CN110958458B - Digital image encryption method and image decryption method based on modular inverse operation - Google Patents

Abstract

The invention discloses a digital image encryption method based on modular inverse operation, which comprises the following steps: giving an original image A; the pixel point in the ith row and the jth column in A is represented as p_i,jAll the pixel points with the value of i + j being an odd number are classified into a first class, and all the pixel points with the value of i + j being an even number are classified into a second class; performing modular inverse operation on all pixel points of the first type or the second type, and replacing the original pixel value with the obtained modular inverse value to obtain an encrypted image A'; performing modular inversion on the pixel points obtained by performing modular inversion on the pixel points of the first type or the second type in the A' according to claim 1; and replacing the original pixel value with the obtained modulus inverse value to restore the original image A. The method for classifying the pixel points of the image is simple and easy to implement, the encryption operation of the pixel points is simple, no additional information is needed in the whole encryption and recovery process, the image information transmission efficiency is high, and the error of the individual pixel points can not cause the error diffusion phenomenon.

Description

Digital image encryption method and image decryption method based on modular inverse operation

Technical Field

The invention relates to the technical field of encryption and recovery in image processing, in particular to an image encryption method and an image decryption method.

Background

The rapid development of the information technology brings great convenience to the life of people on one hand, and on the other hand, the information safety is threatened to a certain extent by the problems caused by information leakage or tampering in the transmission process. Digital images, one of the main carriers for information transmission, are inevitably attacked by illegal attacks. How to transmit digital images efficiently and prevent information from being leaked is one of important research contents in the field of information security.

Unlike the encryption of text, voice and other media, the encryption of digital images has its unique features: first, the digital image itself contains a large amount of data, and thus, encrypting it requires a large storage space. Secondly, digital images place high demands on the real-time performance of data recovery, because independent partial image data has no meaning, and only when most of the data is recovered, the information of the image can be recognized. The existing image encryption technology almost surrounds the characteristics of the two aspects: such as scrambling-based encryption techniques and computer graphics-based image encryption techniques. The two aspects of the good encryption effect and the small storage space can not be obtained at the same time, for example, the image encryption technology based on scrambling has a good encryption effect, but the storage space is generally larger as required; computer graphics-based encryption techniques require less memory space, but the encryption effect needs to be further improved.

Disclosure of Invention

The invention aims to provide an image encryption method and an image decryption method for solving the contradiction that smaller storage space and good encryption effect cannot be obtained at the same time.

In order to achieve the above object, the present disclosure provides a digital image encryption method based on modular inverse operation, including the following steps:

s1: giving an original image A;

s2: the pixel point in the ith row and the jth column in A is represented as p_i,jAll the pixel points with the value of i + j being an odd number are classified into a first class, and all the pixel points with the value of i + j being an even number are classified into a second class;

s3: and performing modular inverse operation on all the pixel points of the first type or the second type, and replacing the original pixel value with the obtained modular inverse value to obtain an encrypted image A'.

The image decryption method is used for decrypting the image A' encrypted by the digital image encryption method, and comprises the following steps:

a1: performing modulo inversion operation on the pixels of the first type or the second type in A' according to claim 1 to obtain a modulo inversion value of the pixel;

a2: and replacing the original pixel value with the obtained modulus inverse value to restore the original image A.

The invention has the beneficial effects that:

1. in the invention, the classification of the pixel points of the image is determined according to the parity of the row mark and the column mark, so the classification method is simple and easy to implement;

2. the encryption of the pixel point is obtained by solving the modulo inversion of the pixel value of the point, and the operation is simple because other operations are not involved;

3. according to the digital image encryption method and the image decryption method based on the modular inverse operation, the system does not need extra information in the whole encryption and recovery process, so that the image information transmission efficiency is high;

4. when the encrypted image provided by the invention is recovered, the modulo inversion of the pixel value at the encrypted position is only required to be solved, and the value can be obtained by looking up a table. Therefore, the method for recovering the encrypted image is simple and efficient, and requires a small amount of computation.

5. In the process of encrypting and decrypting the image, each pixel point is independent, so that the error of the individual pixel point can not cause the diffusion phenomenon of the error.

On the basis of the technical scheme, the invention can be further improved as follows:

preferably, the pixel point p is selected in S3_i,jInverse of its modulus

The method comprises the following steps:

drawings

The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure without limiting the disclosure. In the drawings:

FIG. 1 is a flow chart of an image encryption method based on modular inverse operation according to the present invention;

FIG. 2 is a flow chart of the image decryption method based on modular inverse operation according to the present invention;

fig. 3 shows an original image a and an encrypted image a' based on the modulo inversion operation according to the present invention.

Detailed Description

The following detailed description of specific embodiments of the present disclosure is provided in connection with the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present disclosure, are given by way of illustration and explanation only, not limitation.

As shown in fig. 1, the digital image encryption method based on modular inverse operation includes the following steps:

(1) giving an original image A;

(2) the pixel point in the ith row and the jth column in A is represented as p_i,jAll the pixel points with the value of i + j being an odd number are classified into a first class, and all the pixel points with the value of i + j being an even number are classified into a second class;

(3) and performing modular inverse operation on all the pixel points of the first type or the second type, and replacing the original pixel value with the obtained modular inverse value to obtain an encrypted image A'.

