Information security underpins many aspects of modern society. However, silicon chips are vulnerable to hazards such as counterfeiting, tampering and information leakage through side-channel attacks (for example, by measuring power consumption, timing or electromagnetic radiation). Single-walled carbon nanotubes are a potential replacement for silicon as the channel material of transistors due to their superb electrical properties and intrinsic ultrathin body, but problems such as limited semiconducting purity and non-ideal assembly still need to be addressed before they can deliver high-performance electronics. Here, we show that by using these inherent imperfections, an unclonable electronic random structure can be constructed at low cost from carbon nanotubes. The nanotubes are self-assembled into patterned HfO2 trenches using ion-exchange chemistry, and the width of the trench is optimized to maximize the randomness of the nanotube placement. With this approach, two-dimensional (2D) random bit arrays are created that can offer ternary-bit architecture by determining the connection yield and switching type of the nanotube devices. As a result, our cryptographic keys provide a significantly higher level of security than conventional binary-bit architecture with the same key size.