Reversible medical image cryptography using spatial XOR-rotation and chaos-driven permutation and diffusion schemes.

Reversible medical image cryptography using spatial XOR-rotation and chaos-driven permutation and diffusion schemes - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( Lock Locked padlock icon ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide PERMALINK Copy As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Mar 7;16:12536. doi: 10.1038/s41598-026-41579-z Search in PMC Search in PubMed View in NLM Catalog Add to search Reversible medical image cryptography using spatial XOR-rotation and chaos-driven permutation and diffusion schemes Dola Sundeep Dola Sundeep 1 Department of Electronics and Communication Engineering, Indian Institute of Information Technology Design and Manufacturing (IIITDM), Jagannathagattu Hill,, Kurnool, Andhra Pradesh 518008 India Find articles by Dola Sundeep 1, ✉ , Kovuri Umadevi Kovuri Umadevi 2 Department of Pathology, MNJ Institute of Oncology and Regional Cancer Center, Red Hills, Hyderabad, Telangana 500004 India Find articles by Kovuri Umadevi 2 , Bhagya Prasad Bugge Bhagya Prasad Bugge 3 Department of ECE, S.R.K.R Engineering College, Bhimavaram, Andhra Pradesh 534204 India Find articles by Bhagya Prasad Bugge 3 , C Chandrasekhara Sastry C Chandrasekhara Sastry 4 Department of Mechanical Engineering, Indian Institute of Information Technology Design and Manufacturing (IIITDM), Jagannathagattu Hill, Kurnool, Andhra Pradesh 518008 India Find articles by C Chandrasekhara Sastry 4 , Sachin Salunkhe Sachin Salunkhe 5 Department of Mechanical Engineering, Gazi University, Ankara, Turkey Find articles by Sachin Salunkhe 5 , Robert Cep Robert Cep 6 Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic Find articles by Robert Cep 6 Author information Article notes Copyright and License information 1 Department of Electronics and Communication Engineering, Indian Institute of Information Technology Design and Manufacturing (IIITDM), Jagannathagattu Hill,, Kurnool, Andhra Pradesh 518008 India 2 Department of Pathology, MNJ Institute of Oncology and Regional Cancer Center, Red Hills, Hyderabad, Telangana 500004 India 3 Department of ECE, S.R.K.R Engineering College, Bhimavaram, Andhra Pradesh 534204 India 4 Department of Mechanical Engineering, Indian Institute of Information Technology Design and Manufacturing (IIITDM), Jagannathagattu Hill, Kurnool, Andhra Pradesh 518008 India 5 Department of Mechanical Engineering, Gazi University, Ankara, Turkey 6 Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic ✉ Corresponding author. Received 2025 Dec 1; Accepted 2026 Feb 20; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13087248  PMID: 41794819 Abstract The rapid growth of telemedicine, cloud-assisted diagnostics, and picture archiving systems has made the secure handling of medical images a central requirement in modern healthcare. Yet many existing medical image ciphers are either computationally heavy, which often require complex arithmetic, multiple chaotic maps, or public-key primitives that hinder implementation on resource-constrained platforms and complicate formal security tuning. To address these limitations, we designed two lightweight, fully reversible image encryption schemes that achieve near-ideal statistical security while remaining practical for end-to-end clinical workflows. We designed two complementary symmetric ciphers that act directly in the pixel domain. The first is a spatial pixel-wise rotation and XOR-based lightweight encryption scheme (SPiRAL), that links pixels through chained XOR operations along image rows and columns, combined with index-dependent circular rotations and a lightweight key-driven permutation masking layer. The second is a chaotic reordering and nonlinear XOR encryption (CHRONEX), which employs coupled logistic maps to generate a key-dependent permutation of pixel indices followed by nonlinear S-box-based XOR diffusion. The experiments show that SPiRAL and CHRONEX produce cipher images with entropy values above 7.999 bits, number of pixels change rate (NPCR) and unified average changing intensity (UACI) with maximum of and respectively, and almost zero neighbour correlation, while guaranteeing exact recovery of the original images. Statistical significance testing confirms that the chaos-enhanced CHRONEX scheme, in particular, offers consistently higher randomness and differential robustness than competing techniques. These results demonstrate that carefully structured pixel-domain primitives can deliver transaction level security for medical images without sacrificing reversibility or real-time feasibility, making the proposed ciphers suitable for deployment from edge devices to hospital-scale archives. Keywords: Cryptography, Diffusion, Encryption, Entropy, Security Subject terms: Engineering, Mathematics and computing Introduction The growth of digital media and internet access has amplified concerns surrounding intellectual property violations, such as unauthorized copying, editing, and distribution of digital content, including images, audio, and video. The transmission of multimedia information, especially images, over open networks has become increasingly frequent and vulnerable to security threats. The rapid expansion of telemedicine, cloud-assisted diagnostics, and large-scale medical archives has made secure handling of medical images a critical requirement in modern healthcare systems. Recent survey work shows that contemporary medical image encryption and compression schemes still struggle to simultaneously meet demanding confidentiality, integrity, and real-time performance constraints in clinical workflows 1 , while a systematic review of AES-centred