Performance of Chaos-Based Encryption Algorithm for Digital Image

Presentation of information in digital form is highly vulnerable againts information abusing. Digital image is one of digital information which is frequently becomes a target of crime. Therefore, reliable, secure, and fast security techniques are required in digital image information. In this study, chaos-based encryption algorithm for digital image is built to improve endurance from brute force and known plaintext attack. The algorithm use logistic map as a random number generator for key stream. According to test and analysis, this algorithm has key space of 10 , key sensitivity up to 10 , the key stream is proved random, and the distribution of pixels value from encrypted image is proved uniform. So, it can be concluded that, the algorithm is very difficult to be cracked by brute force attack and also known plaintext attack.


Introduction
Performance of an algorithm can be seen from the algorithm endurance security against attacks and computation time.The traditional cipher like Data Encryption Standard (DES), International Data Encryption Algorithm (IDEA), Advanced Encryption Standard (AES), and Rivest-Shamir-Adleman Algorithm (RSA) require a large computational time and high computing power.However, the image encryption ciphers are preferable which take lesser amount of time and at the same time without compromising security [1], [2] To provide a better solution for the security problem of digital image, a number of image encryption techniques have been proposed including the chaos -based image encryption.These techniques provide a good combination of speed, high security, complexity, and computational power, etc [3]- [6] Chaos-based encryption also been extensively studied by researchers because of its superior in safety and complexity [2], [3], [6]- [12].
Chaos is the type of behavior of a system or function that is random, sensitive to initial values, and ergodicity.Function that has chaos properties was called chaos function.Chaos function have been proved very suitable to design facilities for data protection [4], [5], [13].With these properties, chaos function can be used as a random number generator.One of the simple function that shows the chaos properties is the logistic equation or commonly called the logistic map.Logistic map function is defined as a function : → , 1 which is a function of one variable and is a fixed parameter.The value of variable in the interval 0,1 and in the interval 0,4 .Meanwhile, the presentation of logistic map function is in the form of iterative.It is : where 0 , 1,2,3 . ... and is the initial value of iteration [2], [3].In this paper, we will discuss about security of digital image using chaos -based encryption method, by using the logistic map as a chaos function.Testing of algorithm was done based on the encryption and decryption average time, size of the key space, and key sensitivity analysis.Beside that, we conducted a randomness analysis of key stream which generated by these algorithm, and uniform distribution analysis of pixel values in the image that has been encrypted.The analysis was carried out to see the resistance againts brute force attack and known plaintext attack.

Encryption Algorithm
Encryption algorithm for digital image in this paper uses logistic map as a chaos function.The sequence of the process of securing the digital image can be seen in Figure 1 and process to regain access to the original digital image can be seen in Figure 2:  2 shows the flow in securing digital images.Function key stream generator is the logistic map.The input of this algorithm are the original image and the key, the key is and λ.The output is an image that has been encrypted or image has been safe.To regain access to the original image, then we do the decryption process as shown in Figure 2. Input of the decryption process are the image that has been encrypted and the key.The key used in the decryption process is the same during the encryption process.The output is the original image.Encryption algorithm is described in the step 1 to step 5 [12]: Step 1 : Insert the key , and original image with size Step 2: Do 200 times iteration the logistic map equation (1) and we will get decimal fractions.
Step 3a : If yes, then do 3 times the logistic map iteration and we will obtain the results are decimal fractions , such as .Step 3b : If not, so the encyption process is done for all part of image and we will obtain encrypted image.
Step 4 : Check whether the iteration is the last or not.
Step 4a : If yes, then do a real transformation to an integer, with procedures: Select the first 15 number behind the decimal from decimal fraction that has been placed before ( for example ), that are the result of 3 iterations logistic map.Then divide 15 number to p integer with each integernya has 3 points.Then take as much ., integer .Do operation mod 256 to each integer, so we get ., byte integer. 1 byte this integer number is called key stream .Step 4a.1 : Take the pixel value information at each grayscale as much as ., .Each 1 byte information of the image is called P. Step 4a.2 : Do step 5 . , times.All test data in Table 1 will be used in the encryption process to be shown time encryption and decryption of the algorithm.Then it will be testing the durability of the chaosbased encryption algorithm.The first test is the test of resistance to brute force attacks with key sensitivity analysis and determination of the size of the key space.A second test is the test of resistance to known plaintext attack by randomness of key stream analysis and histogram analysis.3 that the time between the encryption and decryption process is not much different or relatively similar.For color images takes time encryption and decryption process is longer when compared to the grayscale image.That is because, the encryption process is done for each component of each grayscale red, green and blue, so it takes a longer process than just doing the encryption process on a grayscale image.
Time analysis from this proposed algorithm is better if compare with the algorithm by Gao.et.al [10].Those were shown in Figure 4, Figure 5, Figure 6, and Figure 7.The test data which was used were Data 6 to Data 15 (Table 1).Based on the Figure 4 to Figure 7, it is shown that the encryption and decryption processing time on Figure 5 and Figure 7 is better then encryption and decryption processing time on Figure 4 and Figure 6.In terms of encryption and decryption processing time, the algorithm in this proposed algorithm is better than algorithm that was used by Gao H, et.al. [10].

