow \mathrm{Bloom}\_\mathrm{filter}\left(W,L,{\mathit{I}}^{\prime}\right)$.
- Query hashed code generation: By using the same IFO hash groups $\left[{H}_{1}\left({\mathit{B}}^{\prime}\right),\dots ,{H}_{n}\left({\mathit{B}}^{\prime}\right)\right]$ with their respective permutations, $n$ number of query hashed codes $\left[{\mathit{C}}_{1}^{\prime},{\mathit{C}}_{2}^{\prime},\dots ,{\mathit{C}}_{n}^{\prime}\right]$ can be generated.
- Key retrieval: To prepare for key retrieval, we first generate an empty array denoted as ${\mathit{K}}^{\prime}={\left\{{{k}_{j}}^{\prime}\right\}}_{j=1}^{n}$ where ${{k}_{j}}^{\prime}\in \left\{0,1\right\}$ and $n$ is the cryptographic key length generated via the matching between the query and the reference hashed codes. Given any pre-defined threshold $t$, matching can be carried out by calculating the similarity score $\mathrm{S}({\mathit{C}}_{j},{\mathit{C}}_{j}^{\prime})$ between the reference hashed code ${\mathit{C}}_{j}$ and the query hashed code ${\mathit{C}}_{j}^{\prime}.$ If $\mathrm{S}({\mathit{C}}_{j},{\mathit{C}}_{j}^{\prime})\text{}\ge \mathrm{t}$, set ${{k}_{j}}^{\prime}=1$, otherwise, ${{k}_{j}}^{\prime}=0$.
- Eventually, a final key ${\mathit{K}}^{\prime}={\left\{0,1\right\}}^{\mathrm{n}}$ can be retrieved.

#### 3.3. The Relation of Key Retrieval Rate to Jaccard Similarity

#### 3.4. Example

## 4. Performance Evaluation

#### 4.1. Performance of Original IrisCode and Bloom Filter IrisCode

#### 4.2. Performance of the Proposed Key Binding Method

#### 4.3. Evaluation on Similarity Score Threshold, $t$

#### 4.4. Evaluation on Cryptographic Key Length, n

#### 4.5. Evaluation on Hashed Code Length, m

## 5. Security Analysis

#### 5.1. Indistinguishability Between Genuine and Synthetic Templates

- To start the game, given a group IFO hash function $H,$ the challenger allows the adversary to choose any class/individual from the database.
- After a class is chosen by the adversary, the challenger selects a random Bloom filtered IrisCode of that individual and generates ${\mathit{B}}_{g}\leftarrow \mathrm{Bloom}\_\mathrm{filter}\left(W=7,L=20,\mathit{I}\right).$
- The challenger can then produce the IFO hashed code ${\mathit{C}}_{g}\leftarrow H\left({\mathit{B}}_{g}\right)$ and give ${\mathit{C}}_{g}$ to the adversary.
- After that, the challenger flips a fair coin $b\in \left\{0,1\right\}$. If $b=1$, the challenger selects another Bloom filtered IrisCode of the selected person ${{\mathit{B}}_{g}}^{\prime}$ with a threshold ${t}^{\prime}\in \left[0,1\right]$, such that $\mathrm{JA}\left({\mathit{B}}_{g},{{\mathit{B}}_{g}}^{\prime}\right)\le {t}^{\prime}$ and generates $\mathit{C}\leftarrow H\left({{\mathit{B}}_{g}}^{\prime}\right)$. In addition, hashed code ${{\mathit{B}}_{g}}^{\prime}$. can also be generated by adding random noise to the filtered IrisCode as long as $\mathrm{JA}\left({\mathit{B}}_{g},{{\mathit{B}}_{g}}^{\prime}\right)\le t\prime $. If $b=0$, the challenger permutes the Bloom filtered IrisCode ${\mathit{B}}_{s}\leftarrow \mathrm{Perm}\text{}\left({\mathit{B}}_{g}\right)$ and generates $\mathit{C}\leftarrow H\left({\mathit{B}}_{s}\right)$. Then challenger gives $\mathit{C}$ to the adversary.
- The adversary outputs a word $\widehat{k}$ $\in $ $\left\{0,1\right\}$ and wins if $\widehat{k}=k$.

#### 5.2. Cancelability and Renewal

#### 5.3. Potential Attacks

#### 5.3.1. Brute Force Attack

#### 5.3.2. False Accept Attack

#### 5.4. Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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CASIA v3 Database [29] | Equal Error Rate (EER %) |
---|---|

