Research Article - Biomedical Research (2018) Volume 29, Issue 19

## Quantum-assisted CR directed encrypted biomedical signal transmission using knight's tour

**Revathy K ^{*} and Thenmozhi K**

School of Electrical and Electronics Engineering, SASTRA University, Thanjavur, India

- *Corresponding Author:
- Revathy K

School of Electrical and Electronics Engineering

SASTRA University, India

**Accepted on** December 21, 2017

### Abstract

Exchange of biomedical data through the internet has achieved tremendous success in the recent past, with the necessity of security in every transmission. It has become indispensable to replenish secrecy in biomedical data by avoiding the access of illegitimate users. To evade such disclosure of medical data, a proposal of encryption system along with Cognitive Radio (CR) has been employed. In this paper, CR has been programmed to choose the non-availability of the primary user and by automatically detecting the presence of available spectrum in the channel using Universal Software Radio Peripheral (USRP). Then using the identified free spectrum, encrypted medical data has been transmitted and exchanged between the authenticated users in rural healthcare units. The proposed encryption technique initiates Latin Square Image Cipher (LSIC) which offers double encryption by making use of two different random keys. Then the output has been subjected to a quantum computation encryption method in which Quantum Walks (QW) serves as a key generator which is meant for its natural nonlinear chaotic behaviour. QW is followed up by the disintegration of Knight’s tour permutation process which helps in tamper proofing and authentication. Finally, shear based affine transform has been employed to avoid imperfections in the medical data. The proposed scheme curtails the insecure medical image communication in biomedical research by creating an authenticated communication link among peers. Metrics such as Number of Pixel Changing Rate (NPCR), Unified Average Changing Intensity (UACI), correlation coefficients, chi-square tests, global and local entropies were estimated and compared with the available literature results.

## Keywords

Image encryption, CR, LSIC, Knights tour, Quantum walk.

## Introduction

The importance of image encryption has grown widely during the past decades. The primary reason is to prevent the issue of the critical information being disclosed to the unauthorized users [1-3]. Due to these reasons, many encryption techniques have been introduced. Many of those techniques are easy to implement when the data that are being transmitted through internet which is not only in text but also images, audio data and video file are easily hacked [4,5]. To overcome such drawback technique should be designed in such a way that information is highly secured and algorithm must be efficient. Anyhow image data requires more security as to how much extensively they are used. For example, in the military it is essential to protect image data, video conferencing, etc. illegal access has extensively increased with the improvement of computer processor processing power and storage [6-10]. Nowadays internet has become the fastest mode of transmission of more critical and high volume data. Since the internet has become the dominant source for transmission of information, it is highly prone to many attacks. To protect data from unauthorised sources, many techniques have been used such as watermarking, masking data, and encryption. Mostly encryption assures security for data that has been passed through public channels.

Medical image encryption has increased drastically during the past decades. The motivation of medical image encryption is to increase the robustness of patient data which contributed to the development of digital Imaging in Communication and Medicine (DICOM) in 1993. The primary reason for medical image encryption is to provide confidentiality and authentication to patient information [11-13].

LSIC technique is the one where no pixels will be present in more than a rows or column. It helps in providing confusion and diffusion of the pixels to the more significant extent [14-16]. It employs two different random keys to encrypt the image. The concept of LSIC resembles Sudoku principle.

Knight’s tour is an algorithm which has the base of chess model [17,18]. This algorithm provides diffusion to the image pixels, since no pixel can revisit a position more than once. There are several possibilities for the sequences. Hence it is not so easy to be detected or prone to attacks.

With the advancement of quantum computation, quantum image processing has increased drastically in the recent period [19-23]. This is because of the quantum key distribution which provides secured way of information transmission. They have also promoted a new way approach for both image encryption and processing. The affine transform is a technique used for avoiding the imperfections of the image while performing some processes over them. When the image is subjected to an affine transform, they are sheared from their original position.

Cognitive radio is the one, which automatically programs itself to adapt its parameters according to the network range and users demand. It promotes a licensed channel for accessing the spectrum. The CR user will be observing the absence of a primary user and will make use of the band [24-26].

Now-a-days wireless communication has been used in electronic health (e-health) care for transferring the medical information. The medical information can be transmitted by using the wireless technologies such as WiFi, Bluetooth, Zigbee. A wireless network can be created for transferring the data using standard such as 802.11 and 802.22 in communication medium [27-30]. The Electronic health care unit utilizes both the licensed and unlicensed band for accessing the wireless network. This leads to EMI effects on the operating equipment and insufficient medical band [31-36]. The medical devices can be protected from the harmful interference. This can be achieved by modifying the transmit power of the wireless device. The biomedical devices can also be protected by implementing a wireless healthcare service which uses priority scheme for medical and non-medical devices.

