1. Introduction
Modern day technology is highly interlinked with digital communication over the internet, however, the privacy of data during transmission is a highly important issue. For instance, when using multimedia for e-business, military organization, medical purposes, education, meteorology, space organization, etc., privacy and security are of the utmost interest [
1]. Thus, due to the immense threat posed by hackers and hacking tools, there is an ongoing need for efficient cryptographic techniques to protect sensitive information provided over open network channels. In response to this need, a number of symmetric and asymmetric cryptographic techniques are in use to safeguard sensitive information. ECC is one of the newest and most popular asymmetric approaches used to support encryption techniques. The primary advantage of ECC lies in the fact that it is hard to solve the underlying elliptic curve discrete logarithm problem (ECDLP). Furthermore, owing to its shorter key length, ECC systems are more demanding and widely applicable. It is imperative to mention that the RSA system provides security with a 1024–3072 bit-length key, whereas ECC provides the same security with only a 160–256 bit-length key [
2]. ECC has gained a respectable status among cryptographic researchers due to its low memory use, bandwidth savings, and lower power consumption in hardware implementations [
3,
4,
5]. Digital images need to be securely transferred over communication channels while considering a reliable encryption scheme. Despite several advantages of ECC in image encryption, several issues must be considered before designing a cryptosystem, viz. key size, key space, and the chosen elliptic curve. The primary focus of encryption schemes is to enhance key strength in order to resist an exhaustive key search attack. If proper attention is paid when choosing elliptic curves, then the best known attacks are considerably weaker against solving ECDLP compared to the best algorithms for solving the discrete logarithm problem [
6].
Recently, Dawahdeh et al. [
7] proposed an encryption scheme combining the elliptic curve and Hill cipher techniques. This scheme is mainly intended to protect image data while ensuring fast transmission of highly correlated multimedia data. The idea underlying the said scheme is to change the Hill cipher technique from symmetric to asymmetric using the generated parameters of ECC to develop the secret key. However, there is a serious loophole in the existing scheme in the form of secret keys, which makes it vulnerable to brute force attacks.
The use of ECC in combination with other symmetric techniques has been widely used in image and text encryption schemes [
2,
8,
9,
10,
11,
12,
13]. In [
8], the authors presented an efficient cryptosystem using an elliptic curve over finite rings in combination with S-boxes. The scheme in [
12] proposed text encryption that could encrypt any script with defined ASCII values by making use of elliptic curves. Moreover, in [
9] the authors made use of elliptic curves to simultaneously encrypt and compress multimedia data. On the other side, for instance, in Khoirom et al. [
14], used cryptanalysis against the scheme in [
9] to expose the secret key from the public key. Furthermore, Abd El-Latif et al. [
10] presented an algorithm using a chaotic map and the elliptic curve which, while it seemed difficult to hack due to the complex structure of key generators, was broken through cryptanalysis by Hong et al. [
15]. In this paper, cryptanalysis of the scheme proposed in [
7] is carried out, revealing that the strength of the secret key can be easily broken through an exhaustive key search. Due to the linearity of the Hill cipher, it is vulnerable against smaller key spaces. Furthermore, the same weaker secret key is used to generated the self-invertible matrix, and is used for both encryption and decryption.
In this work, we examine the security of the scheme in [
7] and develop a corresponding efficient and improved version for greater security of image data. Keeping in mind that ECC and affine Hill ciphers are popular encryption techniques that can provide better performance and higher levels of security, we revamp the existing scheme by replacing the Hill cipher by an affine Hill cipher in the key domain of
and
. Furthermore, the confusion and diffusion architecture of the scheme is covered via a 3D Arnold map using ECC and bit-wise XOR operations. In addition, the chaotic behavior of this novel scheme makes it more efficient, unpredictable, and strong in resisting illicit hackers [
16,
17]. Thus, systems modified with chaotic maps shows more efficacy than the normal symmetric and asymmetric systems. It is appropriate to mention that higher-dimensional chaotic maps are known for their high quality of encryption. In this direction, a combination of a private and a public technique is used to design a secure algorithm for image encryption in the presence of higher-dimensional chaotic maps [
18]. The numerical outcomes demonstrate the efficiency and stalwartness of the proposed scheme. Furthermore, detailed comparisons with existing schemes [
7,
9,
10,
13,
19,
20] serve to validate the higher efficiency and security of the proposed scheme.
The outline of the article is as follows:
Section 2 presents the basic mathematical theories involved;
Section 3 highlights the encryption scheme of the cryptosystem [
7]; in
Section 4, the cryptanalysis of the scheme [
7] and its improvement are explained; and
Section 5 presents a demonstration of the improved version. Finally, experimental analysis is carried out in
Section 6, detailed numerical simulations are presented in
Section 7, and the conclusions of the work are presented in
Section 8.