An Image Encryption and Text Encryption Scheme Based on an Elliptic Curve using Montgomery Curve and Haga s function

Medical images demand robust privacy protection, driving research into advanced image encryption (IE) schemes. However, current IE schemes still encounter certain challenges in both security and efficiency. Fractional-order Hopfield neural networks (HNNs) demonstrate unique advantages in IE. The introduction of fractional-order calculus operators enables them to possess more complex dynamical behaviors, creating more random and unpredictable keystreams. To enhance privacy protection, this paper introduces a high-performance medical IE scheme that integrates a novel 4D fractional-order HNN with a differentiated encryption strategy (MIES-FHNN-DE). Specifically, MIES-FHNN-DE leverages this 4D fractional-order HNN alongside a 2D hyperchaotic map to generate keystreams collaboratively. This design not only capitalizes on the 4D fractional-order HNN’s intricate dynamics but also sidesteps the efficiency constraints of recent IE schemes. Moreover, MIES-FHNN-DE boosts encryption efficiency through pixel bit splitting and weighted accumulation, ensuring robust security. Rigorous evaluations confirm that MIES-FHNN-DE delivers cutting-edge security performance. It features a large key space (2383), exceptional key sensitivity, extremely low ciphertext pixel correlations (<0.002), excellent ciphertext entropy values (>7.999 bits), uniform ciphertext pixel distributions, outstanding resistance to differential attacks (with average NPCR and UACI values of 99.6096% and 33.4638%, respectively), and remarkable robustness against data loss. Most importantly, MIES-FHNN-DE achieves an average encryption rate as high as 102.5623 Mbps. Compared with recent leading counterparts, MIES-FHNN-DE better meets the privacy protection demands for medical images in emerging fields like medical intelligent analysis and medical cloud services.

<abstract> <p>Elliptic curve (EC) cryptography supplies an efficient, secure, and lightweight method for executing computer cryptographic protocols. Its widespread use in various applications, including secure communications, digital signatures, and key agreement protocols, highlights its importance in modern computing. Moreover, EC-based image encryption is gaining popularity in cryptography as it offers strong protection with a relatively smaller key size than other famous cryptosystems. Inspired by this, we proposed a novel image encryption scheme that leverages ECs over a binary extension field (BEF). This approach also reduces computational workload using EC over BEF instead of large primes. Also, BEF can represent large numbers in a compact form, which is helpful in applications that require efficient data storage and transmission. Our scheme involves three main steps. Initially, we utilize points of an EC over a BEF and a piecewise function to mask the plain image. Next, to introduce a high level of confusion in the plain text, we create a substitution box (S-box) based on the EC and operation of BEF of order 256, which is then used to permute the pixels of the masked image. Finally, we generate pseudo-random numbers (PRNs) using EC coordinates and BEF characteristics to create diffusion in the image and obtain a cipher image. In addition, we accomplished computational experiments demonstrating that our proposed cryptosystem provides excellent security against linear, differential, and statistical attacks compared to existing cryptosystems.</p> </abstract>

PSO-based image encryption scheme using modular integrated logistic exponential map

Chaos and compressive sensing based novel image encryption scheme

In this paper, a novel chaotic circuit with one memcapacitor is designed, which has abundant dynamic behaviors. As a potential application, combining the DNA binding mode and the characteristics of the chaotic system, a new image encryption scheme is proposed. Firstly, the original image is processed and generates a set of hash values by the SHA-3 algorithm. The generated hash value and original image are performed XOR operation. The hash values are processed to generate the initial value of the chaotic system by the Hamming distance. Furthermore, the elliptic curve with the hyperchaotic sequence is used to construct the Hill encryption matrix, and the plaintext image is permuted and encrypted. At last, the proposed chaotic system is used to scramble the image. The simulation results and theoretical analysis show that the chaotic system has abundant dynamic behaviors, and the proposed algorithm has a better anti-interference ability for image and information encryption.

