Hybrid Image Encryption Using Elliptic Curve Cryptography, Hadamard Transform and Hill Cipher

Security of information is becoming main criteria while transferring information through communication networks. Nowadays images are used as information source; therefore its security from unauthorized or unintended access is important. Image encryption play an important role in protecting images from hacking and stealing while sending over an unsecured channel. The proposed method is a combination of encryption using Hill cipher algorithm along with Elliptic curve for enhanced security. Elliptic curve cryptographic method is used to make the system to asymmetric from the less secured symmetric key encryption technique; hill cipher algorithm. In our proposed method we use both grayscale images as well as color images regardless its size. Steganography of actual image with a cover image before encryption is an advantage. The cover image is selected as it mocks like an informative to unauthorized access. Least Significant Bit (LSB) steganography method is used here as it provides more security than any other methods.

Data exchange has been rapidly increased recently by increasing the use of mobile networks. Sharing information (text, image, audio and video) over unsecured mobile network channels is liable for attacking and stealing. Encryption techniques are the most suitable methods to protect information from hackers. Hill cipher algorithm is one of symmetric techniques, it has a simple structure and fast computations, but weak security because sender and receiver need to use and share the same private key within a non-secure channel. Therefore, a novel hybrid encryption approach between elliptic curve cryptosystem and hill cipher (ECCHC) is proposed in this paper to convert Hill Cipher from symmetric technique (private key) to asymmetric one (public key) and increase its security and efficiency and resist the hackers. Thus, no need to share the secret key between sender and receiver and both can generate it from the private and public keys. Therefore, the proposed approach presents a new contribution by its ability to encrypt every character in the 128 ASCII table by using its ASCII value direct without needing to assign a numerical value for each character. The main advantages of the proposed method are represented in the computation simplicity, security efficiency and faster computation.

Many researchers have used the properties of the popular Elliptic Curve Cryptography(ECC) to devise a stronger and faster image encryption algorithm to assure the secrecy of images during online transmission. In this paper, a robust Elliptic curve based image encryption and authentication model for both grayscale and color images has been proposed. The model uses the secure Elliptic Curve Diffie-Hellman(ECDH) key exchange to compute a shared session key along with the improved ElGamal encoding scheme. 3D and 4D Arnold Cat maps are used to effectively scramble and transform the values of plain image pixels. A well-structured digital signature is used to verify the authenticity of the encrypted image prior to decryption. The model produces good-quality cipher images with an average entropy of 7.9993 for grayscale and 7.99925 for the individual components of color images. The model has high average NPCR of 99.6%, average UACI of 33.3% and low correlation for both grayscale and color images. The model has low computational costs with minimized point multiplication operations. The proposed model is robust with high resilience against statistical, differential, chosen-plaintext(CPA), known-plaintext(KPA) and occlusion attacks.

Elliptic curve cryptosystem (ECC) was proposed by Miller [10] and Koblitz [9] which relies on the difficulty of elliptic curve discrete logarithmic problem (ECDLP). It is gaining wide acceptance as an alternative to the conventional public key cryptosystem such as RSA [24], DSA [25], DH [26]. Also it is noted that the wireless sensor networks (WSN) based on the rapid progress of wireless communications and embedded micro electro mechanical systems technologies are becoming important part in our daily life. The security of the WSN becomes one of the major concerns in its applications. Even ECC prominently offers great potential benefits for WSN security there is still a lot of work needs to be done due to WSN has very restraint running conditions such as limited energy source, capability of computing, etc. It is well known that scalar multiplication operation in ECC accounts for about 80% of key calculation time on wireless sensor network motes. In this paper we present an optimized dynamic window based on our previous research works. The whole quality of service (QoS) has been improved under this algorism in particularly the power consuming is more efficiently. The simulation results showed that the average calculation time, due to fuzzy conditions decreased from previous 26 to current 9 as a whole the calculation time, decreased by approximately 18% in comparison to our previous algorithms in an ECC wireless sensor network [23].

