CN102664727A - Virtual optical encryption method based on chaotic mapping - Google Patents

Abstract

The invention discloses a virtual optical encryption method based on chaotic mapping and belongs to the field of information security technology and non-mathematical encryption and decryption technology. Random templates of key parameters are generated through spatial-temporal chaotic mapping, system security is enhanced and an information encryption method based on a virtual optical system is formed. Aiming at the most important problem in a virtual optical encryption system, namely, generation of the random templates, the method is based on the spatial-temporal chaotic mapping and the random templates with fine statistical performance are generated. Combining the random templates with other key parameters in the virtual optical encryption system, an encrypted ciphertext is obtained by calculating discrete Fresnel transform of a plaintext and the random templates and discretion of complex amplitude transmittance function of a lens. A decrypted plaintext is obtained by calculating reverse Fresnel transform.

Description

A kind of virtual optics encryption method based on chaotic maps

Technical field

The present invention relates to a kind of virtual optics encryption method, belong to field of information security technology based on the space-time chaos mapping.

Background technology

Traditional cipher mechanism all is based on mathematical theory; And be to utilize optical imaging concept based on the virtual optics encryption mechanism of optical imaging system; Adopt the computer programing method to realize the optical encryption process; As key, realize the data encryption and the Information hiding of High Security Level with the geometric parameter of propagation law in the two-phonon process and structure.Because the particularity of optical imaging system; Light wave is a kind of information carrier of multidimensional; Have multiple attributes such as amplitude, phase place, wavelength, polarization, the adding of key element such as random mask in the virtual optics encryption system simultaneously makes its key space more broad; But and have the characteristic of parallel computation, for information encryption provides new means.But compare with encryption system based on mathematical theory; The Fundamentals of Mathematics of virtual optics encryption system lack systematic Study; Characteristic and generation, key management, enciphering and deciphering algorithm like safety analysis, key space are analyzed or the like, and the foundation of these Fundamentals of Mathematics will make the real trend of virtual optics encryption system improve and use.

Summary of the invention

Technical problem to be solved by this invention is the generation problem according to random mask key in the virtual optics encryption system, makes up the random mask that statistical nature is good, forms key space and encryption method in the virtual optics encryption system.

The present invention adopts following technical scheme for solving the problems of the technologies described above:

A kind of virtual optics encryption method based on chaotic maps specifically may further comprise the steps:

Random mask (U in step 1, the generation key parameter _m) as one of encryption key parameters, specific as follows:

To selected parameter (init, w, α), produce a two dimension, size is equal to the space-time chaos sequence U of information plane to be encrypted _m:

$\left\{\begin{array}{c}{x}_0^i=f_{\mathrm{Logistic}}(\mathrm{init},w)\\ x_{n+1}^i=(1-\mathrm{\ϵ})f_{\mathrm{Tent}}(x_n^i,\mathrm{\α})+\frac{\mathrm{\ϵ}}{2}[f_{\mathrm{Tent}}(x_n^{i-1},\mathrm{\α})+f_{\mathrm{Tent}}(x_n^{i+1},\mathrm{\α})]\end{array}\right.$

Wherein, f _LogisticExpression Logistic chaotic maps is used to produce the system drive sequence, i.e. the initial value of 0 each grid of the moment; Init, w are respectively initial value and the Control Parameter that chaos drives the Logistic mapping; f _TentExpression tent chaotic maps is system's local state EVOLUTION EQUATION; Represent i grid at n state constantly, i=1,2 ..., M, M are the line number of information plane matrix to be encrypted, n=1, and 2 ..., N, N are information plane matrix column number to be encrypted; α is the Control Parameter of tent mapping;

Logistic chaotic maps function is: x _N+1=wx _n(1-x _n), x _n∈ [0,1], w ∈ [0,4].