Optical image authentication and encryption scheme with computational ghost imaging

This paper presents a new scheme for simultaneous image compression and encryption. First, the approach of wavelet packet transform is used to decompose an image. Herein, the image is divided into four different types and self-adaptive approaches are designed to process the four signals. Second, a fleeting image encryption algorithm based on multi-chaotic systems is proposed to protect the security of the image. The above method not only balances the compression ratio and reconstruction quality, but also greatly improves the encryption speed and transmission security of the image. More importantly, the proposed scheme solves a long-standing contradiction that a signal should be first compressed or encrypted, which often appears in traditional image compression and encryption systems. Computer simulations and numerical analysis validate that the proposed scheme possesses superior security, high efficiency and promising practical value for images encryption and transmission.

Due to the extensive demand for digital images across all fields, the security of multimedia data over insecure networks is a challenging task. The majority of the existing modern encryption schemes are merely developed that ensure the confidentiality of the image data. This manuscript presents a new image encryption scheme that ensures confidentiality, user authentications, and secure key sharing among the communicating parties. Initially, the users share a secret parameter using Diffie-Hellman over the elliptic curve and pass it through SHA-256. Afterwards, the proposed scheme uses the first 128-bits for the confidentiality of the data, while the remaining 128-bits are for authentication. In the encryption algorithm, the confusion module is achieved by affine power affine transformation. At the same time, the diffusion module is attained through highly nonlinear sequences, which are generated through the elliptic curve. Experimental testing and the latest available security tools are used to verify the effectiveness of the proposed algorithm. The simulation findings and the comparison of the proposed scheme with the existing image encryption techniques reveal that the suggested scheme offers a sufficient degree of security. Furthermore, the outcome of the simulation results divulges several advantages of the proposed scheme, including a large key space, resistance to differential attacks, high efficiency, and strong statistical performance.

Image compression scheme proposed by researchers have no consideration of security. Similarly image encryption scheme proposed by the authors have no consideration of image size. In this paper a simultaneous image compression and encryption scheme is discussed. The order of the two processes viz. compression and encryption is EC i.e. image encryption is performed first then the image compression is applied. For image encryption a symmetric key cryptography multiplicative cipher is used. Similarly for compression Discrete Cosine Transform is used. Image Compression is concerned with minimizing the number of bit required to represent an image. The compression can be lossless or lossy. Image Encryption is hiding image from unauthorized access with the help of secret key that key can be private or public.

This paper is simply the gathering of recent developments in the field of image security and presents further improvements in the same field. Images are the most important utility of our life. They are used in many applications. There are two main goals of image security: image encryption and authentication. During the past years, several image encryption and authentication algorithms have been proposed. Image encryption techniques scramble the pixels of the image and decrease the correlation among the pixels, such that the encrypted image cannot be accessed by unauthorized user. Chaotic encryption method seems to be much better day by day. Chaotic encryption technique is the new way of cryptography. Many chaos-based encryption methods have been proposed in the last decade. This paper presents a survey of different chaotic image encryption schemes proposed in the last decade. The paper also presents different image encryption and authentication schemes and discusses the problems and resolution associated with them. Emphasizing the image security, the paper discusses a hybrid scheme for image encryption and authentication, such that further advances in the field of image security can be enhanced.

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA) [2]. It is well known that the problem of discrete logarithm is NP-hard on group on elliptic curve (EC) [5]. The orders of groups of an algebraic affine and projective curves of Edwards [3, 9] over the finite field Fpn is studied by us. We research Edwards algebraic curves over a finite field, which are one of the most promising supports of sets of points which are used for fast group operations [1]. We construct a new method for counting the order of an Edwards curve [F ] d p E over a finite field Fp . It should be noted that this method can be applied to the order of elliptic curves due to the birational equivalence between elliptic curves and Edwards curves. The method we have proposed has much less complexity 22 O p log p at not large values p in comparison with the best Schoof basic algorithm with complexity 8 2 O(log pn ) , as well as a variant of the Schoof algorithm that uses fast arithmetic, which has complexity 42O(log pn ) , but works only for Elkis or Atkin primes. We not only find a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, but we additionally find a general formula by which one can determine whether a curve [F ] d p E is supersingular over this field or not. The symmetric of the Edwards curve form and the parity of all degrees made it possible to represent the shape curves and apply the method of calculating the residual coincidences. A birational isomorphism between the Montgomery curve and the Edwards curve is also constructed. A oneto- one correspondence between the Edwards supersingular curves and Montgomery supersingular curves is established. The criterion of supersingularity for Edwards curves is found over F pn .