cryptographic frameworks for multimedia data highlights ongoing challenges in key management, implementation overhead, and resistance to emerging attacks 2 . At the level of individual ciphers, researchers have explored diverse confusion and diffusion architectures, including ternary-value exclusive-OR logic for grayscale image encryption 3 , a 3D axis-aligned bounding-box representation driven by multi-wing hyper-chaotic dynamics 4 , and OptiSecure-3D, which integrates stacked autoencoders with optimized 3D chaotic maps for compressed image encryption 5 . Parallel efforts in visual cryptography address key-management and usability issues by using QR-code-based, expansion-free extended VCS with meaningful shares 6 and progressive meaningful visual cryptography that produces non-expanding, visually plausible grayscale medical shares 7 . Beyond these general and visual-cryptography mechanisms, a rich body of work has focused specifically on medical image security. DNA-inspired and chaos-enhanced constructions combine DNA encoding with elliptic-curve cryptography to achieve strong confidentiality for diagnostic images 8 , or employ multiple chaotic maps with DNA diffusion operations tailored to medical data protection 9 . Chaotic map driven medical ciphers further strengthen confusion and diffusion through Laplace transform augmented substitution permutation structures 10 , stacked multi-image representations with Baker-map-controlled block processing for simultaneous encryption of multiple medical images 11 , and MILE-based chaotic maps coupled with multi-level Q-sequence matrices to enhance randomness and differential robustness 12 . Complementary transform- and curve-based approaches combine dual-transform optical cryptography and hyper-elliptic curve cryptography into a two-layer image protection pipeline 13 , while lightweight colour-image schemes relying on 2-D Henon chaotic maps and LFSR-generated keystreams provide fast, statistically secure encryption suitable for resource-constrained platforms 14 . Application-specific frameworks target facial privacy in UAV-acquired imagery via chaos DNA-based encryption of face regions 15 . In healthcare-focused deployments, security requirements extend beyond standalone algorithms to full-stack architectures that integrate IoT devices, embedded platforms, and cloud services. An IoT-enabled e-healthcare framework secures both sensor readings and associated medical images using a combined chaotic system with selective shuffling and inter-/intra-pixel diffusion, implemented on Raspberry Pi nodes and ThingSpeak cloud infrastructure 16 . At the hardware level, integrity-verified lightweight ciphering on FPGA/SoC platforms employs Lorentz-attractor based diffusion, LFSR-driven confusion, CBC chaining, and Whirlpool hashing to protect DICOM images and detect tampering during embedded transmission 17 . In parallel, hybrid public-key schemes for cloud-hosted healthcare data use group keys derived from RSA and adaptive elliptic-curve cryptography to selectively protect sensitive attributes in electronic medical records while reducing computational cost compared with single-algorithm designs 18 . These developments collectively illustrate a clear trajectory from generic multimedia ciphers toward domain-adapted, chaos- and DNA-enhanced, IoT-aware cryptographic frameworks explicitly engineered for secure medical image communication. In recent years, a variety of chaos driven and hybrid cryptographic schemes have been proposed to secure medical imagery. A cryptographic framework for smart healthcare environments combines symmetric AES encryption of DICOM images with RSA based key management and secure storage and retrieval modules deployed across acquisition, transmission and archiving stages in 19 . A dynamically parameterized three dimensional hyperchaotic cat map is used to generate key dependent permutation matrices and diffusion sequences. So that pixel positions and gray levels are simultaneously scrambled and modified through iterative chaotic updates in 20 . In 21 a two dimensional chaotic map is exploited in to drive both confusion and diffusion: the map’s orbits produce permutation indices and nonlinear modular operations that update each pixel using its neighbors and a keystream. Refined trigonometric maps have also been engineered specifically for medical image protection in 22 : a refined sine-derived chaotic map generates highly sensitive trajectories that control block permutation and pixel-wise XOR/addition diffusion in a telemedicine setting. An improved sine tangent map yields enhanced chaotic sequences that feed position shuffling and multi round gray level updating for medical images is given in 23 . For real time IoT applications, improved chaotic sequences are embedded in a lightweight pipeline that interleaves block permutation, circular shifts and modular diffusion, enabling high-throughput encryption of streaming medical data is given in 24 . Region based protection is considered in 25 , where advanced zigzag scanning and a 2D logistic-sine map perform ROI-driven block scrambling followed by chaotic diffusion, so that only diagnostically relevant regions are strongly encrypted. A resource optimized selective scheme further combines multiple chaotic systems to encrypt salient regions via cascaded confusion and diffusion layers while leaving background areas lightly processed to reduce computation 26 . Finally, chaos and DNA coding are jointly used in 27 , where pixel values are DNA encoded, permuted under key controlled chaotic sequences, and diffused using DNA addition and complement rules, producing a cipher image whose statistics are dominated by the underlying chaotic DNA operations. Although a wide range of