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Cryptographic frameworks depend on key sharing for ensuring security of data. While the keys in cryptographic frameworks must be correctly reproducible and not unequivocally connected to the identity of a user, in biometric frameworks this is different. Joining cryptography techniques with biometrics can solve these issues. We present a biometric authentication method based on the discrete logarithm problem and Bose-Chaudhuri-Hocquenghem (BCH) codes, perform its security analysis, and demonstrate its security characteristics. We evaluate a biometric cryptosystem using our own dataset of electroencephalography (EEG) data collected from 42 subjects. The experimental results show that the described biometric user authentication system is effective, achieving an Equal Error Rate (ERR) of 0.024.

Brain computer interface (BCI) is a highly growing field of research with application in healthcare systems (from fall prevention to neuronal rehabilitation) to educational, self-regulation, production, marketing, and security as well as games and entertainment. BCI aims to provide a channel of communication that does not depend on the usual use of peripheral nerves and muscles [

Recently, BCI applications for biometrics have attracted increased attention from the researchers. Biometrics provides means for identifying people based on their physiological characteristics [

The EEG-based subject identification is relatively new. The advantages of using EEG for biometrics are its low exposability (cannot be casually obtained or stolen by external observers) and resistance to forced extraction because under-stress brain activity changes [

The suitability of using EEG for privacy and security applications can be attributed to morphological, anatomical, and functional plasticity (behaviour-related lasting changes in functional connections) traits [

The difficulties related to using EEG data are its instability over time (the EEG permanence problem [

Here we propose a secure EEG-based cryptographic authentication scheme based on the commitment scheme adopted from [

Cognitive biometrics [

Liang et al. [

Hema et al. [

Mu and Hu [

Zúquete et al. [

Chuang et al. [

Dan et al. [

Delpozo-Banos et al. [

Abo-Zahhad et al. [

Crobe et al. [

Several studies presented the fusion of EEG with other modalities to get a multimodal biometric system such as in [

First, we provide definitions required for understating of the biometric authentication method as given in [

Let

Given a prime number

A block code

Let

Given code set

Error correction threshold

Let

Let

The method, proposed by [

Let

(

(

(

(

(

First we define the commitment function

Commitment protocol

for any

To set the system parameters, Trent executes the following procedure.

(1)

(2)

(3)

(4)

Let

A commitment protocol

The hiding property of the biometrical scheme describes the resilience of the system against adversarial attempts performed by impostor

The binding property represents the resistance of the system against adversarial attempts by an impostor

For hiding and binding, we have two different adversaries [

the

the

A commitment protocol satisfies the hiding security property if no adversary exists such that the probability of winning the hiding game is (significantly) better than a blind guess [

Let

(1) The adversary U is given the output of Setup procedure and asked to choose two messages.

(2) The game randomly selects one of them and calls Commit procedure to compute its commitment.

(3) The adversary U is asked to guess which one of the two messages the commitment corresponds to.

(4) The game outputs 1 if the guess of the adversary U is correct.

A commitment protocol satisfies the binding security property if no adversary exists such that the probability of winning the binding game is higher than negligible [

Let

(1) The adversary B is given the output of Setup procedure and asked to bind two messages to the same commitment value.

(2) The game outputs 1 if the two messages differ and the commitment is valid for both the messages, that is, if both can be verified by calling the Open procedure.

Here we present the biometric cryptosystem using the EEG signals. Its implementation consists of the system initialization stage, the enrolment stage, and the authentication stage as represented in Figure

EEG-based user identification/authentication framework.

At the start of enrolment (see Algorithm

Next, we compute

And perform normalization of

The result is a matrix that contains binary codeword of 400 bit length (obtained from 20 × 20 covariance matrix). The procedure is summarized in Algorithm

(

(

(

(

(

(

(

(

At the same time, a random cryptographic key

Authentication phase is described in Algorithm

(

(

(

(

(

The biometric scheme is summarized in Figure

Summary of the proposed EEG biometric scheme.