IrisCode | 0.38 |

Bloom filtered IrisCode | 0.50 |

Bloom filtered IrisCode (IFO applied) | 0.58 |

$\mathit{t}$ | FRR (%) | FAR (%) | EER (%) |
---|---|---|---|

0.16 | 0.15 | 12.14 | 6.97 |

0.17 | 0.31 | 3.23 | 1.77 |

0.18 | 0.62 | 0.62 | 0.62 |

0.19 | 1.65 | 0.05 | 0.85 |

0.20 | 2.65 | 0.00 | 1.33 |

0.21 | 3.80 | 0.00 | 1.90 |

0.22 | 5.61 | 0.00 | 2.81 |

0.23 | 8.26 | 0.00 | 4.13 |

0.24 | 11.56 | 0.00 | 5.78 |

0.25 | 15.40 | 0.00 | 7.70 |

$\mathit{n}$ | GAR (%) | FAR (%) | EER (%) |
---|---|---|---|

10 | 97.35 | 0.00 | 1.33 |

20 | 96.67 | 0.00 | 1.67 |

40 | 96.67 | 0.00 | 1.67 |

60 | 96.37 | 0.00 | 1.82 |

80 | 96.37 | 0.00 | 1.82 |

100 | 96.37 | 0.00 | 1.82 |

150 | 96.37 | 0.00 | 1.82 |

200 | 96.37 | 0.00 | 1.82 |

$\mathit{m}$ | GAR (%) | FAR (%) | EER (%) | $\mathbf{Storage}/\mathbf{bit}\text{}(\mathbf{k}\mathbf{B}/\mathit{n})$ |
---|---|---|---|---|

10 | 89.51 | 0 | 5.25 | 0.19 |

50 | 95.97 | 0 | 2.02 | 0.94 |

100 | 96.37 | 0 | 1.82 | 1.90 |

150 | 96.37 | 0 | 1.82 | 2.81 |

200 | 96.37 | 0 | 1.82 | 3.75 |

250 | 96.37 | 0 | 1.82 | 4.69 |

300 | 96.37 | 0 | 1.82 | 5.63 |

$\mathit{S}\left({\mathit{B}}_{\mathit{g}},{\mathit{B}}^{\prime}\right)$ | $Ad{v}_{\mathbf{G}\mathbf{e}\mathbf{n}-\mathbf{S}\mathbf{y}\mathbf{n}}$$(\mathit{n}=1)$ | $\mathbf{A}\mathbf{d}{\mathbf{v}}_{\mathbf{G}\mathbf{e}\mathbf{n}-\mathbf{S}\mathbf{y}\mathbf{n}}^{\mathit{n}}$$(\mathit{n}=50)$ | $\mathbf{A}\mathbf{d}{\mathbf{v}}_{\mathbf{G}\mathbf{e}\mathbf{n}-\mathbf{S}\mathbf{y}\mathbf{n}}^{\mathit{n}}$$(\mathit{n}=100)$ | $\mathbf{A}\mathbf{d}{\mathbf{v}}_{\mathbf{G}\mathbf{e}\mathbf{n}-\mathbf{S}\mathbf{y}\mathbf{n}}^{\mathit{n}}$$(\mathit{n}=200)$ |
---|---|---|---|---|

0.16 | $2.0561\times {10}^{-26}$ | $1.0281\times {10}^{-24}$ | $2.0561\times {10}^{-24}$ | $4.1122\times {10}^{-24}$ |

0.17 | $3.0075\times {10}^{-15}$ | $1.5038\times {10}^{-13}$ | $3.0075\times {10}^{-13}$ | $6.015\times {10}^{-13}$ |

0.18 | $1.4936\times {10}^{-7}$ | $7.6480\times {10}^{-6}$ | $1.4936\times {10}^{-5}$ | $2.9872\times {10}^{-5}$ |

0.19 | 0.0058 | 0.29 | 0.58 | 1.16 |

$\mathit{S}\left({\mathit{B}}_{\mathit{g}},{\mathit{B}}^{\prime}\right)$ | $\mathbf{B}{\mathbf{f}}_{\mathit{n}=100}$ | $\mathbf{f}{\mathbf{a}}_{\mathit{K}\mathit{R}{\mathit{R}}_{imp}}$ |
---|---|---|

0.195 | ${2}^{100}$ | ${2}^{162}$ |

0.196 | ${2}^{100}$ | ${2}^{133}$ |

0.197 | ${2}^{100}$ | ${2}^{107}$ |

0.198 | ${2}^{100}$ | ${2}^{85}\text{}$ |

0.199 | ${2}^{100}$ | ${2}^{66}$ |

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## Share and Cite

**MDPI and ACS Style**

Chai, T.-Y.; Goi, B.-M.; Tay, Y.-H.; Jin, Z.
A New Design for Alignment-Free Chaffed Cancelable Iris Key Binding Scheme. *Symmetry* **2019**, *11*, 164.
https://doi.org/10.3390/sym11020164

**AMA Style**

Chai T-Y, Goi B-M, Tay Y-H, Jin Z.
A New Design for Alignment-Free Chaffed Cancelable Iris Key Binding Scheme. *Symmetry*. 2019; 11(2):164.
https://doi.org/10.3390/sym11020164

**Chicago/Turabian Style**

Chai, Tong-Yuen, Bok-Min Goi, Yong-Haur Tay, and Zhe Jin.
2019. "A New Design for Alignment-Free Chaffed Cancelable Iris Key Binding Scheme" *Symmetry* 11, no. 2: 164.
https://doi.org/10.3390/sym11020164