We present a comprehensive investigation into the complexity of a new private key storage apparatus: a novel silicon photonic physical unclonable function (PUF) based on ultrafast nonlinear optical interactions in a chaotic silicon microcavity that is both unclonable and impossible to emulate. This device provides remarkable improvements to total information content (raw cryptographic material), information density, and key generation rates over existing optical scattering PUFs and is also more easily integrated with both CMOS electronics and telecommunications hardware. Our device exploits the natural nonlinear optical behavior of silicon to neutralize commonly used attacks against PUFs and vastly enhance device complexity. We confirm this phenomenon with thorough experimental results on prototype devices and present a detailed estimate of their total information content. Our compact, micron-scale approach represents an entirely new generation of ultrafast and high information density photonic PUF devices that can be directly incorporated into integrated circuits to ensure authenticity and provide secure physical storage of private key material.