# On Improving Reliability of SRAM-Based Physically Unclonable Functions
## 1 Introduction  
A computing system is built with multiple layers of abstraction from application to operating systems, to instruction set architecture and transistor level design. Generally speaking, a higher layer of abstraction such as application or OS is built atop a stack of abstracted layers beneath it which it must trust. The initial sources of this trust are known as _roots of trust_, which are typically hardware features. Such features must be small and secure by design to perform one or more security related functions such as verifying software, authenticating a device and protecting cryptographic keys. Silicon physically unclonable functions (PUFs) have been proposed as such roots of trust [1].  
At a circuit level, a PUF harnesses device parametric variations to create a binary digital mapping that maps \(m\)-bit input challenge, \(c\), to an \(n\)-bit response, \(r\). The tuple \((c,r)\) is called a challenge-response pair (CRP) of the PUF. PUFs with a limited challenge set, with low values of \(m\), are called _Weak_ PUFs [2], which are used for key generation. PUFs with exponential CRPs are called _Strong_ PUFs [2] and primarily target authentication applications. Various circuits have been proposed to harness manufacturing process variations [3] to create Strong or Weak PUFs. SRAM based PUFs, which exploit start-up values in SRAM cells [4; 5], and Arbiter PUFs [6], which exploit signal races, have received the most attention.  
The salient properties that make a PUF attractive for security applications are its _tamper-proof_ nature and _uniqueness_. It has been claimed that PUFs are tamper-proof because they exploit inherent disorder in the manufacturing process, and any attempt to break package or delayer metal interconnections will change that physical disorder [2]. _Uniqueness_, on the other hand, is harnessed by exploiting inherent variations of the semiconductor manufacturing process to create uniqueidentifiers/keys. Thus, PUFs are unclonable by both the manufacturer and designer. These properties provide a major advantage over non-volatile memory based key storage, which has been shown to be vulnerable to physical attacks [7]. SRAM PUFs are the most popular Weak PUFs. An SRAM usually starts up in the same initial state upon power-up [4]. This state varies from chip to chip. This is the basis of SRAM PUF function [8].  
Unfortunately, PUF circuit characteristics are affected by environmental variations, noise and aging. This impacts repeatability of the response, which is called _reliability_, in the context of PUFs. Reliability of PUFs is a key design concern in Weak PUFs, as the responses are typically used for cryptographic key generation (or identification) and need to be quite robust to prevent data corruption downstream.  
The primary focus of this work is on improving the reliability of Weak PUFs. First, we propose a new voter based technique to reduce the error rate of the SRAM-based PUF responses by harnessing the statistical bias. Next, we present analytical results on error rate pertaining to the voter design. To enable a complete solution, we then propose a design for Design for Test (DFT)/testing based approach that capitalizes on the voter based characterization to improve overall reliability of the system. We have simulated example designs of the proposed method to measure error rates, area, performance, and yield of the proposed method, and compare it against prior approaches to demonstrate the benefits of this solution.  
The paper is arranged as follows. In Section 2, we present the related background and literature. In Section 3, we present proposed voter method along with the related circuit design. In Section 4, we analyze our proposed method in greater detail using _random walk_ models and also present DFT techniques to improve the overall reliability. In Section 5, we discuss the results and design examples and differentiate with related schemes. Finally, we conclude the paper in Section 6 with insight into future works.