Step 2, calculating discrete fresnel transform expressly:

By key parameter (d ₀, λ) calculate information plane U ₀Discrete fresnel transform DFD [U to the lens front surface ₀(k, l), λ, d ₀]:

$U_1(m,n)=\mathrm{DFD}[U_0(k,l),\mathrm{\λ},d_0]$

$=\frac{1}{\mathrm{j\λ}{d}_0}\exp \left(j\frac{2\mathrm{\π}{d}_0}{\mathrm{\λ}}\right)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}{d}_0}(m^2{\mathrm{\Δ\ϵ}}^2+n^2{\mathrm{\Δ\η}}^2)\right]\×$

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{U}_0(k,l)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}{d}_0}(k^2{\mathrm{\Δx}}^2+l^2{\mathrm{\Δy}}^2)\right]\×\exp [-j2\mathrm{\π}(\frac{\mathrm{mk}}{N}+\frac{\mathrm{nl}}{N})]$

Wherein, j is a plural number, and Δ ε, Δ η are respectively the sampling step length of lens front surface complex amplitude on x direction and y direction; Δ x, Δ y are respectively the sampling step length of lens information plane complex amplitude on x direction and y direction; D0 is the distance of information plane to the imaging len front surface, and λ is a wavelength, step-length subscript k, and l, m, n=0,1 ..., N-1;

By key parameter (λ f), adopts same discrete processes method that the complex amplitude transmittance function t of lens is carried out discrete calculation, obtains its discrete form:

$t(m,n,\mathrm{\λ},f)=\mathrm{Exp}[-j\frac{\mathrm{\π}}{\mathrm{\λ\; f}}(m^2{\mathrm{\Δ\; \ϵ}}^2+n^2{\mathrm{\Δ\; \η}}^2)],$ Wherein f is the focal length of lens.

Step 3: calculate random mask (U _m) discrete fresnel transform:

(d λ) calculates two-dimensional random template (U by key parameter _m) to the discrete fresnel transform DFD [U of lens front surface _m, λ, d]:

$U_2(m,n)=\mathrm{DFD}[U_m(k,l),\mathrm{\λ},d]$

$=\frac{1}{\mathrm{j\λ}d}\exp \left(j\frac{2\mathrm{\π}d}{\mathrm{\λ}}\right)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}d}(m^2{\mathrm{\Δ\ϵ}}^2+n^2{\mathrm{\Δ\η}}^2)\right]\×$

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{U}_m(k,l)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}d}(k^2{\mathrm{\Δx}}^2+l^2{\mathrm{\Δy}}^2)\right]\×\exp [-j2\mathrm{\π}(\frac{\mathrm{mk}}{N}+\frac{\mathrm{nl}}{N})]$

Wherein, d represents two-dimension time-space chaos sequence U _mTo the distance of lens front surface, j is a plural number.

Step 4: calculate ciphertext U _c:

According to discrete fresnel transform and random mask (U expressly _m) discrete fresnel transform, and the discrete transform of complex amplitude transmittance function t calculates ciphertext U _c:

U _c＝{DFD[U ₀(k，l)，λ，d ₀]+DFD[U _m(k，l)，λ，d]}×t(m，n，λ，f)。

Step 5: calculate expressly U ₀:

Decrypting process is the inverse operation process of above-mentioned ciphering process, that is:

DFD[U ₀(k，l)，λ，d ₀]＝U _c/t(m，n，λ，f)-DFD[U _m(k，l)，λ，d]；

U ₀＝IDFD[U ₀(k，l)，λ，d ₀]。

The present invention adopts above technical scheme compared with prior art, has following technique effect:

But the present invention designs the random mask generation method in a kind of applying virtual optical encryption system; Shine upon based on space-time chaos; Generate the good key parameter of statistic property, thereby constituted the higher virtual optics encryption system of fail safe, can be applied to the encryption of information.Be characterized in that the random mask statistic property that generates is good, the virtual encryption system of formation is safe, is easy to realize.

