Nanoscale physical unclonable function labels that offer multiple, independently operating keys and can be used for high-speed multipurpose identification can be created by exploiting the non-deterministic molecular self-assembly of block co-polymers. Hardware-based cryptography that exploits physical unclonable functions is required for the secure identification and authentication of devices in the Internet of Things. However, physical unclonable functions are typically based on anticounterfeit identifiers created from randomized microscale patterns or non-predictable fluctuations of electrical response in semiconductor devices, and the validation of an encrypted signature relies on a single-purpose method such as microscopy or electrical measurement. Here we report nanoscale physical unclonable function labels that exploit non-deterministic molecular self-assembly. The labels are created from the multilayer superpositions of metallic nanopatterns replicated from self-assembled block co-polymer nanotemplates. Due to the nanoscale dimensions and diverse material options of the system, physical unclonable functions are intrinsically difficult to replicate, robust for authentication and resistant to external disturbance. Multiple, independently operating keys-which use electrical resistance, optical dichroism or Raman signals-can be generated from a single physical unclonable function, offering millisecond-level validation speeds. We also show that our physical unclonable function labels can be used on a range of different surfaces including dollar bills, human hair and microscopic bacteria.