chaos-based, transform-domain, DNA-inspired, and public-key image ciphers have been proposed for medical data, many of these schemes are multi-stage and rely on heavy components such as DWT/DCT stacks, optical transforms, or elliptic and hyper-elliptic curve operations, which increase computational cost and implementation complexity in practice. Multi-map chaotic diffusion and DNA-domain manipulation further enlarge the key and parameter spaces, making hardware realization, fixed-point tuning, and formal verification difficult, especially on resource constrained IoT sensors and embedded clinical devices. Several works are evaluated mainly through entropy, NPCR, and UACI scores on small offline datasets, with limited consideration of exact reversibility, unified handling of both grayscale and colour modalities, and tight latency budgets in end to end e-health architectures. To address these limitations, we propose two complementary lightweight symmetric encryption schemes that operate directly in the spatial pixel domain, thereby avoiding heavy transform stacks and big-integer arithmetic. In this work, we focus exclusively on cryptography-based protection of medical images and introduce two complementary, fully reversible encryption schemes that are explicitly tailored to clinical workflows. Building on the general permutation and diffusion paradigm and existing chaos-based ciphers, we redesign the core operations so that they act directly in the pixel domain and preserve strict losslessness, which is essential for diagnostic use. The first method operates entirely in the spatial domain and combines pixel-wise XOR diffusion with index-adaptive row-column rotations, thereby enforcing strong local dependencies while retaining the geometric structure of the image grid. This design yields a lightweight cipher that can be implemented on resource-constrained imaging devices, yet still delivers high confusion and diffusion. This makes it resistant to common statistical and differential attacks while guaranteeing exact reconstruction of diagnostic content after decryption. The second method CHRONEX, applies a key-driven chaotic permutation to the flattened image followed by cumulative S-box driven XOR diffusion, providing a global permutation and diffusion technique with high sensitivity to initial conditions, and strong avalanche behaviour. Taken together, these two schemes form a flexible toolbox for privacy-aware medical imaging: the spatial row - column cipher is suitable for low-latency integration in acquisition and viewing pipelines, whereas CHRONEX offers a more aggressive, chaos-driven protection layer for storage, archiving, and transmission over untrusted networks. While the individual building blocks (XOR diffusion, circular shifts, chaotic maps, and S-boxes) are well established, their specific combination into fully reversible, pixel-domain designs, evaluated systematically on medical image datasets with entropy, NPCR, UACI, correlation analysis, and statistical significance testing, constitutes the main novelty and practical contribution of this study for telemedicine platforms, hospital PACS systems, and other security-critical medical applications. The proposed medical image cryptography techniques The proposed technique-I (SPiRAL) In this work, we propose a novel two layer SPiRAL technique, which combines chained XOR diffusion with index-adaptive row-column rotations and a key-driven permutation masking layer for secure and reversible medical image protection. Let denote an input grayscale image, where M and N are the numbers of rows and columns, respectively, and each entry I ( i , j ) represents an 8-bit pixel intensity. The proposed cipher operates directly on this spatial representation and, for each index k , applies a local XOR-based diffusion stage followed by an index-adaptive spatial scrambling stage on the k -th row and k -th column. The resulting intermediate image is then flattened and processed by a second layer that performs a key-dependent permutation and XOR masking driven by a pseudorandom generator seeded with the secret key K . All stages are strictly invertible, ensuring that the original image can be recovered without any loss of diagnostic content. Encryption procedure For a grayscale image , the encryption algorithm first applies the spatial diffusion and scrambling layer. The proposed SPiRAL encryption technique is given in Algorithm-I. Let 1 At each index k in ( 1 ), two operations are performed on the k -th row and k -th column of a working copy J of the image. Step 1: Pixel-wise XOR diffusion. The algorithm first establishes strong local dependencies between neighbouring pixels by chaining XOR operations along the selected row and column. The k -th row and k -th column are updated as 2 3 where denotes bitwise XOR. After the diffusion step in ( 2 ) and ( 3 ), each pixel in the processed row depends on all preceding pixels in that row, and each pixel in the processed column depends on all pixels above it. This cumulative dependency amplifies the avalanche effect and complicates any attempt to infer original values from local statistics. Step 2: Index-adaptive rotation scrambling. To further decorrelate neighbouring pixels and conceal local texture patterns, the diffused row and column undergo circular rotations whose direction and magnitude are determined by the same index k . Let be a small positive threshold (in this work, ). For each k , the following rule is applied: If , perform a circular left rotation of the k -th row by k positions and a circular upward rotation of the k -th column by k positions. If , compute and perform a circular right rotation of the k -th row by s positions and a circular downward rotation of the k -th column by s