Abstract The f -invariant is an isomorphism invariant of free-group measure-preserving actions introduced by Lewis Bowen, who first used it to show that two finite-entropy Bernoulli shifts over a finitely generated free group can be isomorphic only if their base measures have the same Shannon entropy. Bowen also showed that the f -invariant is a variant of sofic entropy; in particular, it is the exponential growth rate of the expected number of good models over a uniform random homomorphism. In this paper we present an analogous formula for the relative f -invariant and use it to prove a formula for the exponential growth rate of the expected number of good models over a random sofic approximation which is a type of stochastic block model.
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Physical Layer Authentication via Fingerprint Embedding: Min-Entropy Analysis
One of the difficulties of implementing and analyzing algorithms that achieve information theoretic limits is adapting asymptotic results to the finite block-length regime. Results on secrecy for both regimes utilize Shannon entropy and mutual information as metrics for security. In this paper, we determine that Shannon entropy does not necessarily have equal utility for wireless authentication in finite block-length regimes with a focus on the fingerprint embedding framework. Then, we apply a new security performance metric to the framework that is linked to min-entropy rather than Shannon entropy and is similar to cheating probability used in the literature. The metric is based upon an adversary's ability to correctly guess the secret key over many observations using maximum likelihood decoding. We demonstrate the effect that system parameters such as the length of the key and the identification tag have on an adversary's ability to attack successfully. We find that if given a large key, it is better to use it all at once, than to use some and then renew the key with the remaining bits after a certain number of transmissions.
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- PAR ID:
- 10095331
- Date Published:
- Journal Name:
- Conference on Information Science and Systems
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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