The majority of imaging techniques use symmetric and asymmetric cryptography algorithms to encrypt digital media. Most of the research works contributed in the literature focus primarily on the Advanced Encryption Standard (AES) algorithm for encryption and decryption. This paper propose an analysis for performing image encryption and decryption by hybridization of Elliptic Curve Cryptography (ECC) with Hill Cipher (HC), ECC with Advanced Encryption Standard (AES) and ElGamal with Double Playfair Cipher (DPC). This analysis is based on the following parameters: (i) Encryption and decryption time, (ii) entropy of encrypted image, (iii) loss in intensity of the decrypted image, (iv) Peak Signal to Noise Ratio (PSNR), (v) Number of Pixels Change Rate (NPCR), and (vi) Unified Average Changing Intensity (UACI). The hybrid process involves the speed and ease of implementation from symmetric algorithms, as well as improved security from asymmetric algorithms. ECC and ElGamal cryptosystems provide asymmetric key cryptography, while HC, AES, and DPC are symmetric key algorithms. ECC with AES are perfect for remote or private communications with smaller image sizes based on the amount of time needed for encryption and decryption. The metric measurement with test cases finds that ECC and HC have a good overall solution for image encryption.

Hill Cipher is one of the methods used in Cryptography. In the Hill Cipher algorithm, the key square matrix must have an inverse modulo. One special matrix that definitely has an inverse is the unimodular matrix. The unimodular matrix can be used as a key in an encryption process. The purpose of this research is to show an alternative in securing digital image data. The type of cryptography used is symmetric cryptography. The algorithm presented by generating a unimodular matrix using the Logistic Map. First, to get a unimodular matrix, we use an identity matrix. The sequence of real number in (0,1) of Logistic Map then converted into integer number from 0 to 255. That number then occupies upper triangular entries of the unimodular matrix. We use the Elementary Row Operation to obtain the complete matrix as a key. Then the multiplication of matrix modulo is used as an encryption process. The unimodular matrix generated by the proposed algorithm guarantees a key in the Hill Cipher for all matrix sizes (n > 4) and only need two parameters (password 1 and password 2). We also tested the algorithm in python language on two digital images (grayscale and color) with different sizes. The results show that the encrypted images are very difficult to read by third parties. The time needed is based on password 1, that is the size of the key matrix. So, the unimodular matrix and logistic map work very well with Hill Cipher to encrypt a digital image.

The use of public-key cryptosystems (PKC) received considerable attention. They are beneficial in encryption as well as signing which play an essential role in electronic banking and financial transactions. Elliptic Curve Cryptography (ECC) is one of best public key techniques because of its small key size and high security. Secure applications in smart cards present implementation challenges particular to the platform's memory, bandwidth, and computation constraints. ECC's unique properties make it especially well suited to smart card applications. ECC systems provide the highest strength per bit of any cryptosystem known today. The paper presents a new method for smart card implementation of elliptic curves, explaining how ECC can not only significantly reduce the cost, but also accelerate the deployment of smart cards in new applications. ECC permits reductions in key and certificate size that translate to smaller memory requirements (especially for EEPROM), which represent significant cost savings. This added functionality can play an effective role in electronic payment and online banking technologies.

An elliptic curve cryptosystem (ECC) is one of public key cryptosystem, whose security is based on elliptic curve discrete logarithm problem (ECDLP). An elliptic curve is uniquely determined by mathematical parameters such as j-invariant of an elliptic curve. By giving trace of elliptic curve, t, a definition field \(\mathbb F_{p}\), and discriminant D, an elliptic curve with order \(\sharp {E(\mathbb F_{p})} = n\) is determined. Therefore it is an open problem to determine explicit relations between the mathematical parameters and the embedding degrees k. Hirasawa and Miyaji presented concrete relations between the mathematical parameters and the embedding degrees. In this research, a new explicit relation between elliptic-curve parameters and embedding degrees is investigated by generalizing their research.

This paper discusses parallelization of elliptic curve cryptography hardware accelerators using elliptic curves over binary fields F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m</sub> . Elliptic curve point multiplication, which is the operation used in every elliptic curve cryptosystem, is hierarchical in nature, and parallelism can be utilized in different hierarchy levels as shown in many publications. However, a comprehensive analysis on the effects of parallelization has not been previously presented. This paper provides tools for evaluating the use of parallelism and shows where it should be used in order to maximize efficiency. Special attention is given for a family of curves called Koblitz curves because they offer very efficient point multiplication. A new method where the latency of point multiplication is reduced with parallel field arithmetic processors is introduced. It is shown to outperform the previously presented multiple field multiplier techniques in the cases of Koblitz curves and generic curves with fixed base points. A highly efficient general elliptic curve cryptography processor architecture is presented and analyzed. Based on this architecture and analysis on the effects of parallelization, a few designs are implemented on an Altera Stratix II field-programmable gate array (FPGA).