Description of drawings

Fig. 1 is the sketch map of virtual optics encryption system.

Fig. 2 is based on the sketch map of the virtual optics encryption system of space-time chaos mapping.

Fig. 3 is the realization calculation process of method.

Fig. 4 is the plaintext two-dimension code in the embodiment.

Fig. 5 is the random mask that generates in the embodiment.

Fig. 6 is the encryption ciphertext that generates in the embodiment.

Fig. 7 is the plaintext that reduces in the embodiment.

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is done further detailed description:

As shown in Figure 1, be a virtual optics encryption system, wherein information plane U ₀Be expressly, be the ciphertext U after encrypting as the plane _c, λ is a wavelength, f is the focal length of lens, d ₀Be the distance of information plane to the imaging len front surface, d _iBe the distance that the picture plane is arrived on the surface behind the lens, d d ₁+ d ₂, d ₁Be the distance of random mask to optical splitter, d ₂Be the distance of lens to optical splitter, d represents the distance of two-dimension time-space chaos sequence to the lens front surface; Key is Θ=(U _m, d ₀, d, λ, f), U wherein _mBe random mask, will generate by following method.

To selected parameter (init, w, α), produce a two dimension, size is equal to the space-time chaos sequence U of information plane to be encrypted _m:

$\left\{\begin{array}{c}{x}_0^i=f_{\mathrm{Logistic}}(\mathrm{init},w)\\ x_{n+1}^i=(1-\mathrm{\ϵ})f_{\mathrm{Tent}}(x_n^i,\mathrm{\α})+\frac{\mathrm{\ϵ}}{2}[f_{\mathrm{Tent}}(x_n^{i-1},\mathrm{\α})+f_{\mathrm{Tent}}(x_n^{i+1},\mathrm{\α})]\end{array}\right.;$

Wherein, f _LogisticExpression Logistic chaotic maps is used to produce the system drive sequence, i.e. the initial value of 0 each grid of the moment; Init, w are respectively initial value and the Control Parameter that chaos drives the Logistic mapping; f _TentExpression tent chaotic maps is system's local state EVOLUTION EQUATION;

Represent i grid at n state constantly, i=1,2 ..., M, M are the line number of information plane matrix to be encrypted, n=1, and 2 ..., N, N are information plane matrix column number to be encrypted; α is the Control Parameter of tent mapping;

Wherein, Logistic chaotic maps function is: x _N+1=wx _n(1-x _n), x _n∈ [0,1], w ∈ [0,4].

As shown in Figure 2, adopt the space-time chaos system to produce two space-time chaos sequences, and as random mask.

As shown in Figure 3; The cleartext information of selecting for use to be encrypted is the two-dimension code (hits N=256) of 256 * 256 * 1bit; Chaos drives the initial value init=0.5706 of Logistic mapping, Control Parameter w=4, tent mapping parameters α=0.001; The two-dimension time-space chaos sequence to the lens front surface apart from d=0.01m, information plane to the lens front surface apart from d ₀=0.1m, wavelength 2=623 * 10 ^-9M, focal length of lens f=0.025m.Expressly as shown in Figure 4.

According to above parameter, generate random mask, as shown in Figure 5.

Calculate discrete fresnel transform expressly: by key parameter (d ₀, λ) calculate information plane U ₀Discrete fresnel transform DFD [U to the lens front surface ₀(k, l), λ, d ₀]:

$U_1(m,n)=\mathrm{DFD}[U_0(k,l),\mathrm{\λ},d_0]$

$=\frac{1}{\mathrm{j\λ}{d}_0}\exp \left(j\frac{2\mathrm{\π}{d}_0}{\mathrm{\λ}}\right)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}{d}_0}(m^2{\mathrm{\Δ\ϵ}}^2+n^2{\mathrm{\Δ\η}}^2)\right]\×$

