Anti-counterfeiting technology based on chaotic images

　　With the development of anti-counterfeiting technology today, it has become a considerable and rapidly growing industry, with countless specific methods, technologies and products. The current main anti-counterfeiting technologies include: laser anti-counterfeiting technology, biological anti-counterfeiting technology, nuclear track anti-counterfeiting technology, packaging anti-counterfeiting technology, query and identification anti-counterfeiting technology, etc. There are many anti-counterfeiting technologies, but no matter what kind of anti-counterfeiting technology is used, there are only two types: digital and analog. Chaos anti-counterfeiting technology combines these two types and establishes a one-to-one correspondence between analog information and data information. To achieve the purpose of anti-counterfeiting. Since the analog information cannot be copied, the entire anti-counterfeiting mark cannot be copied or decrypted. In addition, due to its large amount of information, even if there are some stains on this anti-counterfeiting mark, it will not affect the identification of true and false, and it has strong anti-interference ability.

　　1 Generation of chaotic images

　　Chaos phenomena are everywhere. As long as you pay careful attention, you will find chaos phenomena everywhere around you. For example, if you take a piece of paper and tear it randomly, you will find that there are many burrs on the edge of the paper. These glitches are neither regular nor reproducible. Similar to the above phenomenon, when you use a pen to draw a line on damp paper, the ink immediately penetrates the paper, and countless "burrs" of different lengths and shapes appear on both sides of the line. This is also a chaotic phenomenon and cannot be replicated. Chaos anti-counterfeiting technology is based on this chaotic phenomenon. Obviously, this method is easy to make, low cost, and is very suitable for application to a variety of tickets. In this article, in order to increase the amount of information and beauty of anti-counterfeiting, four parallel lines of equal length and length were drawn with a pen on the damp paper, and a positioning frame was added to form a chaotic anti-counterfeiting image (Figure 1). There are four chaotic orbits in the picture, and each chaotic orbit is surrounded by burrs of varying lengths and different bends. Chaos anti-counterfeiting technology utilizes the non-replicability of these chaotic orbits to achieve the purpose of anti-counterfeiting.

　　2. Identification and informatization of chaotic anti-counterfeiting marks

　　The image obtained from the camera is uncertain both in terms of geometry (size, tilt angle) and illumination. In order to be able to analyze the image, the above information must first be obtained, that is to say, the image must be positioned and then normalized to a certain geometric shape and illumination. In specific implementation, locators need to be designed around the chaotic anti-counterfeiting image. The identification process is shown in Figure 2. Image processing technologies such as image pattern recognition, image positioning, image illumination intensity analysis, image equalization, image enlargement, reduction and rotation are used to obtain the geometry, illumination and other information of the locator. Then the chaotic anti-counterfeiting image is normalized based on the information of the locator, so that the anti-counterfeiting image has strong geometric adaptability and illumination adaptability, and strong anti-interference ability, thus greatly reducing the cost of hardware. Since each chaotic track is uncertain relative to the chaotic anti-counterfeiting image, after image recognition and positioning, the digital information of the chaotic anti-counterfeiting image cannot be directly read, and a straight line fitting method must be used to locate each chaotic track (results in Figure 1 ). Consider the zigzag curve composed of many "burrs" in Figure 1 as an irregular waveform. Then sample it. So the following sequence can be obtained: xi=x1x2x3…xi…xn (1)

　　3. Extract feature values ​​using complexity algorithm

　　Due to the large amount of information and subtle structure of chaotic images, but the accuracy of existing instruments is very limited, it is not suitable to directly calculate the length of "burrs" as the characteristic information of chaotic images. To this end, this paper adopts a method similar to symbolic dynamics, that is, a coarse-grained method, and uses the complexity measure of sequence 1 as the characteristic sequence of chaotic orbits. The complexity method calculates the complexity of a given sequence. Any signal is basically a sequence, and the complexity measure reflects an important nonlinear characteristic of this sequence. First take the mean of sequence (1):