Elliptic curves cryptography was introduced independently by Victor Miller (Miller, 1986) and Neal Koblitz (Koblitz, 1987(Koblitz, ) in 1985. .At that time elliptic curve cryptography was not actually seen as a promising cryptographic technique.As time progress and further research and intensive development done especially on the implementation side, elliptic curve cryptography is now being implemented widely.Elliptic curves cryptography offers smaller key size, bandwidth savings and faster in implementations when compared to the RSA (Rivest-Shamir-Adleman) cryptography which based its security on the integer factorization problem.The most interesting feature of the elliptic curves is the group structure of the points generated by the curves, where points on the elliptic curves form a group.The security of elliptic curves cryptography relies on the elliptic curves discrete logarithm problem.The elliptic curve discrete logarithm problem is analogous to the ordinary algebraic discrete logarithm problem, l = g x , where given the l and g, it is infeasible to compute the x.Elliptic curve discrete logarithm problem deals with solving for n the relation P = nG.Given the point P and the point G, then it is very hard to find the integer n.To implement the discrete logarithm problem in elliptic curve cryptography, the main task is to compute the order of group of the curves or in other words the number of points on the curve.Computation to find the number of points on a curve, has given rise to several point counting algorithms.The Schoof and the SEA (Schoof-Elkies-Atkin) point counting algorithms will be part of the discussion in this chapter.This chapter is organized as follows: Section 2, gives some preliminaries on elliptic curves, and in section 3, elliptic curve discrete logarithm problem is discussed.Some relevant issues on elliptic curve cryptography is discussed in section 4, in which the Diffie-Hellman key exchange scheme, ElGamal elliptic curve cryptosystem and elliptic curve digital signature scheme are discussed here accompanied with some examples.Section 5 discussed the two point counting algorithms, Schoof algorithm and the SEA (Schoof-Elkies-Atkin) algorithm.Following the discussion in section 5, section 6 summaries some similarities and the differences between these two algorithms.Section 7 gives some brief literature on these two point counting algorithms.Finally, section 8 is the concluding remarks for this chapter. Elliptic curvesElliptic curves obtained their name from their relation to elliptic integrals that arise from the computation of the arc length of ellipses (Lawrence & Wade, 2006).Elliptic curves are www.intechopen.com Cryptography and Security in Computing1 1 2 3 4 2 2 4 Fig. 1.1. 2(1 ) (1 ) yx x x   www.intechopen.com

Cryptography is one of the most important technological areas which will provide security to the data by using various cryptographic algorithms. The Hill cipher (HC) is a known symmetric encryption algorithm using linear matrix transformation. In spite of the simplicity of Hill cipher algorithm, there are several advantages such as masquerading letter frequencies of the plaintext and high throughput. The traditional Hill cipher founds a serious setback due to the vulnerability against known plaintext–ciphertext attacks. So, to enhance security, a new variant of the Hill cipher method is proposed. The proposed algorithm develops in three stages, firstly, convert the plaintext into 8-bit binary form; in the second stage, we remove the last two bits from MSB positions as they are 0 in the MSB and 1 in the MSB-1 position, respectively, and this reduces the size of the data. Now, apply Radix 64 conversion to each row; in the last stage, we perform the traditional Hill cipher algorithm (modulo 64), where we use the invertible matrix as key, and this produces the ciphertext. The proposed technique reduces the size of ciphertext data after encryption. The security analysis of the modified algorithm using avalanche effect shows three-fold increase than comparing to tradition Hill cipher algorithm. Further, the data size dependence on the performance of the modified Hill cipher algorithm is also addressed and found that the encryption time is increased with increase of data size.

