TWI746296B - Homomorphic multi-level visual image encryption system and method and its application - Google Patents

Abstract

The present invention discloses a homomorphic multi-level visual image encryption system and method and its application. The gray-level plaintext image is quantified to obtain a multi-level plaintext image, and the multi-level plaintext image is calculated through a cipher copy generation technology. The complex cipher image is then visually encrypted, so that the complex cipher image must be modulo arithmetic addition and modulo arithmetic multiplication at the same time to obtain a plaintext image, which is the complex cipher image and a set of keys respectively (P _i ) The formed congruence equations are sequentially homomorphically encrypted to obtain a complex homomorphic ciphertext image, and then the complex homomorphic ciphertext image is decrypted according to the Chinese remainder theorem to obtain a decrypted ciphertext image, It can be set by functions such as visual encryption and homomorphic encryption, so in addition to the image secret sharing function, it also has the double guarantee function of using the homomorphic password to further encrypt the result of the secret sharing, and the visual encryption and the same The method of state encryption can also sort the priority of secret sharing, thereby effectively improving the level of image secrets.

Description

Homomorphic multi-level visual image encryption system and method and its application

The present invention relates to a homomorphic multi-level visual image encryption system and method and its application, in particular to an image secret sharing function that can be set by visual encryption and homomorphic encryption, and can use homomorphic ciphers to encrypt secrets. The shared results are further encrypted with a homomorphic multi-level visual image encryption technology with dual guarantee functions.

Generally speaking, in the cloud era, cloud services are very important tasks. If the client's data can be kept confidential and transmitted to the server-side service is an important problem, this problem can be solved by mathematical methods. As far as we know, an important feature of homomorphic functions is that they can be mapped to another field for operation. When mapped back to the original field, the inverse homomorphic function can be used to return, so through homomorphic encryption (Homomorphic Encryption) The principle of, let the client's data achieve the purpose of confidentiality, and the client's encrypted data can also be calculated. On many occasions, such systems as cloud services and copyright sharing applications are needed. With the continuous advancement of technology, the computing of personal computers will gradually become lonely, replaced by various computing services on the cloud, such as Infrastructure as a Service, Platform as a Service, and Software as a Service. Service (Software as a Service) etc. And when we upload data to the cloud and prepare for computing, have we considered that our data may fall into a crisis of peeping on the service platform, so we plan to explore whether we can encrypt and protect the data before uploading it to cloud computing. Let the cloud use the encrypted data to calculate, and decrypt the returned result on the user side After that, you can get the same result as the unencrypted calculation data. If the design can not only keep the client's data confidential, but also allow the server to perform data computing services, this method can be called Homomorphic Encryption.

Furthermore, secret sharing is an encryption method in which multiple people share a plaintext. If you want to share a secret, you can use this method for encryption. There is a problem in the development of visual encryption, that is, when one of the shared secrets has collected the secrets of other shared secrets, the person can forge or alter the secrets if there is a complete secret, in order to improve. For this lack, the current practice is to perform another encryption on the secret shared secret; however, most encryption methods do not have the feature of ciphertext operation, so that the secret sharing wants to reply to the plaintext modulus addition cannot be satisfied. Calculations, resulting in inconvenience and troubles in use. Therefore, how to develop a set of functions that can combine visual encryption and homomorphic encryption to have image secret sharing and the result of using homomorphic passwords to share secrets. The homomorphic multi-level visual image encryption technology with encryption function has actually become a technical issue that the industry in the related technical field urgently wants to challenge and solve.

In view of this, none of the above-mentioned conventional image encryption technologies is perfect, and there is still a need for improvement. Moreover, based on the urgent needs of related industries, the inventor relies on years of practical experience in training equipment design and related expertise. Knowledge, through continuous efforts in research and development, finally developed an invention that is different from the above-mentioned conventional technology and the previously disclosed patent.