This paper proposes a CR based procedure for identifying the unused spectrum using USRP, then using the available spectrum, the encrypted quantum key generated biomedical data were transmitted between legitimate users in rural health care units. Section 2 proposes the methodology used, section 3 provides the results and discussion part, and finally, conclusions are drawn in section 4.

**Methodology**

*Cognitive radio technology*

One of the efficient energy detectors has been used to detect the presence of the primary user. Here the resultant signal of the bandpass filter has been converted to digital form to calculate the threshold value. The transformed bits are used to detect the presence of the primary user. The outcome of transformed bits is known as chi-square distribution. Chisquare distribution is given through Gaussian distribution form

Where n is the number of the samples, σ_{n} ^{2}, σ_{s} ^{2} are the
variances of the noise and received signal s (t) respectively;
threshold λ can be calculated as

where t_{s} is the observation time, and K is the bandwidth of the
spectrum, the minimum sampling rate should be 2K from the
Nyquist sampling theorem, so n can be represented as 2t_{s}K. By
analysing the signal spectrum using the RX1 antenna in the NI
USRP with the bandwidth limit of 88 MHz to 100 MHz and
gain of 20 dB, the presence of the primary user is detected at
98 MHz. Other than the primary user signal at 98 MHz, the
remaining spectrum is considered as spectrum holes. To
remove interference of primary user signals, a suitable
frequency is chosen, say 92 MHz.

*Encryption techniques*

**Latin square image cipher:** Latin square image cipher is a
permutation network. It is an encryption technique where two
different random keys are used. A DICOM image of size 256 ×
256 has been used. LSIC provides substitution and
permutation. The objective of LSIC is to provide excellent
resistance to attacks, more keyspace, highly sensitive,
confusion and diffusion properties. Usage of two different keys
provides good key sensitivity. The size of two different keys
used here is 256 × 256.

**Quantum computation: **Quantum walks based robust
encryption algorithm has been used to generate secret key
using quantum walks [19,20]. Quantum based image
encryption has paved its way for merging image encryption
and quantum computation which provides more advantages
such more protection to the data from being accessed by the
unauthorised users. Quantum based encryption is performed
using the following formula from [19,20].

Here C_{i} refers to cipher image where i=1, 2, 3….M × N, K_{i} refers to key, V_{i} refers to pixels.

**Permutation: **Image scrambling process is done using knight’s
tour mapping. It has originated from chess game in which
knight’s tour has been traced. A knight can travel throughout
the board only in L shape. This technique provides more
security. Since the pixels cannot get back to the location, if it
has visited once. It provides beautiful scrambling to the image.
So that pixel gets dislocated very far from their initial
positions. There are so many possibilities for the knight’s
sequence. For a 4 × 4 blocks, there are nearly 78 possible
sequences. Similarly, for 8 × 8 blocks, there are more than
1000 possible sequences can be performed for scrambling.
Knight’s sequence for 4 × 4 images can be calculated as

Here, d refers to the size of a block.

**Affine transformation: **The shear based affine transformation
has been used in the proposed scheme. The image is sheared
from (a, b) to (a’, b’). There are various types of affine
transformations such as geometric, scaling, reflection and
rotation. Affine transform performs the displacement of the
pixel position from one index to another index.

*System design*

The encryption segment and the spectral sensing unit have
been illustrated through the block diagram in **Figure 1**.

*Spectrum sensing procedure*

1. To make use of the spectrum, CR users have to observe the presence of the primary user in the channel.

2. If primary user is not accessing the channel, then the information is transmitted as bits through USRP transmitter at a frequency of F=92 M.

3. The bits are then manipulated using fast Fourier transform, integration and compared with the threshold to find the presence of the primary user.

where H_{0} refers to the presence of a user

H1 refers to the absence of user

u (t) denotes signal waveform

n (t) denotes zero-mean AWGN

4. The probability of detection p_{d} and the probability of false
alarm p_{fa} can be expressed as

b. Here λ stands for threshold, p_{f} should be kept as low as
possible, and p_{d} should be kept as high as possible to prevent
underutilization of transmission opportunities.

