# On Improving Reliability of SRAM-Based Physically Unclonable Functions

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. SRAM PUF and Reliability

#### 2.2. Related Literature

#### 2.2.1. Error-Correcting Codes and Fuzzy Extractor

#### 2.2.2. Circuit and Manufacturing Technology Solutions

## 3. Proposed Technique

#### 3.1. Harnessing Statistical Bias for Improving Reliability

#### 3.2. Temporal Majority Voting

#### 3.3. New Voter Design

#### 3.4. Circuit Design

#### 3.5. Error Rate from Simulation

## 4. Analysis of the Proposed Counter Based Design

#### 4.1. Operation of the Proposed Voter as Random Walk

#### 4.2. Error Rate

#### 4.3. UP/DOWN Counter vs. TMV

#### 4.4. DFT Based on Trials to Settlement

## 5. Results and Case Studies

#### 5.1. Case Study: Redundancy to Improve Yield and Reduce Error Rate

#### 5.2. Design Area/Performance Comparisons

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Modified Cell schematic and timing diagram. (

**a**) modified SRAM cell for multiple evaluations; and (

**b**) timing diagrams for bit evaluation.

Symbols | Definitions |
---|---|

p | Probability of logic-1 from a PUF cell |

$q=1-p$ | Probability of logic-0 from a PUF cell |

n | Length of the UP/DOWN counter |

T | Total number of trials |

$k=\frac{({2}^{n}-2)}{2}$ | Initialization state—it is also the number of steps from initialization to end states |

${P}_{s}$ | Probability of logic-1 from UP/DOWN counter (probability of success) |

${P}_{e}$ | Probability of logic-0 from UP/DOWN counter (probability of error) |

**Table 2.**Area estimates using Nangate Cell Library [29].

Implementation | Area ($\mathsf{\mu}{\mathit{m}}^{2}$) | |
---|---|---|

repetition[9,1,9]; Golay[23,12,7] [32] | 7648 | |

repetition[9,1,9]; Reed Muller[16,5,8] [32] | 7945 | |

UP/DOWN counter scheme | $4:1$ Mux | 4538 |

$8:1$ Mux | 3266 | |

$16:1$ Mux | 2630 |

Implementation | # Bits generated | # Cycles | |
---|---|---|---|

Bhargava et al. [30] | 171 | 286 | |

Our Approach | 4:1 | 192 | 248 |

8:1 | 448 | ||

16:1 | 848 |

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**MDPI and ACS Style**

Vijayakumar, A.; Patil, V.C.; Kundu, S.
On Improving Reliability of SRAM-Based Physically Unclonable Functions. *J. Low Power Electron. Appl.* **2017**, *7*, 2.
https://doi.org/10.3390/jlpea7010002

**AMA Style**

Vijayakumar A, Patil VC, Kundu S.
On Improving Reliability of SRAM-Based Physically Unclonable Functions. *Journal of Low Power Electronics and Applications*. 2017; 7(1):2.
https://doi.org/10.3390/jlpea7010002

**Chicago/Turabian Style**

Vijayakumar, Arunkumar, Vinay C. Patil, and Sandip Kundu.
2017. "On Improving Reliability of SRAM-Based Physically Unclonable Functions" *Journal of Low Power Electronics and Applications* 7, no. 1: 2.
https://doi.org/10.3390/jlpea7010002