On combining Arbiter based PUFs

Article Type

Research Article

Publication Title

Cryptography and Communications

Abstract

An Arbiter based Physical Unclonable Function (PUF) is a hardware based pseudorandom bit generator whose pseudorandomness in the output bits depends on device specific delay parameters. An n-length Arbiter based PUF takes a binary string as input (can be interpreted as an element in {0,1}n or {-1,1}n) and generates a single bit as output. Thus, an Arbiter based PUF can be analyzed as an n-variable Boolean function. Recently, it was shown (Roy et al. 2021) that a negligible portion of the Boolean functions class can be generated from an n-length Arbiter PUF. In 2017, Soroceanu showed the connection between Arbiter PUF and threshold functions (Muroga et al. J. Franklin Inst. 271(5), 376–418, 1961). Here, we consider this connection and first point out some miscalculations done by Yajima and Ibaraki (1965), regarding the number of Boolean functions generated from a threshold function, and present improved combinatorial results, explaining new ideas to distinguish the Arbiter PUFs from other Boolean functions. Also, we study the combination (extendability) of such Arbiter based PUFs and investigate the XOR of two n-length such devices with arbitrary inputs. We checked, for some small dimensions, that among all the XORNF (Exclusive OR Normal Form) representations of two Arbiter PUFs of the same length, the XOR of two Arbiter PUFs of the same length produces a large portion of the Boolean functions class. Based upon extensive computations, we therefore propose a conjecture. Finally, we concentrate on a general PUF combiner and compute the probability of two outputs from a combiner model PUF corresponding to two different challenge inputs being the same.

First Page

493

Last Page

510

DOI

10.1007/s12095-024-00769-0

Publication Date

3-1-2025

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