PAC learning of arbiter PUFs

Abstract

The general concept of physically unclonable functions (PUFs) has been nowadays widely accepted and adopted to meet the requirements of secure identification and key generation/storage for cryptographic ciphers. However, shattered by different attacks, e.g., modeling attacks, it has been proved that the promised security features of arbiter PUFs, including unclonability and unpredictability, are not supported unconditionally. However, so far the success of existing modeling attacks relies on pure trial and error estimates. This means that neither the probability of obtaining a useful model (confidence), nor the sufficient number of CRPs, nor the probability of correct prediction (accuracy) is guaranteed. To address these issues, this work presents a probably approximately correct (PAC) learning algorithm. Based on a crucial discretization process, we are able to define a Deterministic finite automaton (of polynomial size), which exactly accepts the regular language corresponding to the challenges mapped by the given PUF to one responses.

A Privacy-Preserving, Mutual PUF-Based Authentication Protocol

“…In particular, the path that dominates the timing for cases where paths reconverge and have nearly equal nominal delays will be different from chip-to-chip. Third, ML algorithms such as Probably Approximately Correct (PAC) that have been effective against arbiter PUFs, guarantee success only when the model is polynomial in size [5,35,36]. Our preliminary work on the physical model indicate that the model has components that appear to be exponential in size, eliminating the possibility of a "guaranteed" success.…”

On the Physical Security of Physically Unclonable Functions

“…Modeling attacks require a subset of CRPs to create a model on that and predict the PUF responses for all possible challenges [41]. It has been reported that an Arbiter PUF under the Deterministic Finite Automata (DFA) representation can be Probably Approximately Correct (PAC) learned with a given level of accuracy and confidence [26].…”

“…Here we elaborate briefly on an example of how the LFI can be combined with a well-established ML framework to break the security of an XOR Arbiter PUF. If the attacker could access the response of each individual Arbiter PUF in an XOR Arbiter PUF, each chain can be modeled separately in polynomial time, e.g., following the procedure in [26]. By obtaining a model of the challenge-response behavior of each Arbiter PUF individually, the challenge-response of an XOR Arbiter PUF can be predicted, and hence, the security of the XOR Arbiter PUF is broken.…”

“…It has been proven that an Arbiter PUF can be learned under a Deterministic Finite Automaton (DFA)-based representation by collecting only a polynomial number of CRPs for given accuracy and confidence levels (i.e., PAC learning) [26]. The accuracy level shows the error of the model whereas the confidence level represents the likelihood of delivering the model.…”

“…To compute the maximum number of CRPs required to PAC-learn an individual Arbiter PUF, we follow the procedure introduced in [26]. To establish the DFA-based representation, by applying a statistical discretization and a mapping process, the real-valued delays are mapped to integer-valued delays lying within [0,M ], where M is the maximum variation of delay values.…”