positions. These index-controlled rotations act as spatial permutations that spread local structures over multiple positions and increase the visual randomness of the intermediate image J . In combination with the XOR diffusion in ( 2 ) and ( 3 ), they realise a compact permutation and diffusion mechanism entirely in the pixel domain. Step 3: Key-dependent permutation and XOR masking. After processing all indices , the spatially encrypted image J is passed through a second, key-driven layer. Let be the total number of pixels. The matrix J is first flattened in row-major order to obtain a vector A cryptographically secure pseudorandom number generator is initialised with the secret key K as its seed. Using , a random permutation of the indices is generated, together with a keystream The permuted and masked vector C is then computed as 4 5 Finally, C is reshaped back to size in row-major order to obtain the ciphertext image . This second layer ensures that even if an attacker were to partially exploit the structure of the spatial operations, the pixel positions and intensities are globally permuted and masked in a key-dependent manner. The block diagram of the proposed SPiRAL encryption and decryption process is given in Fig. 1 . Fig. 1. Open in a new tab Block diagram of the proposed technique-I (SPiRAL). For colour images, the input is decomposed into three channels, R , G , and B . The two-layer encryption pipeline, defined by ( 1 ) , ( 2 ) and ( 3 ), the index-adaptive rotations, and the subsequent key-dependent permutation and XOR masking in ( 4 ) and ( 5 ), is applied independently to each channel, and the encrypted channels are finally recombined to form the colour cipher image. Decryption procedure Decryption inverts the encryption steps in exact reverse order, ensuring bit-wise reconstruction of the original image. For a given encrypted image of size , the decryption first removes the key-dependent masking and permutation to recover the intermediate spatially encrypted image J , and then reverses the spatial operations index by index. The decryption process is given in Algorithm-2. Step 1: Inverse permutation and XOR unmasking. Let and flatten in row-major order to obtain The same pseudorandom generator is initialised with the identical seed K , producing the same permutation vector and keystream S . The keystream masking in ( 5 ) is first inverted as after which the inverse permutation is applied by filling an initially empty vector F according to Reshaping F back to size in row-major order yields the intermediate image J , which corresponds to the output of the spatial diffusion and scrambling layer during encryption. Step 2: Inverse index-adaptive rotation. The index-adaptive rotations are then undone in reverse order of k . Let and traverse 6 For each k in ( 6 ), the circular shifts are inverted using the same threshold . If , the k -th column is circularly shifted downward by k positions and the k -th row is circularly shifted to the right by k positions. If , the shift amount is recomputed as , and the column is circularly shifted upward by s positions while the row is circularly shifted to the left by s positions. This step restores the spatial ordering that existed immediately after the XOR diffusion defined in ( 2 )–( 3 ) during encryption. Step 3: Reverse pixel-wise XOR diffusion. Once the rotations have been inverted, the XOR chains are reversed by processing the affected row and column in the opposite directions. Specifically, the k -th column is traversed from bottom to top, and each pixel is updated as 7 and the k -th row is traversed from right to left, with 8 Because XOR is an involutive operation and the traversal order is reversed, the reverse diffusion in ( 7 )–( 8 ) exactly cancels the forward diffusion introduced by ( 2 )–( 3 ), recovering the original pixel values at index k . For colour images, the same decryption stages are applied independently to the encrypted R , G , and B channels: first the key-dependent permutation and XOR unmasking (Step 1), then the inverse index-adaptive rotations (Step 2), and finally the reverse XOR diffusion (Step 3). Since both the global permutation and masking layer and the spatial XOR/rotation layer are bijective for each fixed key K , the overall mapping from plaintext image to ciphertext and back is one-to-one and onto, ensuring that no diagnostic information is lost in the encryption–decryption cycle. The S-box generated using the is given below. Algorithm 1. Open in a new tab The Encryption Algorithm for the proposed technique-I (SPiRAL) Algorithm 2. Open in a new tab The decryption algorithm for the proposed technique-I (SPiRAL) The proposed technique-II (CHRONEX) Encryption process Consider a grayscale medical image I of size . The total number of pixels is given by 9 For processing, the two-dimensional image is converted into a one-dimensional vector of length M by stacking the rows of I in raster order. The proposed encryption process of CHRONEX is given in Algorithm-3. The CHRONEX encryption process consists of two main stages: Chaotic permutation generation with coupled logistic maps Keyed S-box generation and nonlinear XOR diffusion. Stage-1: Chaotic permutation generation with coupled logistic maps Two internal state variables and are used to drive a simple coupled chaotic mechanism. They are initialized from integer parameters a , b and secret keys and through key-stretching functions 10 where and map the integer inputs to real values in the open interval (0, 1). The logistic control parameters and are selected adaptively from the remaining integer parameters c , d , x , y as 11 so that both and lie in a strongly chaotic regime. A coupling bias 12 is derived from the parameter p and the secret