The main purpose of the present invention is to provide a homomorphic multi-level visual image encryption system and method and its application, which are mainly set by visual encryption and homomorphic encryption, etc., so that in addition to the image secret sharing function, it also has the use of The homomorphic password further encrypts the result of secret sharing, and the double guarantee function, and the visual encryption and homomorphic encryption methods can also sort the priority of secret sharing, thereby effectively improving the level of image secret. The technical means to achieve the main purpose of the invention is to quantify the gray-scale plaintext image to obtain a multi-level plaintext image, and calculate the multi-level plaintext image through the cipher generation technology to obtain a complex cipher image, and then combine the complex cipher image For visual encryption, the complex cipher image must be combined and multiplied by modular arithmetic at the same time to obtain a plaintext image. The congruence equation formed by _{the complex cipher image and a set of keys (P i) is based on} The sequence is homomorphic encryption to obtain a complex homomorphic ciphertext image, and then the complex homomorphic ciphertext image is decrypted according to the Chinese remainder theorem to obtain a decrypted ciphertext image.

FIG. 1 is a schematic diagram of a multi-level image error dispersion block diagram of the present invention.

FIG. 2 is a schematic diagram of the implementation of graphics conversion for generating multi-level images of the present invention.

Figure 3 is a schematic diagram of the implementation of the multi-level image visual encryption of the present invention.

Figure 4 is a schematic diagram of the implementation of the homomorphic multi-level image visual encryption of the present invention.

Figure 5 is a schematic diagram of the process implementation of the homomorphic cipher encryption method of the present invention.

Figure 6 is a schematic diagram of block control implementation of homomorphic cipher encryption according to the present invention.

Figure 7 is a schematic diagram of block control implementation of homomorphic encryption decryption according to the present invention.

FIG. 8 is a schematic diagram of the implementation of the visual encryption calculation packet structure of the present invention.

Fig. 9 is a schematic diagram of the implementation of the post-sequence calculation of the packet header of the present invention.

In order to allow your reviewer to further understand the overall technical features of the present invention and the technical means to achieve the purpose of the invention, specific examples and drawings are used to describe in detail as follows:

Please refer to Figs. 1~4. In order to achieve the main purpose of the invention, the specific embodiment includes the following steps:

The multi-level image generation step is to obtain a multi-level plain text image after quantizing the gray-level plain text image.

In the visual encryption step, the multi-level plaintext image is calculated by a cipher generation technology to obtain a complex cipher image, and the complex cipher image is visually encrypted, so that the complex cipher image must be subjected to modular operation addition and modular operation multiplication at the same time The plaintext image can be obtained.

In the homomorphic encryption step, the congruence equations formed by the complex cipher image and a set of keys (P _i ) are respectively homomorphically encrypted in sequence to obtain the complex homomorphic ciphertext image.

In the homomorphic decryption step, the complex number homomorphic ciphertext image is decrypted according to the Chinese remainder theorem to obtain the decrypted ciphertext image, and then substituted into the visual encryption step, so that the complex ciphertext image must be subjected to modular addition and modular operation at the same time Multiply together to get the restored plaintext image.

In the embodiment shown in FIG. 1 of the present invention, in the step of generating the multi-level image, the plain text image is _{quantized with a multi-level threshold (t i} ) to obtain a multi-level plain text image, and the plain text image is subtracted from the multi-level plain text image. The error dispersion value e _{x, y} is obtained from the plaintext image, and then the error dispersion value e _{x, y is} substituted into an error filtering technique for filtering processing, so that the filtering result is added to the plaintext image to perform a multi-level critical value (t _i ) Quantization process to get the next multi-level plaintext image, and then repeat the above steps until the last multi-level plaintext image is obtained.

In a specific embodiment, the first cipher text image generated by the cipher text generation technique is randomly generated from the p- order multi-value image in the Z _p field, and the first one after the self-defined addition and multiplication modulus is calculated. The cipher text image is the second cipher text image, and then the inverse element of the second cipher text image and the plaintext image are modulated to generate the last cipher text image.