**Encryption algorithm**

5. Read the DICOM images of size 256 × 256.

6. Get the input key 1 and key 2.

7. The LSIC of the input image is obtained using keys 1 and 2.

8. The image is XORed with key 1, and the resultant image is XORed with key 2.

9. Quantum computation encrypts the image, and the key for the quantum computation is calculated using the below equation

10. Multiply all the values in the resized matrix by 10^{8} modulo
256 to obtain the key; then the sequence can be denoted as
k={k_{1}, k_{2}...k_{m × n}} where m × n is the size of the original
image.

11. Convert the original image into one dimensional vector as
P={p_{1}, p_{2}...p_{m × m}}.

12. Then calculate the sum of the pixels as

13. Calculate ci using the equation from [2].

14. The encrypted image is subjected to permutation by disintegrating the image to 4 × 4 blocks using knight’s tour mapping.

15. Then finally affine transformation is taken for the resultant image.

16. The spatial affine transformation is applied using the matrix

17. Using the above matrix, the image is sheared from (a, b) to (a’, b’).

18. Combine the blocks to get the encrypted biomedical image.

Then using the sensed spectrum, the encrypted biomedical data was transmitted between the authenticated and legitimate users.

## Results and Discussions

In a wireless network the CR users check the availability of
primary user, if the user is not present at the search, then the
encrypted bits are transmitted through USRP transmitter.
Through analysing the spectrum by making use of RX1
antenna in USRP with the gain of 15 dB and the frequency
bandwidth of 88 MHz to 100 MHz is utilised as shown in **Figure 2a**. The primary user presence is detected at 92 MHz,
and other ranges of frequencies are considered to be spectrum
holes. The suitable range of frequency spectrum is selected to
be 98 MHz to remove interference from the primary user. **Figures 2a **and **2b** depicts the spectrum sensing block diagram
and the front panel respectively.

The **Figure 3** illustrates that the cipher image pixel elements
are converted to 16-bit binary information. This information is
modulated by QAM modulation and transmitted by TX1
antenna of NI USRP with the carrier frequency of 98 MHz. **Figure 3** also presents the block diagram and the front panel of
the transmitted data.

At the receiver antenna, RX1 of NI USRP is maintained at 98
MHz, the frequency at which the data was to be transmitted.
QAM then demodulates it and the 16-bit binary data is
retrieved back when the signal is received which is shown in the **Figure 4**. Figures 4a and 4b shows the block diagram of
reception of encrypted data.

In this section, CT and MRI images of size 256 × 256 and 512
× 512 were considered to evaluate the proposed encryption
scheme as shown in **Figures 5a-5e**.

*Statistical analysis of the proposed scheme*

Statistical analysis can be estimated for the proposed scheme to validate the robustness and the sternness towards various statistical attacks. Histogram analysis, correlation coefficient and chi-square tests are the various analysis involved in it.

Histogram analysis of the proposed scheme: The pictorial
representation of the pixel values of the original and the
encrypted image over the grey levels represents the histogram
analysis. **Figure 6a** represents the original test image and **Figures 6b** and **6c** represents the histogram of the original and
the encrypted images respectively. From the figures, it is
evident that, the pixel distribution is concentrated over the
grayscale region and it is flat and uniformly distributed over
the entire region for the encrypted image histogram.

**Chi-square test: **It is one of the statistical analyses to check
the strength of a proposed encryption algorithm in which a set
of expected and observed values are calculated. When the chisquare
value is below the theoretical table value, then the
pixels are uniformly encrypted. The chi-square parameter can
be measured as

Where u_{i} and v_{i} are the expected and observed values, i is the
number of a number of grey values. **Table 1**, provides the chisquare
estimation for various test images. From the table, it is
clear that the estimated chi-square values are below the
theoretical table value for the degrees of freedom of 255.
Hence the encrypted image pixels are uniformly distributed
over the entire grayscale region.

Test images | χ^{2} |
---|---|

Proposed image | 264.3569 |

MR-1 | 263.4587 |

CT-1 | 264.2542 |

MR-2 | 266.7245 |

CT-2 | 265.1254 |

**Table 1.** Histogram analysis based on Chi-Square test.

**Histogram deviation:** Histogram deviation can evaluate the
measure of deviation between the original and encrypted image
and the equation provides it

Where ci is absolute difference of ith pixel, M × N is the size of the proposed image.

**Irregular deviation: **It is used to measure, how much
deviation is provided by the encryption algorithm and it can be
analysed as

Where histogram deviation

**Deviation from ideality**: The measure of strength of
encryption algorithm in which how the algorithm decreases the
deviation of encrypted image and it can be calculated using the
equation

where A (C) is the histogram of the encrypted image.

