CN110086606B - Quantum mechanism-based multi-party secret sharing method for black and white images - Google Patents

Abstract

The invention provides a quantum mechanism-based multi-party secret sharing method for black and white images, which encodes each pixel in a secret image into an n-quantum-bit superposition state, and then distributes each quantum bit to participants as a share; when a participant wants to recover the original secret image, all share shares are collected, and the recovery is carried out by executing exclusive-or operation through a quantum circuit. Has the advantages that: the operation of each pixel is realized, and each share is disordered by using the uncertainty of a quantum superposition state; and the secret image can be completely recovered without distortion.

Description

Quantum mechanism-based multi-party secret sharing method for black and white images

Technical Field

The invention belongs to the field of quantum computation and visual secret sharing, and particularly relates to a quantum mechanism-based black and white image multiparty secret sharing method.

Background

Secret sharing is an important research field in classical cryptography, and aims to share secrets in a proper mode, each share after sharing is managed by different participants, secret information cannot be recovered by a single participant, and secret information can be recovered only by cooperation of a plurality of participants. Visual Secret Sharing (VSS) is derived from a secret sharing technology, and is characterized in that when a secret image is encrypted, each secret pixel point is divided into pixel blocks consisting of m sub-pixel points, so that a binary secret image is shared to generate a plurality of noise-like shared shares (shares). Since each shared share is just like random noise, an attacker cannot directly solve the secret information from the ciphertext. However, the share is m times of the original secret image, so that the pixel expansion exists, and the problem of resolution loss exists in the restored image, namely the visual quality of the restored image is poor. Another feature of visual secret sharing is that the decryption process is very simple, and the human visual system can directly recognize the secret information by printing a certain number of shared shares onto the transparent film and superimposing them. Due to the theoretical security of visual secret sharing and the simplicity of secret recovery, the method can be widely applied to the fields of group participation or control, such as password storage, key management, digital watermarking, signature authentication and the like.

Quantum Secret Sharing (QSS) is an extension of classical secret sharing in the quantum field, and multi-user secret key share sharing and recovery are realized by means of quantum mechanical correlation characteristics, so that potential unconditional security of different classical schemes is realized. Over the past 20 years, various quantum secret sharing schemes have been proposed by many scholars, playing an important role in practical issues such as quantum key distribution, non-counterfeit quantum cash, secure quantum storage, multiparty quantum communication, and so on. However, there has been little research on quantum-based visual cryptography.

Recently, Song et al proposed a quantum image secret sharing method, in which the whole secret image (all pixels) is encoded into a quantum state during the sharing process, and then the image is divided into 2 by quantum measurement and other strategies^kA share; in the recovery process, flexible quantum wires are added into the wiring diagram of the shadow image to recover the quantum images to obtain recovered images. Compared with the classic visual secret sharing method, the image storage and transmission method provides stronger safety and less qubit consumption because of the quantum mechanism. However, this scheme is to process the entire image, and does not have the features and advantages of operating VSS in units of pixels.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, provides a quantum mechanism-based multi-party secret sharing method for black and white images, and solves the defect that the conventional QSS scheme cannot meet the requirement of a classical visual password scheme for operating by taking pixels as units; and in the classic visual secret sharing scheme, the problem of resolution loss exists in image recovery. The method is realized by the following technical scheme:

the quantum mechanism-based multi-party secret sharing method for black and white images sets a sharer to send a secret image to n participants Bob₁,Bob₂,…,Bob_nAnd the secret image comprises s black and white pixels; stipulate |0>Represents white, |1>Representing black, the main process of the method comprises a secret image sharing process and a secret image recovery process, wherein the sharing process comprises the following steps:

step 1) a sharer selects any pixel l in the secret image, wherein the pixel l corresponds to the ith pixel, and the color information of the pixel l is encoded into a quantum superposition state | C according to the formula (1)_b>_l；

Where b is 0,1, i is 1,2, …,2^n-1}，j∈{1,2,…,n}，

l∈{1,2,…,s}。

Step 2) sharer will compose | C_b>_lN bits of

Distributed as a shared share to n participants Bob₁,Bob₂,…,Bob_nCompleting the sharing operation of the current pixel, wherein the superscript n represents that the current bit is distributed to the nth participant;

step 3) repeating the steps 1) to 2) until all pixels of the whole image complete sharing operation;

the recovery process comprises the steps of:

step a) participant Bob_jSending out requests to other n-1 bit participants to obtain n share shares corresponding to the ith pixel

Step b) participant Bob_jSelect { |0>,|1>Measure the base, for n share shares

Formed superimposed state | C_b>_lMeasuring to obtain a determined quantum state

Step c) participant Bob_jQuantum state of quantum

Performing XOR operation by quantum circuit to obtain a result state

Step d) participant Bob_jFor the result state

Make a judgment if

Is |0>If the state is "1", the first pixel is white; if it is not

Is |1>If the state is "black", the first pixel is black;

step e) Bob_jAnd repeating the steps a) to d), and recovering the colors of all the pixels to finish the recovery of the original secret image.

The quantum-based multi-party secret sharing method for black and white images further comprises the step of constructing the quantum circuit in the step c) by a CNOT quantum gate.