At S3, pixel point p is pointed out_i,jInverse of its modulus

The method comprises the following steps:

specifically, note S₁Is the set of all the pixel points with the value of i + j being odd number:

S₁＝{p_1,2,p_1,4,...,p_i,j,., where i + j ≡ 1(mod 2)

Note S₂Set of all pixels whose value i + j is even:

S₂＝{p_1,1,p_1,3,...,p_i,j,., where i + j ≡ 0(mod 2)

When the modulo inversion operation is performed on the first type of pixel points,

the image A is encrypted to obtain an image A ', and pixel points p ' of the image A '_i,jComprises the following steps:

the image decryption method is used for decrypting the image A' encrypted by the digital image encryption method, and comprises the following steps:

(1) performing modular inverse operation on the first type of pixel points in A';

(2) and replacing the original pixel value with the obtained modulus inverse value to restore the original image A.

Specifically, the first type pixel point p ' in A ' is subjected to '_i,jThe calculation method of the modular inversion operation comprises the following steps:

wherein, p'_i,j∈S₁

Due to the fact that

Thus, the original image A can be obtained.

In the invention, the classification of the pixel points of the image is determined according to the parity of the row mark and the column mark, so the classification method is simple and easy to implement;

the encryption of the pixel point is obtained by solving the modulo inverse operation of the pixel value of the point, and the method is simple and easy to implement because other operations are not involved;

according to the image encryption and recovery method based on modular inverse operation, the system does not need extra information in the whole encryption and decryption process, so that the image information transmission efficiency is high;

when the encrypted image provided by the invention is recovered, the modulo inversion of the pixel value at the encrypted position is only required to be solved, and the value can be obtained by inquiring the following table. Therefore, the recovery method of the encrypted image is simple and efficient, and the required computation amount is small.

The following table sets the modulo inversions of all possible pixel values, the values in the table being modulo inverses from 1 to 255 with respect to 257, respectively.

1	129	86	193	103	43	147	225	200	180	187	150	178	202	120	241
																121	100	230	90	49	222	190	75	72	89	238	101	195	60	199	249
148	189	235	50	132	115	145	45	163	153	6	111	40	95	175	166
																21	36	126	173	97	119	243	179	248	226	61	30	59	228	102	253
87	74	234	223	149	246	181	25	169	66	24	186	247	201	244	151
																165	210	96	205	127	3	65	184	26	20	209	176	152	216	46	83
53	139	135	18	28	63	5	215	164	177	245	188	224	250	44	218
																116	124	38	113	134	159	54	15	17	158	140	114	220	51	85	255
2	172	206	37	143	117	99	240	242	203	98	123	144	219	133	141
																39	213	7	33	69	12	80	93	42	252	194	229	239	122	118	204
174	211	41	105	81	48	237	231	73	192	254	130	52	161	47	92
																106	13	56	10	71	233	191	88	232	76	11	108	34	23	183	170
4	155	29	198	227	196	31	9	78	14	138	160	84	131	221	236
																91	82	162	217	146	251	104	94	212	112	142	125	207	22	68	109
8	58	197	62	156	19	168	185	182	67	35	208	167	27	157	136
																16	137	55	79	107	70	77	57	32	110	214	154	64	171	128

According to the image encryption and recovery method based on modular inverse operation, the pixel points are independent, so that error diffusion cannot be caused by errors of individual pixel points.

The preferred embodiments of the present disclosure are described in detail with reference to the accompanying drawings, however, the present disclosure is not limited to the specific details of the above embodiments, and various simple modifications may be made to the technical solution of the present disclosure within the technical idea of the present disclosure, and these simple modifications all belong to the protection scope of the present disclosure.

It should be noted that, in the foregoing embodiments, various features described in the above embodiments may be combined in any suitable manner, and in order to avoid unnecessary repetition, various combinations that are possible in the present disclosure are not described again.

In addition, any combination of various embodiments of the present disclosure may be made, and the same should be considered as the disclosure of the present disclosure, as long as it does not depart from the spirit of the present disclosure.

Claims (2)

1. The digital image encryption method based on modular inverse operation is characterized by comprising the following steps of:

s1: giving an original image A;

s2: the pixel point in the ith row and the jth column in A is represented as p_i,jAll the pixel points with the value of i + j being an odd number are classified into a first class, and all the pixel points with the value of i + j being an even number are classified into a second class;

s3: performing modular inverse operation on all pixel points of the first type or the second type, and replacing the pixel value of the original position with the obtained modular inverse value to obtain an encrypted image A', which specifically comprises the following steps: for pixel point p_i,jInverse of its modulus

Is composed of

Specifically, note S₁Is the set of all the pixel points with the value of i + j being odd number: s₁＝{p_1,2,p_1,4,...,p_i,j,., wherein i + j ≡ 1(mod 2); note S₂Set of all pixels whose value i + j is even: s₂＝{p_1,1,p_1,3,...,p_i,j,., wherein i + j ≡ 0(mod 2); when the modulo inversion operation is performed on the first type of pixel points,

wherein p is_i,j∈S₁(ii) a The image A is encrypted to obtain an image A ', and pixel points p ' of the image A '_i,jComprises the following steps:

2. an image decryption method for decrypting an image a' encrypted by the digital image encryption method of claim 1, comprising the steps of:

a1: performing modulo inversion operation on the pixels of the first type or the second type in A' according to claim 1 to obtain a modulo inversion value of the pixel;

a2: and replacing the pixel value of the original position with the obtained modulus inverse value to restore the original image A.

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