keys through a suitable normalization function . For each flattened pixel index i in the range , the coupled logistic states are updated as 13 14 and the combined chaotic sample is formed as 15 Collecting all yields the chaotic sequence . The permutation vector P is then defined as the index order that sorts this sequence in ascending order. Using P , the permuted pixel vector is obtained from the flattened image vector via 16 The mapping in ( 16 ) breaks the original spatial adjacency of pixels and provides the confusion component of the CHRONEX cipher. Stage-2: Keyed S-box generation and nonlinear XOR diffusion To introduce strong diffusion and nonlinearity, CHRONEX employs a random S-box and a keystream that are both derived from the secret keys. First, a seed 17 is computed from using a deterministic hash-like function . This seed initializes a pseudorandom number generator (PRNG), which is used to obtain: a random S-box , defined as a permutation of ; a keystream with . The encrypted one-dimensional sequence is then produced by a chained, S-box driven XOR diffusion. The first element is computed as 18 and for each subsequent index , the recursion 19 20 is applied. Equations ( 18 ) to ( 20 ) ensure that each ciphertext sample depends nonlinearly on the current permuted pixel, the previous ciphertext value and the keystream, thereby enhancing the avalanche effect and improving resistance to differential and linear cryptanalysis. Finally, the encrypted image E is obtained by reshaping back to the original dimensions : 21 For colour images, each channel ( R , G , B ) is flattened, processed with the same permutation and diffusion pipeline described in ( 15 ) to ( 20 ), and then the three encrypted channels are recombined. The block diagram of the proposed CHRONEX encryption and decryption process is given in Fig. 2 . Fig. 2. Open in a new tab Block diagram of the proposed technique-II (CHRONEX). PRNG specification (S-box and keystream generation): In both ciphers, the S-box and keystream are generated using a deterministic pseudorandom number generator (PRNG) seeded by the secret key. In our implementation, we use NumPy’s default_rng with the PCG64 bit-generator (period ), seeded as for CHRONEX and for SPiRAL. The S-box is constructed by applying a Fisher–Yates shuffle to the ordered set using this PRNG, and the keystream is obtained by drawing i.i.d. 8-bit integers uniformly from using the same PRNG instance. Since the PRNG is fully deterministic for a fixed seed, the identical S-box and keystream are reproduced during decryption, ensuring exact reversibility. Concrete definitions of : Let and . We map integer seeds to (0, 1) using: The coupling bias is normalized to (0, 1) as: The PRNG seed for S-box and keystream generation is: Algorithm 3. Open in a new tab The logistic chaos and keyed S-box based encryption algorithm for the proposed technique-II (CHRONEX) Decryption process The decryption process reverses the nonlinear XOR diffusion and the chaotic permutation in the opposite order, ensuring exact reconstruction of the original image. The encrypted image E is first flattened row-wise to obtain of length M defined in ( 9 ). The same chaotic mechanism described in ( 10 ) to ( 15 ) is re-executed with identical parameters and keys to regenerate the chaotic sequence and the corresponding permutation P . The decryption process is given in Algorithm-4. Using the same keys , the PRNG seed in ( 17 ) is recomputed, and the identical S-box and keystream are regenerated. The inverse S-box is then constructed such that 22 The inverse of the nonlinear diffusion recovers the permuted vector . For the first element, 23 and for each , one computes 24 25 Because XOR is involutive and exactly inverts S , ( 23 )–( 25 ) are the precise inverses of the forward diffusion ( 18 )–( 20 ). The inverse permutation is defined through 26 Applying this inverse permutation to the recovered permuted vector yields the original flattened image vector: 27 Thus, the overall CHRONEX mapping from to and back is bijective. Finally, is reshaped to size to obtain the reconstructed image I : 28 For colour images, the decryption steps ( 23 )–( 28 ) are applied independently to each encrypted channel, followed by recombination of the three reconstructed channels. Let denote the number of pixels. In CHRONEX, chaotic sequence generation, permutation application, S-box substitution, and diffusion are each implemented as single linear passes over the M pixels, hence each stage is . However, the permutation P is obtained by sorting (ranking) the chaotic sequence z , which requires time using standard comparison-based sorting. Therefore, the overall time complexity of CHRONEX is , dominated by the sorting step, while the remaining operations are linear; the memory usage is for storing the image and permutation/keystream buffers. (For completeness, SPiRAL does not require sorting and remains time with memory.) If a true linear-time ranking method (e.g., radix/bucket sorting under fixed-precision quantization) is explicitly adopted, the permutation construction can be reduced toward ; otherwise, is the correct bound. Algorithm 4. Open in a new tab The logistic chaos and keyed S-box based decryption algorithm for the proposed technique-II (CHRONEX) Finite-precision and parameter justification (CHRONEX): CHRONEX employs a coupled 2-D logistic map to generate a chaotic sequence used for permutation. In practical digital implementations, chaotic maps are iterated in finite precision, which can introduce quantization, short cycles, and degradation of chaos if the control parameters are not chosen carefully. To mitigate these effects, we (i) select control parameters in the strongly chaotic regime close to 4 (here ), where the logistic map exhibits high sensitivity to initial conditions, and (ii) derive the initial states from 32-bit key-dependent seeds to avoid trivial fixed points (0 and 1) and to maximize the number of reachable states. Furthermore, the map outputs are mixed using a key-dependent coupling bias and are subsequently converted into a permutation by ranking/sorting, which reduces the impact of small numerical perturbations in the absolute values of the chaotic samples. We also regenerate the same chaotic sequence deterministically during decryption using identical arithmetic and key material, ensuring perfect reversibility (MaxDiff in our experiments). Overall, the selected parameter ranges and key-to-state mapping are designed to maintain robust chaotic behavior under finite precision while preserving the deterministic reproducibility required for lossless medical image recovery. Implementation note: All experiments use deterministic IEEE-754 double precision; for strict cross-platform reproducibility, the same numeric type and update order should be preserved. Results and discussion In this section, we present the experimental evaluation of the proposed SPiRAL and CHRONEX schemes on medical image datasets collected from 28 . The test set includes a diverse collection of grayscale medical images as well as colour cancer images, enabling us to assess the robustness of the methods across different modalities and visual characteristics. All quantitative results are reported over 100 colour images and 15 grayscale medical images (115 images total), ensuring that the statistical analysis is not based on a small-sample setting. For each image, we independently evaluate the two proposed encryption schemes, SPiRAL and CHRONEX, which offer complementary security and implementation characteristics. SPiRAL is a lightweight spatial-domain cipher that relies on pixel-wise chained XOR diffusion and index-adaptive row-column rotations, providing strong local confusion and diffusion while preserving a low computational and memory footprint suitable for real-time and resource-constrained medical systems. In contrast, CHRONEX combines key-driven chaotic reordering via coupled logistic maps with a nonlinear S-box-based XOR diffusion layer, introducing both global permutation and strong nonlinearity in the intensity space to harden the cipher against statistical, differential, and brute-force attacks. Together, these two designs demonstrate that it is possible to achieve secure, fully reversible protection of grayscale and colour medical images without degrading diagnostic content, while covering a spectrum of deployment scenarios: from fast, low-complexity encryption (SPiRAL) to higher-entropy, chaos-enhanced protection (CHRONEX) for more adversarial threat models. Table 1 positions SPiRAL and CHRONEX as two points on the security efficiency trade-off: SPiRAL prioritizes deployability (simple pixel-domain operations), while CHRONEX prioritizes security margin (global chaotic permutation and stronger nonlinearity). Observed trade-off in experiments: CHRONEX typically yields marginally stronger diffusion/randomness indicators at the cost of higher runtime (sorting-driven permutation), whereas SPiRAL achieves lower latency while remaining competitive on standard statistical security metrics. Table 1. Head-to-head comparison and selection guidance for the proposed reversible ciphers. Aspect SPiRAL (technique-I) CHRONEX (technique-II) Design intent Lightweight, low-latency reversible cipher for constrained/real-time deployment Higher security margin for high-exposure settings (storage/transit/cloud) Confusion/permutation Local spatial scrambling (index-adaptive rotations) and key-seeded PRNG-based reindexing/masking Global chaotic permutation (chaotic sequence rank/sort index order) Diffusion/nonlinearity Pixel-domain XOR chaining with circular shifts/rotations (fast integer ops) Nonlinear substitution (keyed S-box) plus chained diffusion with ciphertext feedback Key material Single key (seeded PRNG + control parameters) Two-key (or multi-parameter) design: chaotic map parameters + S-box/keystream key Compute footprint XOR + shifts + simple PRNG; minimal arithmetic and memory overhead Chaotic sequence generation + permutation construction + S-box lookup + chaining Time complexity (dominant term) Typically linear passes over pixels: Permutation via sorting/ranking dominates: (unless a linear-time permutation is used) Memory complexity (image-sized buffers) (image + permutation/keystream buffers) Preferred use-case Edge/POC imaging, real-time viewing, embedded gateways where latency/energy dominate Archiving, inter-institution sharing, untrusted network transit, cloud/PACS storage Selection rule (one-liner) Choose when efficiency is the primary constraint Choose when threat exposure is higher and extra compute is acceptable Open in a new tab Histogram analysis Figures 3 and 5 illustrate the histogram analysis of the proposed schemes for grayscale medical images. While Figs. 4 and 6 shows the histogram analysis of the proposed schemes for colour medical images. Each figure displays (i) the original medical image, (ii) its intensity histogram, (iii) the corresponding encrypted image, (iv) the histogram of the encrypted image, and (v) the reconstructed image after decryption. Figures 3 , 4 corresponds to the proposed technique-I SPiRAL, whereas Figs. 5 , 6 shows the results obtained with the proposed technique-II CHRONEX. For the original medical images, the histograms exhibit highly non-uniform, structured distributions, with distinct peaks and clusters associated with specific regions and background areas. In contrast, the histograms of the encrypted images produced by both SPiRAL and CHRONEX