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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this paper, a double-random phase-encoding technique-based text encryption and hiding method is proposed. First, the secret text is transformed into a 2-dimensional array and the higher bits of the elements in the transformed array are used to store the bit stream of the secret text, while the lower bits are filled with specific values. Then, the transformed array is encoded with double-random phase-encoding technique. Finally, the encoded array is superimposed on an expanded host image to obtain the image embedded with hidden data. The performance of the proposed technique, including the hiding capacity, the recovery accuracy of the secret text, and the quality of the image embedded with hidden data, is tested via analytical modeling and test data stream. Experimental results show that the secret text can be recovered either accurately or almost accurately, while maintaining the quality of the host image embedded with hidden data by properly selecting the method of transforming the secret text into an array and the superimposition coefficient. By using optical information processing techniques, the proposed method has been found to significantly improve the security of text information transmission, while ensuring hiding capacity at a prescribed level.

In information security, cryptography, which encrypts the secret message before transmission to avoid information disclosure, is commonly used [

For cryptography, the encrypted secret message,

The traditional information hiding methods usually use digital methods to hide the secret message in the spatial domain [

The existing DRPE-based information hiding methods are usually used for image hiding [

The rest of this paper is organized as follows: in Section 2, the proposed method is introduced. Section 3 incorporates the theoretical performance analysis of the proposed method, including the hiding capacity, the recovery accuracy of the secret text, and the quality of the image embedded with hidden data. Section 4 includes the results and discussions obtained from the numerical simulation experiments. Section 5 presents the concluding remarks.

In this Section, the proposed text encryption and hiding method based on DRPE technique is introduced. The main symbols used in this paper are listed in

The encoding and hiding procedure used in this paper is shown in the block diagram of

In the encoding and hiding procedure, at first, the secret text is transformed into a 2-dimensional array. Then, the transformed array is encoded with the DRPE technique and the encoded array is used to construct the hidden data array. Finally, the hidden data array is hidden into the expanded host image with superimposition. The detailed steps involved in this process are described as follows:

Step 1: Transform the secret text into a 2-dimensional array.

In this step, the secret text is transformed into a 2-dimentional array in the form of an image to encode with the DRPE technique. To transform the secret text

Step 2: Encode the transformed array with the DRPE technique.

In this step, the transformed array is encoded by using the DRPE technique [_{1} with a size of ^{-1}_{1} is defined as:
_{1}_{R}_{1}_{I}_{1}, respectively. Both of these arrays are with size of

Step 3: Construct the hidden data array.

To hide the encoded complex-valued array into the host image, in this step, the hidden data array is constructed from _{1}. There are various ways to construct the hidden data array, which may result in different hiding capacities [_{1}, _{1}_{R}_{1}, _{1}_{I}_{1}_{R}_{1}_{I}_{1}_{R}_{1}_{I}_{1}_{R}_{1}_{I}_{1}_{R}_{1}_{I}

Step 4: Expand the host image.

In this step, the original host image is expanded to hide the hidden data array, which is constructed using the above mentioned procedure. The original host image _{1}_{1}_{1} with a size of 2_{1}_{1}_{1}–1, and y = 0,1,2,…, _{1}–1, respectively. According to the procedure of reference [_{1}, a total of MN pixels are needed (_{1} = _{1} = _{1} _{1} pixels are enough to hide _{1}, where ⌈ ● ⌉ denotes the ceiling operation.

Step 5: Hide the constructed hidden data array into the expanded host image.

In this step, the constructed hidden data array is hidden into the expanded host image _{1} by superimposing each 2 × 2 subarray in the hidden data array into the corresponding 2 × 2 subarray in _{1} by processing one pixel at a time as shown below:

As mentioned in Step 4, _{1}, the image embedded with hidden data _{2} is obtained.

The extraction and recovery procedure for the proposed technique is shown in

To recover the secret text from image _{2}, which is embedded with the hidden data, first, the hidden data array is extracted from _{2} to reconstruct the encoded array _{1}′. Then, _{1}′ is decrypted by using the DRPE technique to obtain the decrypted array

Step 1: Extract the hidden data array from the image embedded with the hidden data.

Depending on whether the hidden data array is constructed with the procedure of reference [_{2} using _{2} using

Step 2: Reconstruct the encoded array.

The data extracted in Step 1 corresponds to the real part or the imaginary part of the complex array encoded with the DRPE technique. With the extracted data, a 2-dimensional complex array _{1}′ with a size of _{1}. Due to computational errors, _{1}′ and _{1} may have slight variations.

Step 3: Decrypt the reconstructed array _{1}′.

By decrypting the reconstructed 2-dimensional complex array _{1}′ with the DRPE technique, an array

Due to computational errors,

Step 4: Recover the secret text.

