Physical Unclonable Function

In practical cryptography, a physical unclonable function or PUF is a function that is embodied in a physical structure and is easy to evaluate but hard to predict. Further, an individual PUF device must be easy to make but practically impossible to duplicate, even given the exact manufacturing process that produced it. In this respect it is the hardware analog of a one-way function. Early references that exploit the physical properties of disordered systems for authentication purposes date back to Bauder in 1983 and Simmons in 1984. Naccache and Frémanteau provided an authentication scheme in 1992 for memory cards. The terms POWF (physical one-way function) and PUF (physical unclonable function) were coined in 2001 and 2002, the latter publication describing the first integrated PUF where unlike PUFs based on optics, the measurement circuitry and the PUF are integrated onto the same electrical circuit (and fabricated on silicon).

Rather than embodying a single cryptographic key, PUFs implement challenge–response authentication. When a physical stimulus is applied to the structure, it reacts in an unpredictable (but repeatable) way due to the complex interaction of the stimulus with the physical microstructure of the device. This exact microstructure depends on physical factors introduced during manufacture which are unpredictable (like a fair coin). The applied stimulus is called the challenge, and the reaction of the PUF is called the response. A specific challenge and its corresponding response together form a challenge–response pair or CRP. The device's identity is established by the properties of the microstructure itself. As this structure is not directly revealed by the challenge-response mechanism such a device is resistant to spoofing attacks.

PUFs can be implemented with a very small hardware investment. Unlike a ROM containing a table of responses to all possible challenges, which would require hardware exponential in the number of challenge bits, a PUF can be constructed in hardware proportional to the number of challenge and response bits.

Unclonability means that each PUF device has a unique and unpredictable way of mapping challenges to responses, even if it was manufactured with the same process as a similar device, and it is infeasible to construct a PUF with the same challenge–response behavior as another given PUF because exact control over the manufacturing process is infeasible. Mathematical unclonability means that it should be very hard to compute an unknown response given the other CRPs or some of the properties of the random components from a PUF. This is because a response is created by a complex interaction of the challenge with many or all of the random components. In other words, given the design of the PUF system, without knowing all of the physical properties of the random components, the CRPs are highly unpredictable. The combination of physical and mathematical unclonability renders a PUF truly unclonable.

Different sources of physical randomness can be used in PUFs. A distinction is made between PUFs in which physical randomness is explicitly introduced and PUFs that use randomness that is intrinsically present in a physical system.