In **Table 2**, the above-said metrics were estimated and
tabulated. From **Table 2**, irregular deviation and deviation from
ideality values are minimal, and the histogram deviation values
are very higher for the proposed scheme. This proves the
robustness of the proposed encryption algorithm.

Test images | Histogram deviation | Irregular deviation | Deviation from ideality |
---|---|---|---|

Proposed image | 2.2542e+003 | 2.2536 | 1.5224 |

MR- 1 | 2.5369e+003 | 2.4525 | 0.3566 |

CT- 1 | 3.7548e+003 | 2.7854 | 1.8547 |

MR-2 | 5.1253e+004 | 4.2542 | 4.2265 |

CT- 1 | 5.0552 e+004 | 4.4215 | 3.9954 |

**Table 2.** Evaluation metrics using histogram.

**Correlation analysis: **Correlation coefficient calculates the
quality of least square fitting of the data. Correlation values
should be very low for the encrypted image to resist various
statistical attacks. The correlation analysis values are tabulated
in **Table 3** which shows the correlation between the adjacent
pixels in horizontal, vertical and diagonal directions
respectively for all the test images.

Test image | Vertical correlation | Diagonal correlation | Horizontal correlation |
---|---|---|---|

Proposed image | -0.024 | 0.0038 | 0.0121 |

MR-1 | -0.652 | 0.0542 | 0.0452 |

CT-1 | 0.0659 | 0.0980 | 0.2512 |

CT-2 | 0.020 | 0.5641 | 0.0125 |

MR-2 | 0.007 | 0.2368 | 0.00354 |

**Table 3.** Correlation analysis of sample images.

Correlation coefficients can be estimated using the equation

where E (i)=Expected value of i, σ (i)=Standard deviation of i

**Figures 7a-7c **represents the pixel distribution of the original
test image, and F**igures 7d-7f** represents the pixel distribution
of the encrypted image in all three directions respectively.

From the figures for the original image, the pixels are more concentrated over a region, and it is uniformly distributed for the encrypted images which prove the robustness of the proposed scheme.

*Entropy analysis*

Entropy analysis or called as global Shannon entropy is used to evaluate the randomness of the proposed scheme and it is given by

where p (n_{i}) is the probability of appearance of the symbol n_{i}.
Global entropy sometimes fails to prove the randomness for
the image that has been encrypted partially. Local Shannon
entropy was introduced which overcomes the shortcomings in
Global Shannon entropy. It can be estimated by initially the
dividing the encrypted image into non-overlapping blocks and
measuring global entropy. **Table 4** provides the estimated the
local and global Shannon entropies. From the table, the entropy
values are closer to the theoretical value of 8, which confirms
the randomness of the proposed scheme.

Sample images | Entropy of the sample images | Encrypted image Global Shannon entropy | Encrypted image Local Shannon entropy |
---|---|---|---|

Proposed image | 3.3346 | 7.9955 | 7.7891 |

MR-1 | 2.7218 | 7.9904 | 7.5972 |

CT-1 | 3.1481 | 7.9518 | 7.7262 |

MR-2 | 2.6336 | 7.9943 | 7.5464 |

CT-2 | 2.9875 | 7.9998 | 7.6138 |

**Table 4.** Entropy analysis.

*Differential analysis*

To strengthen the proposed algorithm, differential analysis like NPCR and UACI were estimated. It can be measured between two encrypted images, one from the original image and the other can be estimated by changing the one-pixel value in the input image. The NPCR and UACI can be calculated as

Where a (u, v)=array of the same size as images D1 and D2

The NPCR and UACI for various test images are listed in **Tables 5** and **6** respectively which proves the stability of the
proposed system.

Test images | Reported value(s) |
---|---|

Proposed image | 99.595 |

MR-1 | 99.843 |

CT-1 | 99.451 |

MR-2 | 97.781 |

**Table 5.** NPCR analysis.

Test images | Theoretically UACI Critical value | |||
---|---|---|---|---|

U*-0.05=33.2824% U*-0.01=33.2255% U*-0.001=33.1594% U*+0.05=33.6447% U*-0.01=33.7016% U*-0.001=33.7677% | ||||

Image encryption methods | Reported value(s) | UACI test results | ||

0.05-level | 0.01-level | 0.001-level | ||

Proposed image | 33.62 | Pass | Pass | Pass |

MR-1 | 33.26 | Pass | Pass | Pass |

CT-1 | 33.69 | Fail | Pass | Pass |

MR-2 | 33.45 | Pass | Pass | Pass |

**Table 6.** UACI analysis of various test images.

From **Table 6**, the estimated UACI values for all the test
images except CT1 pass the theoretical, critical tests values
which evident the sternness of the proposed scheme.