In this step, the secret text

In this Section, the performance of the proposed method is investigated by using three criteria,

The hiding capacity is defined as the number of the bytes of the secret text _{2}. The hiding capacity is directly related to the number of the higher bits of the elements in the transformed array

In this paper, the DRPE technique is used to encrypt and hide the desired secret text. The main objective is to accurately recover the hidden secret text. Assume that each character in the secret text is represented by one byte. To assess the secret text recovery result, the recovered secret text

The recovery accuracy of the secret text is related to the following parameters:

The number of higher bits of the elements in the transformed array

The method used to fill the lower bits of the elements in the transformed array

The value of the superimposition coefficient α. As discussed in references [

The quality of the image embedded with hidden data _{2} is directly related to the value of the superimposition coefficient α. The less the value of α is, the higher the quality of _{2}. To trade off the recovery accuracy of the secret text and the quality of _{2}, the value of α must be considered carefully.

To evaluate the performance of the proposed method, a simulation software was developed for experimentation with real life data. In the experiments, five images each with a size of 256 × 256 pixels were used as the host images as shown in

If ^{8 –} ^{m}

From the experimental results shown in ^{7 – m}. Our experimentation with other host images generated similar results. The reason for such results may be explained as follows: (1) Due to computational errors existing during the procedure of encoding, embedding, extraction and decryption of DRPE based information hiding, slight difference may exist between the decrypted array ^{7 – m}, the higher bits of decrypted value will be invariant compared to those of the original value with the maximum possible, either the decrypted value is greater than or less than the original one. For example, when ^{7 – m}.

From ^{7 – m} to maximize the recovery accuracies of the secret text

With greater value of

The experimental results corresponding to the recovery accuracies with different values of α by using Lena as the host image are shown in

The experimental results corresponding to the qualities of the images embedded with hidden data may be determined by using the peak-signal-noise-ratio (PSNR) as a performance parameter.

From

Based on the above mentioned results, we can infer the following:

To increase the hiding capacity, the value of

To increase the recovery accuracy, the value of

Whatever the value of ^{7 – m} to obtain higher recovery accuracy;

To increase the quality of the image embedded with hidden data, the value of α should be lower.

Thus, to increase the hiding capacity, the value of ^{7 – m}, the recovery accuracy will be 100%. Therefore, to increase the quality of the image embedded with hidden data, for

To demonstrate the above analysis and conclusions more clearly, some images obtained in the simulation experiments are shown below. Here, we show the arrays transformed from the secret text with, the images embedded with hidden data and the recovered transformed arrays. The arrays encoded with the DRPE technique are random resulting from the characteristics of the DRPE technique [^{7 – m} are shown from

The main purpose of this paper is to apply the DRPE-based image hiding method to text encryption and hiding. In this technique, the secret text is transformed to a 2-dimensional array by storing the text bit stream in the higher bits of the transformed array. The transformed array can be viewed as an image. The DRPE-based image hiding technique is used to encode and hide the transformed array to an expanded host image.

Detailed analytical and experimental results show that: (1) the greater number (^{7 – m} results in the best recovery accuracy. By adjusting the values of

The proposed method combines the optical information processing technique by applying optical information hiding method to text encryption and hiding, which increases the security of the secret text and takes use of the advantages of optical information processing technique. In addition, it ensures acceptable hiding capacity and recovery accuracy of the secret text.

This work was supported by National Natural Science Foundation of China (No. 60972105), Natural Science Foundation Project of CQ CSTC (No. 2009BB2210)

Encoding and hiding procedure.

Extraction and recovery procedure.

Images used for simulation experiments (

Recovery accuracies of the secret text with different methods being used to fill the lower bits of the elements in the transformed array

Recovery accuracies of the secret text

The qualities of the images embedded with hidden data with different values of α by using Lena as the host image.

(

(

(

(

Symbols used in the paper.

2-dimentional array transformed from | |

Secret key for DRPE encoding | |

_{1} |
Array obtained by encoding |

Original host image | |

_{1} |
Expanded host image |

_{2} |
Image embedded with hidden data by embedding _{1} into _{1} |

α | Superimposition coefficient |

_{1}′ |
Array extracted from _{2} |

Array decrypted from _{1} with the DRPE technique | |

Recovered secret text |

Recovery accuracies of the secret text ^{7 – m}.

Value of m | m = 1 | |||

Value of lower bits | 64 | |||

Value of α | α = 0.02 | α = 0.05 | ||

Host image | Lena | average | Lena | average |

Recovery accuracy (%) | 100 | 100 | 100 | 100 |

Value of m | m = 2 | |||

Value of lower bits | 32 | |||

Value of α | α = 0.02 | α = 0.05 | ||

Host image | Lena | average | Lena | Average |

Recovery accuracy (%) | 91.6687 | 91.5759 | 100 | 100 |

Value of m | m = 3 | |||

Value of lower bits | 16 | |||

Value of α | α = 0.05 | α = 0.08 | ||

Host image | Lena | average | Lena | Average |

Recovery accuracy (%) | 98.697917 | 98.2568 | 100 | 99.6997 |

Value of m | m = 4 | |||

Value of lower bits | 8 | |||

Value of α | α = 0.08 | α = 0.10 | ||

Host image | Lena | average | Lena | Average |

Recovery accuracy (%) | 94.8029 | 91.7242 | 98.8617 | 94.6265 |