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{U}_0(k,l)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}{d}_0}(k^2{\mathrm{\Δx}}^2+l^2{\mathrm{\Δy}}^2)\right]\×\exp [-j2\mathrm{\π}(\frac{\mathrm{mk}}{N}+\frac{\mathrm{nl}}{N})]$

Wherein, j is a plural number, and Δ ε, Δ η are respectively the sampling step length of lens front surface complex amplitude on x direction and y direction; Δ x, Δ y are respectively the sampling step length of lens information plane complex amplitude on x direction and y direction; d ₀Be the distance of information plane to the imaging len front surface, λ is a wavelength, step-length subscript k, and l, m, n=0,1 ..., N-1.

By key parameter (λ f), adopts same discrete processes method that the complex amplitude transmittance function t of lens is carried out discrete calculation, obtains its discrete form:

$t(m,n,\mathrm{\λ},f)=\mathrm{Exp}[-j\frac{\mathrm{\π}}{\mathrm{\λ\; f}}(m^2{\mathrm{\Δ\; \ϵ}}^2+n^2{\mathrm{\Δ\; \η}}^2)],$ Wherein f is the focal length of lens.

Calculate random mask (U _m) discrete fresnel transform: (d λ) calculates two-dimensional random template (U by key parameter _m) to the discrete fresnel transform DFD [U of lens front surface _m, λ, d]:

$U_2(m,n)=\mathrm{DFD}[U_m(k,l),\mathrm{\λ},d]$

$=\frac{1}{\mathrm{j\λ}d}\exp \left(j\frac{2\mathrm{\π}d}{\mathrm{\λ}}\right)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}d}(m^2{\mathrm{\Δ\ϵ}}^2+n^2{\mathrm{\Δ\η}}^2)\right]\×$

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{U}_m(k,l)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}d}(k^2{\mathrm{\Δx}}^2+l^2{\mathrm{\Δy}}^2)\right]\×\exp [-j2\mathrm{\π}(\frac{\mathrm{mk}}{N}+\frac{\mathrm{nl}}{N})]$

Wherein, d represents two-dimension time-space chaos sequence U _mTo the distance of lens front surface, j is a plural number.

According to formula U _c={ DFD [U ₀(k, l), λ, d ₀]+DFD [U _m(k, l), λ, d] } * (λ f) calculates ciphertext to t, and is as shown in Figure 6 for m, n.

According to formula DFD [U ₀(k, l), λ, d ₀]=U _c/ t (m, n, λ, f)-DFD [U _m(k, l), λ, d] calculate expressly, obtain original image information, as shown in Figure 7.

The content that does not specify among the present invention and explain is the known method in this area, and those of ordinary skills' content disclosed according to the present invention can realize fully.

Claims (1)

1. virtual optics encryption method based on chaotic maps is characterized in that this method may further comprise the steps:

Random mask (U in step 1, the generation key parameter _m) as one of encryption key parameters, specific as follows:

To selected parameter (init, w, α), produce a two dimension, size is equal to the space-time chaos sequence U of information plane to be encrypted _m:

$\left\{\begin{array}{c}{x}_0^i=f_{\mathrm{Logistic}}(\mathrm{init},w)\\ x_{n+1}^i=(1-\mathrm{\ϵ})f_{\mathrm{Tent}}(x_n^i,\mathrm{\α})+\frac{\mathrm{\ϵ}}{2}[f_{\mathrm{Tent}}(x_n^{i-1},\mathrm{\α})+f_{\mathrm{Tent}}(x_n^{i+1},\mathrm{\α})]\end{array}\right.$

Wherein, f _LogisticExpression Logistic chaotic maps is used to produce the system drive sequence, i.e. the initial value of 0 each grid of the moment; Init, w are respectively initial value and the Control Parameter that chaos drives the Logistic mapping; f _TentExpression tent chaotic maps is system's local state EVOLUTION EQUATION;