The congruence equation is as follows:

Wherein, let S densely present image is an integer ring (Ring) algebraic structure, and P _i key and the same state ciphertext image R _i is an algebraic structure of a body (Field) and defines the encryption method is the use of S and P _i two The congruence equation formed by the above is the encrypted output result, and P _i is a prime number and satisfies GCD ( P _i , P _j )=1.

Please refer to the embodiment shown in FIG. 8. In the visual encryption step, the modular multiplication and the modular addition operations are stored in the secret location of the multi-level plaintext image in the form of packets.

The present invention applies the above-mentioned homomorphic multi-level visual image encryption method to an embodiment of superimposed images. In the multi-level image generation step, the at least one gray-level plaintext image includes a first gray-level plaintext image and a second gray-level plaintext image. The first multi-level plaintext image and the second multi-level plaintext image that are superimposed into a display image are obtained after quantization processing respectively; in the visual encryption step, the first multi-level plaintext image is respectively obtained And the second multi-level plaintext image are calculated through the cipher generation technology to obtain a plurality of first cipher images and a plurality of second cipher images, and the plurality of first cipher images and the plural second cipher images are respectively A visual encryption process, the visual encryption process makes the plural first cipher image and the plural second cipher image correspondingly perform modular operation addition and modular operation multiplication to obtain the first multi-level plaintext Image and the second multi-level plaintext image; in the homomorphic encryption step, the plural first cipher images and the plural second cipher images are respectively formed by using a first set of keys and a second set of keys The congruence equations sequentially perform homomorphic encryption to obtain plural first homomorphic ciphertext images and plural second homomorphic ciphertext images respectively, so that the plural first homomorphic ciphertext images and the plural second homomorphic ciphertext images are obtained The image is decrypted by the Chinese remainder theorem to obtain the decrypted plural first cipher image and the plural first Cipher image; among them, a first user who is authorized to only share the first multi-level plaintext image can only be able to see the first multi-level plaintext image in the displayed image; and authorized to share A second user who reaches the first multi-level plaintext image and the second multi-level plaintext image can simultaneously see the superimposed first multi-level plaintext image and the second multi-level plaintext image in the displayed image. Level plaintext image.

In an application embodiment of the present invention, it includes a server-side unit (such as a server) and at least one terminal unit (such as a computer). The server-side unit and the terminal unit are connected through a communication network signal, and the multi-level The image generation step, the visual encryption step, and the homomorphic decryption step are executed in the terminal unit, and the homomorphic encryption step is executed in the server end unit.

The present invention proposes a visual encryption method applied to multi-tone images, which not only has the function of secret sharing, but also has the double guarantee of further encrypting the result of secret sharing by using a homomorphic cipher. In addition, the resultant visual encryption and homomorphic encryption methods can also sort the priority of secret sharing, so that the level of secrets can be achieved. The present invention uses a homomorphic encryption method with ciphertext operable characteristics to encrypt the ciphertext, so that it has a confidential function and can perform modular addition and multiplication operations. In this way, using the combined method of homomorphic encryption under visual encryption to operate on multi-valued images is called homomorphic multi-valued image visual encryption. In addition, in addition to the above functions, the present invention also adds visual encryption generation methods that can use addition and multiplication modes. The function of calculating the secret book.

Generally speaking, the error diffusion method to construct a second-order image has been proposed. Here, the present invention improves the traditional second-order error diffusion method to form a multiple-tone image generation method as follows: Let g _{x, y} and h _{x, y} is a gray-scale image and a multi-level image representation, and h _{x, y} is a multi-level image obtained by quantizing g _{x, y.} The quantization error e _{x,y is} expressed as e _x,y = g _x,y - h _x,y . The multi-level area h _{x, y is} divided into the following formula:

The above-mentioned multi-level image critical value is the error dispersion value e _x,y generated from the original gray-level image. The present invention shows the above-mentioned multi-level image generation method as shown in FIG. 1. Specifically, the error filtering block in FIG. 1 is performed by the following filtering method:

g _{x,y +1} = g _{x,y +1} +(7/16)× e _x,y

g _{x +1, y} = g _{x +1, y} +(5/16)× e _x,y

g _{x +1, y -1} = g _{x +1, y -1} +(3/16)× e _x,y

g _{x +1, y +1} = g _{x +1, y +1} +(1/16)× e _x,y

Figure 2 shows a schematic diagram of the 3-level image generation pattern. As for the above method, any n- order image can be generated, but in the present invention, n = p and p is a prime number. When actually generating multi-level images, we use multi-level numerical indexing. For example, the current critical value of a third-level image is { t ₁ =0, t ₂ =127, t ₃ =255} which actually represents the index in the image The value is:

t ₁ →1

t ₂ →2

t ₃ →3

Furthermore, the visual encryption method is an encryption method that combines multiple ciphers to generate a plaintext, as shown in FIG. 3. In the embodiment of FIG. 3, it is an example of visual encryption of three ciphers. The user S ₁ and the user S ₂ need to be added first and then multiplied by the user S ₃ to obtain the plaintext image G. A major feature of visual encryption is that it can be secretly shared. Suppose there are three secret books S ₁ , S ₂ and S ₃ . The three ciphers need to be decrypted at the same time to obtain the plaintext G. The principle of generating the multi-level image ciphers of the three S ₁ , S ₂ and S ₃ is to use a set of modular multiplication and modular addition operations in Z _p . This set of operations can determine the order of operations and also the order of returning the plaintext. As shown in Figure 3, the ciphertext S ₁ and S ₂ need to be added by modulo operation and then multiplied by the modulo operation of the cipher text to obtain the plaintext G. If there are N cipher book users, the technical process of cipher book generation is as follows:

1. Generate N-1 random ciphers of p- order multi-value images in the Z _{p field (randomly generated).}

2 Turn the N-1 ciphertexts after N-2 self-defined addition and multiplication modulus operations into W, and then find the value of W The inverse element and the plaintext are modulo arithmetic to produce the final Nth ciphertext image.

In addition, homomorphic encryption itself has the characteristic of ciphertext operability, so the present invention utilizes the effect of visual encryption and the homomorphic encryption is applied to multi-level images, which we call homomorphic multi-level image visual encryption. The homomorphic multi-level image visual encryption has the properties of secret sharing and ciphertext operation. After the above two multi-order feature allows the visual image can be encrypted via a modulo multiplication and modulo addition operation can be obtained after a visual encrypted ciphertext H, can decrypt this ciphertext to the ciphertext back to the plaintext H G via inverse homomorphic, This encoding process is shown in Figure 4. Using this feature, it can be applied to cloud computing services and rights sharing... and other occasions. The following will introduce the characteristics of homomorphic functions:

A common homomorphic function is modular operation, as shown in Figure 5. Let S is an integer ring (Ring) algebraic structure, and P _i and R _i is an algebraic structure body (Field), we define the congruence equation encryption method using both M and P _i formed is encrypted output As a result, the following equation is a congruence equation:

The plaintext S is the input, and the output r = [ r ₁ r ₂ L r _l ]'ciphertext is obtained through a set of keys {P ₁ , P ₂ , L, P _{l }.} Therefore, the encryption steps are as follows:

1. Convert the image into a multi-value image and use visual encryption to generate the encrypted copy S.

2. Use { P ₁ , P ₂ ,L, P _l } and S to generate r =[ r ₁ r ₂ L r _l ]'.

When the server-side unit performs the data computing service of the terminal unit, and then returns the encrypted data after the operation to the terminal unit (ie, the client), the client then divides the decryption process into the following steps, namely When the secret sharing terminal wants to reply in plaintext, its decryption process is divided into the following steps:

(a) The sum of key products is Q=P ₁ P ₂ L P _l ;

(b) does not comprise the product of the sum of P _i Q _i = Q / P _i;

(c) The opposite element of Q _i is I _i =[ Q _i ] ^-1 mod P _i ;

。 (d) The final output is

.