The invention has the following advantages:

compared with the method provided by Song et al, the quantum mechanism-based multi-party secret sharing method for the black and white image realizes the operation of each pixel, and makes each share be disordered by using the uncertainty of a quantum superposition state; compared with the classic visual secret sharing, the method can completely recover the secret image and does not have the phenomenon of loss of the resolution of the recovered image.

Drawings

Fig. 1 is a schematic diagram of a quantum encoding process of pixels in a secret image.

Fig. 2 is a schematic diagram of a secret image sharing process.

Fig. 3 is a quantum circuit diagram of an n-quantum-bit accumulated exclusive-or operation.

Fig. 4 is a schematic diagram of a secret image recovery process.

Fig. 5 is an example of a quantum visual secret sharing method for a 4-pixel secret image.

Detailed Description

The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

The quantum-mechanism-based multi-party secret sharing method for black and white images in this embodiment is as shown in fig. 5, and it is assumed that a sharer Alice wants to share a secret image composed of 4 black and white pixels to 3 participants Bob₁，Bob₂And Bob₃I.e., s-4 and n-3, the process consists of the following sharing process (see fig. 2) and recovery process (see fig. 4).

The sharing process of this embodiment is as follows:

step (1) As shown in Step 1 in FIG. 2, Alice needs to encode each pixel, for example, the 1 st pixel, and encode its color information into the 3-qubit superposition state | C₀>₁Inner, | C₀>₁The specific encoding process can be obtained as shown in FIG. 1

Like the 1 st pixel operation, the 2 nd pixel is encoded into

The 3 rd pixel is coded into

The 4 th pixel is coded into

Step (2) As shown in Step 2 in FIG. 2, Alice will constitute the superposed state | C₀>₁As 3 shared shares of 3 qubits

And

distributed to all participants Bob₁，Bob₂And Bob₃。

Step (3) is as shown in Step 3 in fig. 2, and Step 1 and Step 2 are repeated until all pixels of the whole image complete the sharing operation.

The recovery process of this embodiment is as follows:

suppose Bob₂Wanting to restore the original secret image (as shown in the example of FIG. 5)

Step (a) Bob₂The share shares corresponding to the same pixel are obtained from all other participants, which can be shown as Step 1 in fig. 4, assuming that it corresponds to the 1 st pixel,

and

step (b) is as in Step 2, Bob of FIG. 4₂Select { |0>,|1>Measurement base pair

And

form | C₀>₁Measurement is carried out, | C₀>₁Collapse into a defined quantum state

Step (c) is as in Step 3, Bob of FIG. 4₂Will be provided with

Through the quantum circuit as shown in fig. 3. The quantum circuit of fig. 3 is mainly composed of CNOT quantum gates, and the main function is to perform xor operation on input quantum states to obtain result states

Step (d) is as in Step 4, Bob of FIG. 4₂For result state

Making a judgment, if the result state is correct

Is |0>State, the 1 st pixel is white; if the result state is

Is |1>For state, the 1 st pixel is black.

Step (e) is as in Step 5, Bob of FIG. 4₂And repeating the operations from Step 1 to Step 4 until the original secret image is recovered.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. Black-white image based on quantum mechanismThe multi-party secret sharing method is characterized in that a sharer is set to share a secret image to n participants Bob₁,Bob₂,...,Bob_nAnd the secret image comprises s black and white pixels; stipulate |0>Represents white, |1>Representing black, the main process of the method comprises a secret image sharing process and a secret image recovery process, wherein the sharing process comprises the following steps:

step 1) a sharer selects any pixel l in the secret image, the pixel l represents the ith pixel, and the color information of the pixel l is encoded into an n-qubit superposition state | C according to the formula (1)_b>_l；

Where b is 0,1, i is 1,2, …,2^n-1}，j∈{1,2,…,n}，

l∈{1,2,…,s}；

Step 2) sharer will compose | C_b>_lN bits of

Distributed as a shared share to n participants Bob₁,Bob₂,…,Bob_nCompleting the sharing operation of the current pixel, wherein the superscript n represents that the current bit is distributed to the nth participant;

step 3) repeating the steps 1) to 2) until all pixels of the whole image complete sharing operation;

the recovery process comprises the steps of:

step a) participant Bob_jSending out requests to other n-1 bit participants to obtain n share shares corresponding to the ith pixel

Step b) participant Bob_jSelect { |0>,|1>Measure the base, for n share shares

Formed superimposed state | C_b>_lMeasuring to obtain a determined quantum state

Step c) participant Bob_jQuantum state of quantum

Performing XOR operation by quantum circuit to obtain a result state

Step d) participant Bob_jFor the result state

Make a judgment if

Is |0>If the state is "1", the first pixel is white; if it is not

Is |1>If the state is "black", the first pixel is black;

step e) Bob_jAnd repeating the steps a) to d), and recovering the colors of all the pixels to finish the recovery of the original secret image.

2. The quantum-based mechanism secret sharing method between black and white images of claim 1, wherein the quantum circuit in step c) is formed by a CNOT quantum gate.

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