Key Sensitivity Analysis
The value of the key that is used is always same for each digital image test data in this paper.While the decryption process will be tested with various different key value.The results are presented in Figure 8.In Figure 8b and Figure 8c are shown the results of the encryption and decryption process simulation using cat image with the same key that is 0.1 , 4. Thus seen that the decryption process succeeded in opening the original data (Figure 8a).
In Figure 8d are shown that the attempt to decrypt using a key difference between the value by 10 did not succed to get the original image.This is due to one of the properties of the logistic map is sensitive to initial values.Value of 0.1 and 0.1000000000000001 still considered different values by this algorithm.But in Figure 8e, when the difference reaches 10 the decryption proccess got the information of original image.It shows that the numbers 0.1 and 0.10000000000000001 is considered to be the same number that is 0.1.Previously, have been tested using the different decryption key for grayscale and color images ranging from 10 to 10 .So we get the sensitivity of this algorithm is up to 10 .
So we obtain that a brute force attack would be very difficult to get the original image information, because these algorithms are very sensitive to changes in the value of the key.Histogram display for each column in a row is just the components Red (R) that shows the distribution of pixel values (Figure 9).

Size of Key Space
The random number generator which was used to generate key stream is logistic map.Keys that are used on logistic map are and , where and are real number.If we use a higher level of precision, for example 64-bit double precision IEEE standard, the precision level will reach 10 .So, the total of key space are 10 10 10 .Time required to exhaustive key search [14] can be seen in Table 2.It can be concluded that, the algorithm is very difficult to be cracked by brute force attack.

Randomness Key Stream Analysis
Test of randomness performed using international standard testing of the National Institute of Standards and Technology is monobits frequency test [15].With the initial value 0.1 dan 4 testing has been carried out on the key streams generated by the chaos-  Obtained from the randomness analysis of the key stream which generated by this algorithm is completely random.So that, the algorithm is very difficult to be cracked by known plaintext attack that utilizes the statistical properties of the ciphertext.With degrees of freedom 256-1=255, and 1% significance level, the critical value is 310.4573882199.It was seen from the results of the experiment are shown in Table 3 and Table 4, all the test statistic values less than the critical value.It can be concluded that all the tested data proved uniformly distributed.As seen in Figure 9b for component R, histogram diagram from the results of encrypted image is flat, which shows the distribution of encrypted image pixel value, is uniform.
Based on the test results, the distribution encrypted image pixel value, using this algorithm, is uniform.So this ciphertext is very difficult to be cracked by known plaintext attack that utilizes the statistical properties of the ciphertext.

Conclusion
Conclusion of this paper are : a. Performance of chaos-based encryption algorithm are: (i).The time of encryption and decryption processes are relatively similar to each grayscale and color image.(ii).Time of color image encryption and decryption process is longer than grayscale image  ISSN: 1693-6930 TELKOMNIKA Vol. 12, No. 3, September 2014: 675 -682 682 because on the color image , the process of encryption and decryption were done for each component grayscale, they are red, green, and blue.(iii).Encryption algorithm has key space for 10 and key sensitivity that reaches 10 , so the algorithm is very difficult to be cracked by brute force attack.(iv).This encryption algorithm is very difficult to be cracked by known plaintext attack, due to the value distribution of the pixels of the encrypted result is proved uniform (all test statistic value less than the critical value) and key streams that were generated, proved to be completely random with P value = 0.74118 > 0.01.b.So, it can be concluded that, the algorithm is very difficult to be cracked by brute force attack and also known plaintext attack.

5 .
It can be concluded with the significance level of 1 % proven true that the sequence is random because 0.01.

Table 1 .
If not, then do transformation from real to integer, like in the step 4a, but take by p integer.Then take p integer.Do operation mod 256 to each integer, so we get p bytes integer number or p KS.Step 4b.1 : Take the pixel information at each pixel grayscale by p .Each 1 byte information of the image is called P.Step 4b.2 : Do the step 5 by p times.Step 5: Do bitwise XOR operation on each byte integer number with every byte image data.Test Data Image  Performance of Chaos-Based Encryption Algorithm for Digital Image (Suryadi MT) 677 Step 4.b :

Table 2 .
Time Required to Exhaustive Key Search

Table 3 .
Test Statistic Values for Grayscale Image

Table 4 .
Test Statistic Value for Color Image.