are almost flat and highly dispersed over the full 0–255 intensity range, with no visible peaks or periodic patterns. This uniformisation of the gray-level distribution indicates that the proposed ciphers effectively destroy the statistical structure of the plaintext images: the dominant tissue-related intensity ranges are no longer observable, and an attacker cannot infer meaningful information from simple first-order statistics or histogram-based analysis. Taken together, these observations show that the proposed SPiRAL and CHRONEX schemes achieve a favourable trade-off: they significantly increase histogram randomness in the cipher domain, thereby enhancing resistance to statistical and histogram-based attacks, while perfectly preserving the original intensity distribution after decryption for reliable medical interpretation. Fig. 3. Open in a new tab The visualization of original cover images, their encrypted counterparts, corresponding histograms, and the decrypted outputs of the proposed technique-I (SPiRAL). Fig. 5. Open in a new tab The visualization of original cover images, their encrypted counterparts, corresponding histograms, and the decrypted outputs of the proposed technique-II (CHRONEX). Fig. 4. Open in a new tab The visualization of original cover images, their encrypted counterparts, corresponding histograms, and the decrypted outputs of the proposed technique-I (SPiRAL). Fig. 6. Open in a new tab The visualization of original cover images, their encrypted counterparts, corresponding histograms, and the decrypted outputs of the proposed technique-II (CHRONEX). Entropy analysis Table 2 reports the entropy values of the encrypted grayscale and colour medical images for six existing methods 4 , 5 , 8 , 12 , 16 , 17 and the two proposed schemes SPiRAL and CHRONEX (proposed technique-I and proposed technqiue-II). For an 8-bit image, the ideal entropy of a perfectly random cipher is 8 bits. Hence, values closer to 8 indicate stronger randomness and lower information leakage about the underlying plaintext. Table 2. Entropy comparison for existing and proposed techniques. Images Existing techniques Proposed techniques 4 5 8 12 16 17 Proposed technique-I Proposed technique-II Gray_1 7.9985 7.9667 7.9989 7.9997 7.9989 7.9976 7.9993 7.9997 Gray_2 7.9988 7.9650 7.0970 7.9994 7.9932 7.9979 7.9994 7.9998 Gray_3 7.9979 7.9660 7.6410 7.9997 7.9991 7.9982 7.9994 7.9997 Gray_4 7.9988 7.9840 7.1980 7.9997 7.9956 7.9979 7.9993 7.9998 Gray_5 7.9985 7.9830 7.2880 7.9993 7.9972 7.9974 7.9993 7.9998 Colour_1 7.9982 7.9850 7.5448 7.9993 7.9982 7.9978 7.9998 7.9998 Colour_2 7.9992 7.8540 7.6859 7.9993 7.9949 7.9978 7.9998 7.9998 Colour_3 7.9991 7.9870 7.6620 7.9995 7.9919 7.9992 7.9998 7.9998 Colour_4 7.9994 7.9840 7.6660 7.9994 7.9916 7.9966 7.9998 7.9998 Colour_5 7.9989 7.9850 7.5520 7.9993 7.9978 7.9995 7.9997 7.9998 Open in a new tab From the table, it is evident that the proposed techniques consistently achieve entropy values extremely close to the theoretical maximum. Across all test images, the proposed technique-I attains entropies in the narrow range , while the proposed technique-II slightly improves this further, reaching 7.9997 to7.9998 for almost all cases. In contrast, several existing methods exhibit noticeable entropy deficits. For example, Ref. 8 produces significantly lower values (as low as 7.0970 for Gray_2 and around 7.20 to 7.68 for multiple images), indicating residual structure and non-uniformity in the encrypted histograms. Even the stronger existing baselines (4, 5, 16, and 17) typically remain in the 7.96 to7.99 range and show larger variation across images compared to the extremely tight clustering observed for the proposed methods. These results demonstrate that the proposed SPiRAL and CHRONEX-based ciphers are highly effective in flattening the gray-level distributions and suppressing statistical patterns inherent in medical images. The near-ideal and highly stable entropy values across both grayscale and colour cases confirm that the encrypted images leak virtually no first-order statistical information, which is crucial for resisting histogram-based, statistical, and entropy-driven attacks in a medical imaging context. Moreover, the consistently higher entropy of the proposed technique-II compared to the proposed technique-I can be directly attributed to its stronger nonlinear and chaotic design. While the proposed technique-I (SPiRAL) relies on lightweight spatial XOR diffusion with index-adaptive rotations, the proposed technique-II (CHRONEX) introduces an additional layer of complexity through key-dependent chaotic permutations, coupled logistic maps, and a random keyed S-box driving the XOR diffusion. The iterative mixing of (i) global chaotic reordering, (ii) keystream masking, and (iii) nonlinear S-box substitution pushes the cipher histograms closer to perfect uniformity, thereby yielding slightly higher entropy and reducing any residual redundancy that may remain after spatial-domain diffusion alone. In summary, the entropy analysis in Table 2 provides strong quantitative evidence that the proposed schemes not only outperform existing techniques but also operate very close to the theoretical randomness limit. The proposed technique-I offers a low-complexity, high-entropy solution suitable for resource-constrained deployments, while the proposed technique-II delivers even higher entropy and enhanced randomness through its chaos and S-box-based architecture, making it particularly attractive for high-security medical image protection scenarios. For a grayscale image with L possible gray levels and N total pixels, the entropy H is calculated using ( 30 ). 