The security of digital images is an important issue that has been receiving considerable attention in the recent past. Different image encryption techniques have been proposed in the literature. Among the fundamental theories in the number theory, we can find the elliptic curve (EC) which is widely used to construct cryptographic primitives. This paper investigates the security of image encryption schemes based on elliptic curves cryptography (ECC) and Chaos theory. More precisely, in this paper, we propose a new image encryption scheme that utilize a new mapping method based on Piecewise Linear Chaotic Map (PWLCM) that converts each pixel of plain image into a point on an elliptic curve. Encryption and decryption process are given in details. After applying encryption, security analysis is performed to show that our scheme cannot only achieve good encryption, but also resist the statistical attacks.

In this study, the authors introduce new Montgomery and Edwards form elliptic curves targeted at the 256-bit security level. To this end, they work with three primes, namely $p_1:= 2^{506} - 45$p 1 :=2506-45, $p_2:= 2^{510} - 75$p 2 :=2510-75 and $p_3:= 2^{521} - 1$p 3 :=2521-1. While $p_3$p 3 has been considered earlier in the literature, $p_1$p 1 and $p_2$p 2 are new. They define a pair of birationally equivalent Montgomery and Edwards form curves over all the three primes. Efficient 64-bit assembly implementations targeted at Skylake and later generation Intel processors have been made for the shared secret computation phase of the Diffie-Hellman key agreement protocol for the new Montgomery curves. Curve448 of the Transport Layer Security, Version 1.3 is a Montgomery curve which provides security at the 224-bit security level. Compared to the best publicly available 64-bit implementation of Curve448, the new Montgomery curve over $p_1$p 1 leads to a 3-4% slowdown and the new Montgomery curve over $p_2$p 2 leads to a 4.5-5% slowdown; on the other hand, 29 and 30.5 extra bits of security, respectively, are gained. For designers aiming for the 256-bit security level, the new curves over $p_1$p 1 and $p_2$p 2 provide an acceptable trade-off between security and efficiency.

With the wide application of digital images in the network, the problems of information security and transmission efficiency need to be solved urgently. Fractal encoding as an efficient compression method, its security is not guaranteed. To solve these problems, this paper proposes a new image compression and encryption scheme based on chaotic map and frequency division joint compression coding, which uses the combination of fractal encoding and adaptive-thresholding sparsification to compress images. Arnold scrambling and chaos-based plane scrambling diffusion are embedded in two compression processes respectively. In addition, an efficient encryption algorithm is designed based on the coupling-enhanced chaotic map, which encrypt the compressed data as a whole through simultaneous scrambling of parent blocks and sub-blocks and zigzag round-trip diffusion. The simulation results demonstrate that the proposed image compression and encryption scheme is suitable for gray and color images, and can achieve higher compression ratio and improve the efficiency of fractal compression. The designed encryption algorithm is reliable, and more efficient than several advanced image encryption schemes.

Chaotic maps used to shuffle and manipulate the image pixels are important for image encryption (IE). In this study, a novel 2D optimized chaotic map (OPMAP) using a triple-objective differential evolution (TODE) algorithm is presented for IE. A model for OPMAP with eight decision variables is empirically designed, and then its variables are determined utilizing TODE through minimizing a triple-objective function that involving Lyapunov exponent (LE), entropy and 0–1 test. OPMAP is assessed with respect to credible measurements like bifurcation, 3D phase space, LE, 0–1 test, permutation entropy (PE) and sample entropy (SE). The capability of OPMAP is then verified through an IE scheme including permutation and diffusion through various cryptanalyses: key space 2298, mean entropy 7.9995, mean correlation 13.61E-5, number of pixels changing rate (NPCR) 99.6093, unified average changing intensity (UACI) 33.4630 and encryption processing time (EPT) 0.2919 (s). A detailed review of IE schemes reported elsewhere is presented and IE performance of OPMAP is also validated by comparison with those IE schemes with and without optimization used. The 2D-OPMAP-based IE is faster and has low computational complexity. Moreover, the proposed it shows better cryptanalysis results for the most of the comparisons.