Double random phase encryption scheme to multiplex and simultaneous encode multiple images

Ayman Alfalou; Ali Mansour

doi:10.1364/AO.48.005933

Applied Optics
Vol. 48,
Issue 31,
pp. 5933-5947
(2009)
•https://doi.org/10.1364/AO.48.005933

Double random phase encryption scheme to multiplex and simultaneous encode multiple images

Ayman Alfalou and Ali Mansour

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Ayman Alfalou and Ali Mansour, "Double random phase encryption scheme to multiplex and simultaneous encode multiple images," Appl. Opt. 48, 5933-5947 (2009)

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Related Topics
Table of Contents Category
- Fourier Optics and Signal Processing
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fourier optics and signal processing (070.0070)
- Data processing by optical means (070.4560)
- Digital image processing (100.2000)
- Optical data processing (200.4560)

About this Article
History
- Original Manuscript: March 24, 2009
- Revised Manuscript: September 4, 2009
- Manuscript Accepted: September 18, 2009
- Published: October 22, 2009

Abstract

Here we present a new approach of multiplexing and simultaneous encoding of target images. Our approach can enhance the encryption level of a classical double random phase (DRP) encryption system by adding a supplementary security layer. The new approach can be divided into two security layers. The first layer is called the multiplexing level, which consists in using iterative Fourier transformations along with several encryption key images. These latter can be a set of biometric images. At the second layer, we use a classical DRP system. The two layers enable us to encode several target images (multi-encryption) and to reduce, at the same time, the requested decoded information (transmitted or storage information).

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First target image	Second target image	Third target image	Key image

Convergence between $I_{1}$ and $I_{2}$	Convergence between $I_{2}$ and $I_{3}$	Convergence between $I_{3}$ and $I_{4}$

Multiplexed and encrypted image

$\begin{matrix} MSE = 1.738 \times 10^{- 5} \end{matrix}$	$MSE = 4.6182 \times 10^{- 4}$	$\begin{matrix} MSE = 9.3561 \times 10^{- 4} \end{matrix}$

Multi-Encryption	Required Information to Decrypt “4” Target Images	Quantity Expressed in K Bytes	MSE Between the Target and Decrypted Images
Approaches using a classical DRP system	$I_{c 1} e^{i (φ_{c 1})}, \dots, I_{c m} e^{i (φ_{c m})}, φ_{A 21}, φ_{A 22}, \dots, φ_{A 2 m}$	$1048, 5 + \dots + 1048, 5 + 524, 2 + \dots + 524, 2 = 621.1 KBytes$	0.0259
Approaches using a DRP system with two levels	$I_{c} e^{i (φ_{c})}, φ_{A 2}, φ_{A 2}, φ_{2}, \dots, φ_{m - 1}$	$1048, 57 + 524, 2 + \dots + 524, 288 = 3145.7 KBytes$	0.0264

Phase Bits Number	Compression Ratio ( $C_{R}$ )
Phase Bits Number	Compression Ratio ( $C_{R}$ )	Image $I_{0}$ (1)	Image $I_{0}$ (2)
64		$\begin{matrix} {MSE}_{1} = 8.82 \times 10^{- 5} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 6.54 \times 10^{- 4} \end{matrix}$
16		$\begin{matrix} {MSE}_{1} = 1.64 \times 10^{- 4} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 5.82 \times 10^{- 4} \end{matrix}$
8	$C_{R} = 0 %$
8	$C_{R} = 0 %$	$\begin{matrix} {MSE}_{1} = 5.74 \times 10^{- 4} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 4.48 \times 10^{- 3} \end{matrix}$
7	$C_{R} = 12.5 %$	$\begin{matrix} {MSE}_{1} = 1.11 \times 10^{- 3} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 7.31 \times 10^{- 3} \end{matrix}$
6	$C_{R} = 25 %$	$\begin{matrix} {MSE}_{1} = 6.62 \times 10^{- 3} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 2.21 \times 10^{- 2} \end{matrix}$
5	$C_{R} = 37.5 %$
5	$C_{R} = 37.5 %$	$\begin{matrix} {MSE}_{1} = 3.80 \times 10^{- 2} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 3.68 \times 10^{- 2} \end{matrix}$
4	$C_{R} = 50 %$	$\begin{matrix} {MSE}_{1} = 8.11 \times 10^{- 2} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 5.91 \times 10^{- 2} \end{matrix}$
3	$C_{R} = 62.5 %$	$\begin{matrix} {MSE}_{1} = 1.11 \times 10^{- 1} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 9.64 \times 10^{- 2} \end{matrix}$
2	$C_{R} = 75 %$
2	$C_{R} = 75 %$	$\begin{matrix} {MSE}_{1} = 1.25 \times 10^{- 1} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 1.34 \times 10^{- 1} \end{matrix}$
1	$C_{R} = 87.5 %$	$\begin{matrix} {MSE}_{1} = 4.94 \times 10^{- 1} \end{matrix}$	$\begin{matrix} {MSE}_{2} = 1.41 \times 10^{- 1} \end{matrix}$


First target image	Second target image	Third target image	Key image

Convergence between $I_{1}$ and $I_{2}$	Convergence between $I_{2}$ and $I_{3}$	Convergence between $I_{3}$ and $I_{4}$

Multiplexed and encrypted image

$\begin{matrix} MSE = 1.738 \times 10^{- 5} \end{matrix}$	$MSE = 4.6182 \times 10^{- 4}$	$\begin{matrix} MSE = 9.3561 \times 10^{- 4} \end{matrix}$

Multi-Encryption	Required Information to Decrypt “4” Target Images	Quantity Expressed in K Bytes	MSE Between the Target and Decrypted Images
Approaches using a classical DRP system	$I_{c 1} e^{i (φ_{c 1})}, \dots, I_{c m} e^{i (φ_{c m})}, φ_{A 21}, φ_{A 22}, \dots, φ_{A 2 m}$	$1048, 5 + \dots + 1048, 5 + 524, 2 + \dots + 524, 2 = 621.1 KBytes$	0.0259
Approaches using a DRP system with two levels	$I_{c} e^{i (φ_{c})}, φ_{A 2}, φ_{A 2}, φ_{2}, \dots, φ_{m - 1}$	$1048, 57 + 524, 2 + \dots + 524, 288 = 3145.7 KBytes$	0.0264

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