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Continuous-variable quantum authentication of physical unclonable keys

View Article: PubMed Central - PubMed

ABSTRACT

We propose a scheme for authentication of physical keys that are materialized by optical multiple-scattering media. The authentication relies on the optical response of the key when probed by randomly selected coherent states of light, and the use of standard wavefront-shaping techniques that direct the scattered photons coherently to a specific target mode at the output. The quadratures of the electromagnetic field of the scattered light at the target mode are analysed using a homodyne detection scheme, and the acceptance or rejection of the key is decided upon the outcomes of the measurements. The proposed scheme can be implemented with current technology and offers collision resistance and robustness against key cloning.

No MeSH data available.


Related in: MedlinePlus

Typical response of D–close clones (coloured symbols) relative to the response of the true key (star).The responses of 500 random D–close clones is shown in phase-space representation for various values of D (1–5%), and two different numbers of modes. The responses of the clones move away from the response of the true key, as we increase D. Also shown are the mean value (black cross) and the standard deviation (dashed circle) of the responses of the 500 random D-close clones, for each D. Parameters are as in Fig. 5.
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f6: Typical response of D–close clones (coloured symbols) relative to the response of the true key (star).The responses of 500 random D–close clones is shown in phase-space representation for various values of D (1–5%), and two different numbers of modes. The responses of the clones move away from the response of the true key, as we increase D. Also shown are the mean value (black cross) and the standard deviation (dashed circle) of the responses of the 500 random D-close clones, for each D. Parameters are as in Fig. 5.

Mentions: The typical response of D–close clones relative to the response of the true key is shown in Fig. 6. We see that for values of , the response of D–close clones lies very close to the response of the true key. In this case, one may expect high probability for a clone to result in a probability pin very close to Pin. As D increases, however, the responses of the clones move rapidly away from the response of the true key, and pin is also expected to move away from Pin. This behaviour is clearly shown in the probability distributions of Fig. 7(a). As a result, the probability for a D–close clone to pass the verification test, i.e., to result in an estimate pin such that , decreases rapidly with increasing D [see Fig. 7(b)]. Note that for fixed D and , this probability is expected to decrease with decreasing error ε, because the accuracy in the estimation of Pin increases in this case. Figure 7(b) suggests that for and ε ≤ 5 × 10−2, the scattering matrix of a clone should differ from the one of the key in a small fraction of elements (smaller than 3% or so), in order for the clone to have a non-negligible probability to pass the verification test. Cloning of such a high quality is a formidable challenge for today’s technology, because it requires the exact positioning (on a nanometer scale) of millions of scatterers with the exact characteristics411. It is also worth noting here that according to the results of Figs 6 and 7(b), the robustness of the EAP against cloning appears to increase considerably with an increasing number of modes. This finding suggests that if the protocol is realized using existing wavefront shaping set-ups, which have been shown capable of controlling thousands of modes, then the probability for a clone with to pass the verification test will be at most 10−3.


Continuous-variable quantum authentication of physical unclonable keys
Typical response of D–close clones (coloured symbols) relative to the response of the true key (star).The responses of 500 random D–close clones is shown in phase-space representation for various values of D (1–5%), and two different numbers of modes. The responses of the clones move away from the response of the true key, as we increase D. Also shown are the mean value (black cross) and the standard deviation (dashed circle) of the responses of the 500 random D-close clones, for each D. Parameters are as in Fig. 5.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5385567&req=5

f6: Typical response of D–close clones (coloured symbols) relative to the response of the true key (star).The responses of 500 random D–close clones is shown in phase-space representation for various values of D (1–5%), and two different numbers of modes. The responses of the clones move away from the response of the true key, as we increase D. Also shown are the mean value (black cross) and the standard deviation (dashed circle) of the responses of the 500 random D-close clones, for each D. Parameters are as in Fig. 5.
Mentions: The typical response of D–close clones relative to the response of the true key is shown in Fig. 6. We see that for values of , the response of D–close clones lies very close to the response of the true key. In this case, one may expect high probability for a clone to result in a probability pin very close to Pin. As D increases, however, the responses of the clones move rapidly away from the response of the true key, and pin is also expected to move away from Pin. This behaviour is clearly shown in the probability distributions of Fig. 7(a). As a result, the probability for a D–close clone to pass the verification test, i.e., to result in an estimate pin such that , decreases rapidly with increasing D [see Fig. 7(b)]. Note that for fixed D and , this probability is expected to decrease with decreasing error ε, because the accuracy in the estimation of Pin increases in this case. Figure 7(b) suggests that for and ε ≤ 5 × 10−2, the scattering matrix of a clone should differ from the one of the key in a small fraction of elements (smaller than 3% or so), in order for the clone to have a non-negligible probability to pass the verification test. Cloning of such a high quality is a formidable challenge for today’s technology, because it requires the exact positioning (on a nanometer scale) of millions of scatterers with the exact characteristics411. It is also worth noting here that according to the results of Figs 6 and 7(b), the robustness of the EAP against cloning appears to increase considerably with an increasing number of modes. This finding suggests that if the protocol is realized using existing wavefront shaping set-ups, which have been shown capable of controlling thousands of modes, then the probability for a clone with to pass the verification test will be at most 10−3.

View Article: PubMed Central - PubMed

ABSTRACT

We propose a scheme for authentication of physical keys that are materialized by optical multiple-scattering media. The authentication relies on the optical response of the key when probed by randomly selected coherent states of light, and the use of standard wavefront-shaping techniques that direct the scattered photons coherently to a specific target mode at the output. The quadratures of the electromagnetic field of the scattered light at the target mode are analysed using a homodyne detection scheme, and the acceptance or rejection of the key is decided upon the outcomes of the measurements. The proposed scheme can be implemented with current technology and offers collision resistance and robustness against key cloning.

No MeSH data available.


Related in: MedlinePlus