*Key sensitivity*

A strong encryption algorithm requires an important property
of good key generation algorithm. As an overall efficiency of
the encryption algorithm key will be subjected to various test
performances. Key sensitivity shows the concept of creating a
slight change in the key, which in turn should not decrypt the
original image.** Figures 8a-8c** represents the decrypted image encrypted using wrong keys k_{1}-k_{3} respectively; **Figure 8d** illustrates the decrypted image using correct key.

*Cropping attack*

Cropping attack analysis can be estimated by intentionally crop
the encrypted image and passing on the decryption algorithm
to retrieve the original image. **Figures 9a-9c **shows the cropped
image by 3%, 5% and 10% respectively. **Figures 9d-9f** represent the decrypted images of (9a-9c) respectively. From the analysis even after cropping some important images could
be retrieved this shows the robustness of the encryption
algorithm.

*Noise attack*

Addition of noises to the encrypted image will also be added to
check the robustness of the proposed scheme. **Figures 10a-10c** represents the Gaussian noise with the range of 0.04, salt and
pepper noise with the range of 0.02, speckle noise with the
range of 0.04 have been added to the encrypted image
respectively.** Figures 10d-10f** shows the decrypted images of
10a-10c. From the figures, it is clear that the encryption
algorithm is resistant to all kinds’ attacks and provides security
to the encrypted medical data.

*Complexity analysis*

The complexity analysis depends on Quantum Computation
and LSIC techniques. The size of the key used in LSIC is 256
× 256, and it performs substitution-permutation operations for
8 iterations. This encrypted output is subjected to Knight’s
Tour mapping. The next process involved is the quantum
computation method of the key generation which provides less
computation time and provides high security to the data. It has
a key with the size of 256 × 256. Then finally affine transform
has been applied to produce the final encrypted output. Thus
the total complexity of the system is given as 2 × 256 × 2 ×
256 × 8 × 32 × 8 × 8 × 2^{2} × 256 × 2 × 2 × 10^{-4}.

*Performance analysis*

This section illustrates the performance comparison of the
proposed scheme with existing papers in the literature [8-13],
and it is tabulated in **Table 7**. The correlation analysis in
vertical, diagonal and horizontal coefficients, NPCR and
UACI, were compared and estimated. From the estimated
metrics, it is evident that the proposed scheme resist against
statistical and differential attacks.

Metrics | Proposed work | Ref. [8] | Ref. [9] | Ref. [10] | Ref. [11] | Ref. [12] | Ref. [13] |
---|---|---|---|---|---|---|---|

VC | -0.024 | -0.0385 | -0.0033 | 0.0018 | -0.0003 | 0.0056 | 0.0051 |

HC | 0.0121 | -0.0519 | 0.0037 | 0.0037 | 0.0012 | 0.0132 | -0.0125 |

DC | 0.0038 | 0.00046 | 0.0117 | -0.0017 | -0.0087 | -0.0006 | 0.00583 |

NPCR | 99.595 | 99.996 | 99.62 | 99.61 | 99.602 | 99.6077 | 99.54 |

UACI | 33.62 | 33.37 | 33.45 | 32.45 | 33.4682 | 33.4501 | 33.467 |

**Table 7.** Performance comparison of the proposed scheme.

From **Table 7**, it is clear that the correlation coefficients have
better results than the existing methods [8,9,11,12]. NPCR
values are comparable with [8-11] and have better results than
[13]. UACI value shows good analysis than [8-11]. The
computational complexity is estimated and found to be better
than the existing systems.

## Conclusion

The importance of protecting the biomedical data when it is transmitted through a public channel has become the limelight in the rural health care units. In this paper, CR networks were used to identify the unused spectrum; then quantum assisted encrypted biomedical images were transmitted and exchanged between authenticated users in healthcare units. Metrics like NPCR, UACI, correlation, entropies were estimated to prove the randomness of the proposed scheme.

## Acknowledgements

Authors would like to express their sincere thanks to SASTRA University, for the financial support under R&M fund (R&M/ 0027/SEEE-010/2012-13) to carry out this research work. Also, we are grateful to Dr S. Vanoli, Medical Superintendent, Government Hospital, Ariyalur, for his valuable suggestions in carrying out this work.

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