The implementation of the proposed scheme was made in MATLAB 8.6.0.267246 (R2015b) on an Intel (R) Core (TM) i5-4590 CPU (x64), running at 3.30 GHz with 12 GB of RAM in Windows 10 Enterprise ver. 1709. For the performance evaluation, we have used a dataset that consists of 65 EEG samples from 42 different subjects, where each sample consisted of 1000 signal values. The number of subjects satisfies the condition of Lazar et al. [^{−1}.

Electrode locations for collection of EEG data.

To perform code matching, we computed the Hamming distance between two EEG codewords

The intraperson Hamming distances have been computed using EEG samples from the same subjects, while the interperson Hamming distances were computed using samples from different subjects. We carried out 65 comparisons for the same subjects and 118,335 comparisons between different subjects. The result of the probability distribution function (pdf) of the intraperson and interperson Hamming distances is shown in Figure

Probability density functions Hamming distances between the same person and the different persons.

We use the following scenarios as suggested by Gui et al. [

The aim is to identify correctly each of the 42 subjects participating in the study. The training and testing datasets include data from all 42 subjects and the classification outcome belongs to one of 42 classes.

The aim is to identify one subject versus all other 41 subjects. There are only two classes: positive (target subject) and negative (all other subjects). The training dataset was combined using the data from all subjects and the performing resampling so that both classes are balanced.

The performance is evaluated using the correct classification rate (CCR) as follows:

EER is defined as a unique point where FRR is equal to FAR. A lower EER indicates a more accurate system.

This ensures that the threshold found will satisfy the equality condition between FRR and FAR as closely as possible.

We have implemented both Scenarios

Subject-wise correct classification rate.

Note that while the overall accuracy is quite good (mean accuracy 0.895), for some of the subjects, it was quite low (e.g., only 0.446 for subject 15). This result may have been caused by the infamous BCI illiteracy effect [

Cumulative distribution plot of accuracy distribution in subject classification.

As accuracy data is not normally distributed, the Fisher

The subject-wise confusion matrix is presented in Figures

Subject-wise confusion matrix of classification results in Scenario

Subject-wise confusion matrix of classification results in Scenario

For Scenario

Confusion matrix of classification results in Scenario

The values for FAR, FRR, and ERR are represented in Figure

FAR and FRR of the proposed EEG biometric system.

The Area Under Curve (AUC) is calculated as the area under the Receiver Operating Characteristic (ROC) [

We have achieved the following results, which are summarized in Table

Summary of classification results.

TAR | FRR | ERR | AUC | TPR |
---|---|---|---|---|

0.8952 | 0.026 | 0.024 | 0.9271 | 0.9974 |

Comparison of the proposed method with the Fladby’s method [

EER (proposed method + our dataset) | EER (Fladby method + Fladby dataset) | EER (Fladby method + our dataset) |
---|---|---|

0.024 | 0.2142 | 0.3059 (mean, all channels) |

0.2945 (Fp1) | ||

0.2283 (best, P4) |

Comparison of EER of our method and Fladby’s method [

Based on the presented comparison, we can claim that the proposed method achieved better results for subject authentication than the Fladby [

This paper presents a secure cryptographic authentication scheme for EEG-based biometrics based on the fuzzy commitment scheme and the error-correcting Bose-Chaudhuri-Hocquenghem (BCH) codes. The EEG features are derived from the covariance matrix of EEG data from different EEG channels in the 10–20 international system. The biometric system was evaluated using the EEG dataset obtained from 42 subjects. The experimental results show that the system can generate up to 400 bits of cryptographic key from the EEG codes, while tolerating up to 87 bits of error. The performance of the biometric cryptosystem is an Equal Error Rate (EER) of 0.024, True Positive Rate (TPR) of 0.9974, and Area Under Curve (AUC) of 0.927.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The authors would like to acknowledge the support from the Rector pro-quality Grant no. 09/010/RGJ18/0034 at the Silesian University of Technology. The authors would also like to thank professor A. Vainoras of Lithuanian University of Health Sciences for kindly provided EEG dataset.