Physically unclonable function (PUF) and true random number generator (TRNG) are the indispensable primitives for the Internet-of-Things (IoT) security. In this article, a highly robust unified PUF<inline-formula> <tex-math notation="LaTeX">/ </tex-math></inline-formula>TRNG design is demonstrated. An entropy source (ES) chip based on 40-nm resistive random access memory (RRAM) is designed and fabricated, and a pseudo-forming technique is developed to ensure excellent robustness. The unified PUF<inline-formula> <tex-math notation="LaTeX">/ </tex-math></inline-formula>TRNG is tested across <inline-formula> <tex-math notation="LaTeX">- 55\,\,^{\circ }\text{C} </tex-math></inline-formula> to 125 °C with different supply voltages, achieving < 0.001% bit error rate (BER) and >0.999 worst case min-entropy simultaneously. Excellent randomness is verified by NIST SP800-22 and 90B tests. This highly robust unified design can implement an authentication system with the authentication error rate (AER) approaching 0% and thus is promising for future IoT security applications.