Fig. 4: Encryption strength.

Colormaps of the likelihood, or probability, of (a) true positive (\({p}_{{{\rm{TP}}}}\)), (b) false positive (\({p}_{{{\rm{FP}}}}\)), and (c) detectivity (\(D={p}_{{{\rm{TP}}}}-{p}_{{{\rm{FP}}}}\)) as a function of \({\sigma }_{{{\rm{G}}}}\) for \(P\)= 50 encoders. d Corresponding population means. True positive (TP) is an event when a bright pixel in the encoded image corresponds to a bright pixel in the original image, and false positive (FP) is an event when a bright pixel in the encoded image corresponds to a dark pixel in the original image. e The number of brute force trials (BFTs) by the eavesdropper necessary to identify the letter ‘N’ as a function of \({\sigma }_{{{\rm{G}}}}\). Note that BFT = \(1/{D}^{S}\), where \(S\) = 8 × 8 = 64 is the size of the image. f The average energy expenditure for the encryption process as a function of \({\sigma }_{{{\rm{G}}}}\). g A deep neural network (DNN) trained to recognize the MNIST data set for digit classification. The training and testing sets consisted of 60,000 and 10,000 images, respectively. h Representative MNIST images with white Gaussian noise (WGN) of different standard deviations (\(\sigma\)) binarized at a threshold of 1.5, mimicking our MoS₂ memtransistor-based encryption process. i Average inference accuracy for 10,000 encrypted images as a function of \(\sigma\) and the number of hidden layers (\({N}_{{{\rm{Layer}}}}\)). Irrespective of \(\sigma\), the inference accuracy remains low, indicating the robustness of our bio-inspired encryption to trained DNNs.