　　According to formula (3), the sequence (1) can be turned into a symbol sequence {si}=s1s2s3...si...snKolmogorov believes that the complexity of the sequence {si} can replace the complexity of the sequence {xi}. The most basic Kolmogorov complexity algorithm is used to process the sequence {si}. According to Kolmogorov complexity, it can be considered as the minimum number of bits of a computer program that produces a given (0,1) sequence. It can be used to measure the complexity of the sequence. Lempel and Ziv defined the complexity C(n) of a finite sequence composed of elements of a finite set, which reflects the degree to which the sequence is close to random. Repeat the following operations from scratch in a finite sequence: each time you add an element to form a test substring, if the substring has already appeared in the sequence formed before removing the last element added, then the complexity of the new sequence formed The degree remains unchanged and elements are continued to be added until the added substring consisting of the above-mentioned successively added elements has never appeared in the entire sequence formed before the last added element was removed. At this time, the complexity of the entire sequence increases by one, and a new check substring is re-established when elements are added later, and this is repeated until the end. If the last check substring appears in the sequence before removing the last element, the complexity still increases by one. Specifically, it is divided into the following steps: (1) If there is a sequence (x1, x2, x3,...xn), first find the average value m of this sequence, and then reconstruct this sequence. Values ​​greater than the mean m are set to 1; values ​​smaller than the mean m are set to 0. In this way, a new (0,1) sequence (s1, s2,...sn) is formed. (2) A string of characters S = s1, s2, formed in such a (0, 1) sequence. ．．After sr, add one or a string of characters called Q Sr+1 or (Sr+1, Sr+2...Sr+k) to get SQ. Let SQπ be a string of characters SQ minus the last character, and then see if Q belongs to the existing "words" in the SQπ string. If it already exists, add this character to the end and call it "copy". If it does not occur, it is called an "insertion". When "inserting", use a "." to separate the front and back. The next step is to treat all characters before "." as S, and then repeat the above steps. For example, the complexity of the sequence 0010 can be obtained by the following steps: a) The first symbol is always inserted →0. b) S=0, Q=0, SQ=00, SQπ=0, Q belongs to SQπ→0.0. c) S=0, Q=01, SQ=001, SQπ=00, Q does not belong to SQπ→0.01. d) S=001, Q=0, SQ=0010, SQπ=001, Q belongs to SQπ→0.01.0. At this time c(n)=3. For example, the symbol column is 0000. ．．should be the simplest, and its form should be 0.0000..., c(n)=2. The symbol sequence 01010101… should be 0.1.0101…, c(n)=3. (3) As mentioned above, a string divided into segments using "." is obtained. The number of segments divided into is defined as the "complexity" c(n). According to the research of Lampel and Ziv, c(n) for almost all x belonging to the interval [0,1] will tend to a constant value: among them, b(n) is the asymptotic behavior of the random sequence, which can be used to make c (n) Normalization, called "relative complexity". Define relative complexity: C(n)=c(n)/b(n)=[c(n)logn]/n (5) This function is usually used to express the complexity changes of time series. It can be seen from this algorithm that the C(n) value of a completely random sequence tends to 1, while the C(n) value of regular periodic motion tends to 0. If there is a random sequence in which the probability of "1" is not 0.5, then its complexity is considered to be the complexity of a random sequence with probability P. This can be expressed as: h≤1, h is called the source entropy, and its maximum value is at the position of p=0.5. When h < 1, compare the deviation from 1. When the two are very close, the symbol string is considered to be a string with higher complexity, that is, it is a random string; otherwise, it is considered that there is a certain pattern in the symbol string. Kolmogorov complexity is also called algorithm complexity. It is a measure of randomness that reflects the rate at which new patterns appear in a random sequence as its length grows. It shows how close the sequence is to randomness and reflects the symbol to some extent. Structural properties of sequences rather than properties of dynamic systems.

　　4 Application of Chaotic Anti-Counterfeiting Marks

　　The purpose of anti-counterfeiting cannot be achieved by relying only on a chaotic anti-counterfeiting mark. Digital information and chaotic anti-counterfeiting marks must be combined to achieve the purpose of anti-counterfeiting. Specifically, the characteristic data of the chaotic image can be directly encrypted, and the encrypted digital information can be printed next to the anti-counterfeiting mark in the form of a two-dimensional barcode to form a complete anti-counterfeiting mark (Figure 3). During the authenticity identification process, the public key is used to decrypt the digital information of the two-dimensional barcode on the chaotic anti-counterfeiting mark, and then compare it with the characteristic data of the chaotic anti-counterfeiting mark. If they are the same, it is considered a real anti-counterfeiting mark, otherwise it is a fake anti-counterfeiting mark.

　　In addition, you can also combine query anti-counterfeiting technology to directly save chaotic anti-counterfeiting feature numbers on your own server. Chaos anti-counterfeiting technology can be applied to various documents, checks, etc., which will not be introduced in detail here. This article uses non-replicable chaotic images as anti-counterfeiting marks, and then uses complex algorithms to extract feature data. It is a brand-new anti-counterfeiting technology, which is different from laser anti-counterfeiting, biological anti-counterfeiting, barcode anti-counterfeiting and other technologies. The production process does not rely on any technical confidentiality, and no one can fake the exact same anti-counterfeiting mark. Because the chaotic image contains a large number of microstructures similar to those produced by micro-printing on the U.S. dollar, it effectively prevents counterfeiters from making fakes through copying and other means. Chaotic orbits have extremely rich microstructures, so they contain a large amount of information. This creates extremely effective conditions for distinguishing chaotic graphics. It is reported that the fingerprint error rate can reach 1/243, and this technology can easily reach 1/2100. And if necessary, reaching 1/2200 is not a problem. Any irregular pattern that can be produced on paper using physical and chemical methods can be used as an anti-counterfeiting image mark. The anti-counterfeiting technology described in this article has been patented.