Safeguarding and securing a secret data is something that must be done either in personal, organizational, corporate or governmental data but not a few do not know how to secure data, especially in a message, so this research is conducted to provide a way to encrypt messages. In this research using a collaboration of the Hill Cipher algorithm and Arnold cat map, used to get maximum encryption results on data or messages. In its application, the Hill cipher algorithm will be modified using a bios phoenix sound code and image. Hill Cipher and Arnold Cat Map algorithms are suitable to be combined because it will produce strong enough encryption because the results of text-based encryption from the Hill Cipher algorithm will be encrypted again using the image-based Arnold Cat Map algorithm. This research resulted in the modification of a Hill Cipher algorithm and Arnold Cat Map in the encryption process and description to improve the security of data and information. Keywords — Hill Cipher, Arnold Cat Map, Cryptography, Steganography

Objectives: The role of digital images are vast in todays trends and it is exposed to illicit access, modifications that must needs confidentiality during the stages of data archival and communication1, systems, wireless devices. In order to facilitate secret communication, image encryption have bring into being a significant place in both public and private services like as military supervision, health systems, financial services like online trading and video conferencing and so on. Some methods are proposed on the image encryption which they include the Paper2 have developed a method for A Chaotic Key Based Algorithm (CKBA) to change the pixel values of the plain-image. In 3 have developed a protocol for random combinational image encryption approach with bit, pixel and block permutations Paper4 proposed a technique to encrypt an image for secure transmission using the digital signature of the image. Methods: The proposed work is developed that provides secured authentication to integrate the image encryption with Elliptic Curve Cryptography to provide security. In this work, transformation operation of the matrix operations are performed on the original image matrix and the transformed image is further encrypted with the help of a key sequence which is generated from the elliptic Curve. The encrypted image will be authenticated using Elliptic Curve Diffie Helman (ECDH) key exchange algorithm5 and finally decrypted by using the key generated from the chosen elliptic curve and then we perform the reverse transformations on the matrix obtained . So after decryption process to acquire the original image. Findings: In this work we can get better security to image ecryption by application of ECC with matrix operations performed on image data. Because ECC has the well attention of researchers and robust mathematical development and top security among the former existing algorithms. As a result Elliptic Curve Cryptography for image data is developed to meet the current security needs. Application: To transmit securely image data over the wireless channels and systems and so on. Currently this work was currently developed in an ad-hoc fashion and it can be further improved with ECC binary field and various measures of security that includes different attacks.

Nowadays, diagnosing patient diseases remotely is a routine and digital medical images analysis as a part of Telecare Medical Information Systems (TMIS) play a fundamental role in early diagnosing and treating most common and serious diseases such as breast cancer. In this context, altering or distorting even a single pixel of a medical image during its transmission over an unsure channel could lead to a wrong diagnosis and harm patient health, induce damaging delays. Therefore the security and privacy of the transmitted medical images must be addressed most seriously. Several techniques are proposed in the literature to address these issues using different techniques such as chaos theory, more recently, elliptic curves cryptography (ECC) or improved classical methods such as linear cryptography. In this paper, we address the security level concern of an image encryption technique combining ECC with Hill cipher (ECCHC) which has been recently proposed by Dawahdeh et al [13]. Our study rises concerns about some weaknesses and flaws of the analyzed encryption scheme against some plain-text and known plain-text attacks. In addition, and not least issue, it is found that the key length used in Dawahdeh et al. scheme is not sufficiently large to be robust against brute force attack. To fix the found flaws and to improve the encryption scheme, a generalized cryptosystem is suggested. In the enhanced version, the key matrix negotiation is redefined to a cipher that combines a modified EC Integrated Encryption Scheme (ECIES) and the linear multiplication matrix is generalized to key matrix of (2n × 2n), n > 2 to counter efficiently the exhaustive search attack. The effectiveness of the proposed version is evaluated and verified through extensive experimentation and most recent available security tools. Compared with the state-of-the art techniques, the proposed version exhibits excellent security features and can resist to various knowing attacks.

Session Initiation Protocol(SIP) provides authentication and session key agreement to ensure the security of the successive session.In 2010,Yoon et al.(YOON E-J,YOO K-Y.A three-factor authenticated key agreement scheme for SIP on elliptic curves.NSS '10: 4th International Conference on Network and System Security.Piscataway: IEEE,2010: 334-339.) proposed a three-factor authenticated key agreement scheme named TAKA_SIP for SIP.However,the scheme is vulnerable to insider attack,server-spoofing attack,off-line password attack,and losing token attack.Moreover,it does not provide mutual authentication.To overcome these flaws of TAKA_SIP,a new three-factor authentication scheme named ETAKA_SIP based on Elliptic Curve Cryptosystem(ECC) was proposed.ETAKA_SIP,on the basis of elliptic curve discrete logarithm problem,provides higher security than TAKA_SIP.It needs 7 elliptic curve scalar multiplication operations,1 additional operation and up to 6 Hash operations,and of high efficiency.