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Printed Electronics (PE) is a promising technology that provides mechanical flexibility and low-cost fabrication. These features make PE the key enabler for emerging applications, such as smart sensors, wearables, and Internet of Things (IoTs). Since these applications need secure communication and/or authentication, it is vital to utilize security primitives for cryptographic key and identification. Physical Unclonable Functions (PUF) have been adopted widely to provide the secure keys. In this work, we present a weak PUF based on Electrolyte-gated FETs using inorganic inkjet printed electronics. A comprehensive analysis framework including Monte Carlo simulations based on real device measurements is developed to evaluate the proposed PE-PUF. Moreover, a multi-bit PE-PUF design is proposed to optimize area usage. The analysis results show that the PE-PUF has ideal uniqueness, good reliability, and can operates at low voltage which is critical for low-power PE applications. In addition, the proposed multi-bit PE-PUF reduces the area usage around 30%.