Represent i grid at n state constantly, i=1,2 ..., M, M are the line number of information plane matrix to be encrypted, n=1, and 2 ..., N, N are information plane matrix column number to be encrypted; α is the Control Parameter of tent mapping;

Logistic chaotic maps function is: x _N+1=wx _n(1-x _n), x _n∈ [0,1], w ∈ [0,4];

Step 2, calculating discrete fresnel transform expressly:

By key parameter (d ₀, λ) calculate information plane U ₀Discrete fresnel transform DFD [U to the lens front surface ₀(k, l), λ, d ₀]:

$U_1(m,n)=\mathrm{DFD}[U_0(k,l),\mathrm{\λ},d_0]$

$=\frac{1}{\mathrm{j\λ}{d}_0}\exp \left(j\frac{2\mathrm{\π}{d}_0}{\mathrm{\λ}}\right)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}{d}_0}(m^2{\mathrm{\Δ\ϵ}}^2+n^2{\mathrm{\Δ\η}}^2)\right]\×$

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{U}_0(k,l)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}{d}_0}(k^2{\mathrm{\Δx}}^2+l^2{\mathrm{\Δy}}^2)\right]\×\exp [-j2\mathrm{\π}(\frac{\mathrm{mk}}{N}+\frac{\mathrm{nl}}{N})]$

Wherein, j is a plural number, and Δ ε, Δ η are respectively the sampling step length of lens front surface complex amplitude on x direction and y direction; Δ x, Δ y are respectively the sampling step length of lens information plane complex amplitude on x direction and y direction; d ₀Be the distance of information plane to the imaging len front surface, λ is a wavelength, step-length subscript k, and l, m, n=0,1 ..., N-1;

By key parameter (λ f), adopts same discrete processes method that the complex amplitude transmittance function t of lens is carried out discrete calculation, obtains its discrete form:

$t(m,n,\mathrm{\λ},f)=\mathrm{Exp}[-j\frac{\mathrm{\π}}{\mathrm{\λ\; f}}(m^2{\mathrm{\Δ\; \ϵ}}^2+n^2{\mathrm{\Δ\; \η}}^2)],$ Wherein f is the focal length of lens;

Step 3: calculate random mask (U _m) discrete fresnel transform:

(d λ) calculates two-dimensional random template (U by key parameter _m) to the discrete fresnel transform DFD [U of lens front surface _m, λ, d]:

$U_2(m,n)=\mathrm{DFD}[U_m(k,l),\mathrm{\λ},d]$

$=\frac{1}{\mathrm{j\λ}d}\exp \left(j\frac{2\mathrm{\π}d}{\mathrm{\λ}}\right)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}d}(m^2{\mathrm{\Δ\ϵ}}^2+n^2{\mathrm{\Δ\η}}^2)\right]\×$

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{U}_m(k,l)\exp \left[j\frac{\mathrm{\π}}{\mathrm{\λ}d}(k^2{\mathrm{\Δx}}^2+l^2{\mathrm{\Δy}}^2)\right]\×\exp [-j2\mathrm{\π}(\frac{\mathrm{mk}}{N}+\frac{\mathrm{nl}}{N})]$

Wherein, d represents two-dimension time-space chaos sequence U _mTo the distance of lens front surface, j is a plural number;

Step 4: calculate ciphertext U _c:

According to discrete fresnel transform and random mask (U expressly _m) discrete fresnel transform, and the discrete transform of complex amplitude transmittance function t calculates ciphertext U _c:

U _c＝{DFD[U ₀(k，l)，λ，d ₀]+DFD[U _m(k，l)，λ，d]}×t(m，n，λ，f)；

Step 5: calculate expressly U ₀:

Decrypting process is the inverse operation process of above-mentioned ciphering process, that is:

DFD[U ₀(k，l)，λ，d ₀]＝U _c/t(m，n，λ，f)-DFD[U _m(k，l)，λ，d]；

U ₀＝IDFD[U ₀(k，l)，λ，d ₀]。

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