The above process is shown in Figure 7. Finally, the present invention is the encryption effect generated by the first-stage visual encryption combined with the second-stage homomorphic encryption. In the first stage of visual encryption, a feature of the present invention is that it can perform modular addition and modular multiplication operations. Therefore, the calculation process needs to inform the participants who want to secretly share to obtain the secret copy synthesized by the secret sharer. The calculation process of this modular addition and modular multiplication will be stored in the secret location of the multi-value image in the form of a packet. The packet format is shown in Figure 8. As for the method of generating the packet header as a post-order operation, it is shown in Figure 9. Shown.

Secondly, the above is the proposed principle of homomorphic encryption and decryption. However, in practice, the key distribution and selection issues need to be considered. In addition, there is also the issue of how to make the server-end unit aware of the calculation algorithm of the server-end unit. These three issues are explained below. Solve a large polynomial of any order over F _q:

N ( x ) = P ₁ ( x ) P ₂ ( x ) L P _k ( x )

n。其中上述多項式彼此兩兩GCD(P _i (x),P _j (x))=1。上述將N(x)分解成k個原式多項式。現在如果選擇鑰匙數目為n=2,3,L,k，我們可以提供

把鑰匙。 Where k

n . Among them, the above polynomials are paired with each other GCD ( P _i ( x ) , P _j ( x ))=1. The above decomposes N ( x ) into k primitive polynomials. Now if the number of keys is selected as n = 2, 3, L, k , we can provide

Put the key.

The above (1) only provides the number of keys for the homomorphic password, but not all keys are suitable for use. The reason is that the actual plaintext data may not allow the key to perform modular operations, making its own plaintext unable to be encrypted into The issue of ciphertext. This problem can be improved by using the appropriate selection key. Therefore, we rank k keys from small to large as follows:

deg( P ₁ ( x ))>deg( P ₂ ( x ))>L>deg( P _k ( x ))

The selection of key questions The present invention selects a pair of keys with a large order and a key with a small order, which can improve the shortcomings that the small plaintext cannot be encrypted. Therefore, the above-mentioned key is designed as follows:

The above are only feasible embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent implementation of other changes based on the content, characteristics and spirit of the following claims shall be It is included in the scope of the patent of the present invention. The structural features of the invention specifically defined in the claim are not found in similar articles, and are practical and progressive. They have already met the requirements of a patent for invention. The application is filed in accordance with the law. I would like to request that the Bureau of Junction approve the patent in accordance with the law to protect this The legitimate rights and interests of the applicant.

Claims (8)

A homomorphic multi-level visual image encryption method, which includes the following steps: a multi-level image generation step, at least one gray-level plaintext image is quantized to obtain at least one multi-level plaintext image; a visual encryption step, the at least one multi-level plaintext image is obtained The plaintext image is calculated by a cipher copy generation technology to obtain a complex cipher image, and the complex cipher image is subjected to a visual encryption process. The at least one multi-level plaintext image can be obtained by multiplying operations; and the homomorphic encryption step, respectively, using _{the congruence equations formed by at least one set of keys (P i} ) to perform homomorphic encryption in sequence to the complex cipher image, to Obtain a complex homomorphic ciphertext image, and decrypt the complex homomorphic ciphertext image using the Chinese remainder theorem to obtain the decrypted complex ciphertext image; wherein, in the multi-level image generation step, the at least one The gray-scale plaintext image is quantized by a multi-level threshold (t _i ) to obtain the at least one multi-level plaintext image, and the at least one gray-level plaintext image is subtracted from the at least one multi-level plaintext image to obtain the error dispersion value e _{x, y} , and then substitute the error dispersion value e _{x, y} into an error filtering technique for filtering processing, adding the filtering processing result to the plaintext image and performing multi-level critical value (t _i ) quantization processing to obtain the following Repeat the above steps for a multi-level plaintext image until the last multi-level plaintext image is obtained. The homomorphic multi-level visual image encryption method according to claim 1, wherein, in the multi-level image generation step, the multi-level image generation method is set g _{x, y} and h _{x, y} as the at least one The gray-scale image and the at least one multi-level image, and h _x,y is the at least one multi-level image obtained after g _x,y is quantized; a quantization error e _{x,y is} expressed as: e _x,y = g _x,y - h _x,y ; at least one multi-level image h _{x,y is} divided into the following:

The homomorphic multi-level visual image encryption method according to claim 1, wherein the cipher generation technology is to generate the first cipher image that is randomly generated by the p- order multi-value image in the Z _{p field, and} The first cipher image after the custom addition and multiplication modulus is the second cipher image, and then the inverse element of the second cipher image and the plaintext image are modulated to produce the last cipher image . The homomorphic multi-level visual image encryption method described in claim 1, wherein the congruence equation is as follows:

Wherein, let S densely present image is an integer ring (Ring) algebraic structure, and P _i key and the same state ciphertext image R _i is an algebraic structure of a body (Field) and defines the encryption method is the use of S and P _i two The congruence equation formed by the above is the encrypted output result, and P _i is a prime number and satisfies GCD ( P _i , P _j )=1. The homomorphic multi-level visual image encryption method described in claim 4, wherein the following decryption steps are included when the Chinese remainder theorem is executed: (a) The sum of key products is Q = P ₁ P ₂ L P _l ; b) does not comprise the product of the sum of P _i Q _i = Q / P _i; counter-element (c) Q _i is the ^{_{I i = [Q i] -1}} mod P i; and (d) the output of the last

. The homomorphic multi-level visual image encryption method according to claim 1, wherein, in the visual encryption step, the modular operation addition and the modular operation multiplication operation process are stored in the multi-level plaintext image in the form of a packet In the secret location. The homomorphic multi-level visual image encryption method according to claim 1, which further includes providing a server-end unit, at least one terminal unit, and a communication network; the server-end unit and the at least one terminal unit pass through the communication network The multi-level image generation step, the visual encryption step, and the homomorphic decryption step are executed in the at least one terminal unit, and the homomorphic encryption step is executed in the server-end unit. The homomorphic multi-level visual image encryption method according to claim 1, wherein, in the multi-level image generation step, the at least one gray-scale plaintext image includes a first gray-scale plaintext image and a second gray-scale plaintext image, After quantization processing, a first multi-level plaintext image and a second multi-level plaintext image that are superimposed into a display image are obtained; in the visual encryption step, the first multi-level plaintext image and the The second multi-level plaintext image is calculated through the cipher text generation technology to obtain a plurality of first cipher text images and a plurality of second cipher text images, and the plurality of first cipher text images and the plurality of second cipher text images are visualized separately Encryption process, the visual encryption process is to make the plural first cipher image and the plural second cipher image need to perform modular operation addition and modular operation multiplication respectively to obtain the first multi-level plaintext image and The second multi-level plaintext image; in the homomorphic encryption step, the plural first cipher images and the plural second cipher images are respectively used to form congruences formed by a first set of keys and a second set of keys The equations are homomorphically encrypted in sequence to obtain plural first homomorphic ciphertext images and plural second homomorphic ciphertext images respectively, so that the plural first homomorphic ciphertext images are obtained. The homomorphic ciphertext image and the plural second homomorphic ciphertext image are decrypted by the Chinese remainder theorem to obtain the plural first ciphertext image and the plural first ciphertext image; among them, only authorized A first user who can share the first multi-level plaintext image can only share the first multi-level plaintext image in the displayed image; and is authorized to share the first multi-level plaintext image and A second user of the second multilevel plaintext image can simultaneously see the superimposed first multilevel plaintext image and the second multilevel plaintext image in the display image.

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