29 where 30 Here, L is the number of gray levels (for 8-bit images, ); N is the total number of pixels in the image; is the number of pixels whose intensity value equals k ; is the probability of gray level k . The entropy H is measured in bits when the logarithm base is 2, and its maximum value is when all gray levels are equally likely. NPCR and UACI analysis For differential-attack resistance, the NPCR and Unified Average Changing Intensity (UACI) values reported in Tables 3 and 4 demonstrate strong plaintext sensitivity of both proposed ciphers. For an 8-bit image cipher, NPCR values exceeding are widely regarded as near-ideal. In our experiments, both the proposed technique-I (SPiRAL) and technique-II (CHRONEX) consistently yield NPCR values tightly concentrated in the range 99.60 to across all grayscale and colour test images, which is competitive with, and often indistinguishable from, the best-performing existing scheme [5], [8], and [17]. This indicates that a one-pixel perturbation in the plaintext propagates to almost all ciphertext pixels, thereby impeding differential cryptanalysis. Beyond the fraction of changed pixels, UACI captures the average intensity deviation between ciphertexts produced from minimally different plaintexts. Compared with most baselines that remain around 33 to , the proposed technique-I typically attains higher UACI values, approximately 35 to , while the proposed technique-II reaches even larger deviations, about 36 to on several test images. These elevated UACI values imply stronger amplitude-level diffusion in addition to near-ideal NPCR. The improvement of CHRONEX is attributable to its global chaotic permutation and keyed S-box-based nonlinear diffusion, which introduces more aggressive mixing than the lightweight spatial operations in SPiRAL. Overall, the combination of near-ideal NPCR and enhanced UACI confirms that both proposed ciphers and especially CHRONEX provide robust resistance to differential attacks. For completeness, given two images A and B of size with L gray levels, NPCR and UACI are computed using ( 31 ) and ( 32 ), respectively. 31 where 32 Table 3. NPCR comparison for existing and proposed techniques. Images Existing techniques Proposed techniques 4 5 8 12 16 17 Proposed technique-I Proposed technique-II Gray_1 99.63 99.54 99.79 99.52 99.62 99.54 99.60 99.61 Gray_2 99.62 99.35 99.75 99.55 99.61 99.66 99.60 99.61 Gray_3 99.60 99.98 99.86 99.49 99.62 99.69 99.61 99.61 Gray_4 99.60 99.89 99.83 99.57 99.59 99.57 99.63 99.60 Gray_5 99.61 99.99 99.77 99.60 99.61 99.77 99.60 99.62 Colour_1 99.68 99.76 99.89 99.61 99.63 99.66 99.62 99.63 Colour_2 99.69 99.85 99.89 99.61 99.60 99.59 99.61 99.60 Colour_3 99.78 99.89 99.91 99.62 99.59 99.78 99.62 99.62 Colour_4 99.72 99.91 99.92 99.62 99.60 99.73 99.61 99.61 Colour_5 99.71 99.99 99.94 99.62 99.61 99.85 99.61 99.62 Open in a new tab Table 4. UACI comparison for existing and proposed techniques. Images Existing techniques Proposed techniques 4 5 8 12 16 17 Proposed technique-I Proposed technique-II Gray_1 33.49 33.47 35.26 33.12 33.45 33.46 36.94 40.93 Gray_2 33.45 33.47 35.22 33.64 33.37 33.59 36.29 37.28 Gray_3 33.46 33.47 34.96 33.25 33.32 33.46 35.08 36.26 Gray_4 33.41 33.47 34.68 33.97 33.56 33.54 31.22 41.55 Gray_5 33.45 33.47 34.75 33.56 33.41 33.79 37.55 41.96 Colour_1 34.24 33.47 34.09 33.66 33.38 33.59 35.49 36.29 Colour_2 34.19 33.47 34.65 33.72 33.42 33.60 34.74 38.18 Colour_3 34.28 33.46 35.22 33.68 33.30 33.19 34.82 35.66 Colour_4 34.98 33.47 35.09 33.23 33.29 33.49 35.39 38.71 Colour_5 35.02 33.47 34.59 33.26 33.62 33.57 33.16 36.21 Open in a new tab Parameter definitions for NPCR and UACI In ( 31 ) and ( 32 ), the parameters are defined as follows: M number of rows in the image (image height), N number of columns in the image (image width), L number of possible gray levels (for 8-bit images, ), A ( i , j ) gray-level (or colour-channel) value of pixel ( i , j ) in the first image (e.g., plaintext or reference image), B ( i , j ) corresponding gray-level (or colour-channel) value of pixel ( i , j ) in the second image (e.g., ciphertext or modified image), D ( i , j ) binary change indicator used in NPCR: if and otherwise. Correlation analysis The effectiveness of the proposed schemes in decorrelating adjacent pixels is further confirmed by the horizontal, vertical, and diagonal correlation coefficients reported in Tables 5 , 6 , and 7 . For the original medical images, adjacent-pixel correlation is typically very high (close to 1) due to the strong spatial redundancy of anatomical structures. A secure cipher should reduce these coefficients towards zero in all directions, indicating that neighbouring pixels in the encrypted image are effectively uncorrelated. As seen from the tables, several existing methods still exhibit noticeable residual correlations, with absolute values frequently in the range of 0.02 to 0.10 (and even higher in some cases, such as horizontal correlation of existing technique [5] for Gray_2/Gray_4 and vertical correlation of existing technique [17] for Colour_3), revealing that some degree of linear dependence between neighbouring cipher pixels remains. In contrast, both the proposed technique-I (SPiRAL) and the proposed technique-II (CHRONEX) consistently drive all correlation coefficient values extremely close to zero for all grayscale and colour images, typically within and often below in absolute magnitude. These nearly zero, sign-balanced coefficients demonstrate that the proposed encryption schemes successfully destroy the strong local correlations inherent in medical images and prevent an attacker from exploiting spatial redundancy for statistical or correlation-based cryptanalysis. The slightly more symmetric and tightly clustered behaviour of the proposed technique-II further reflects the benefit of combining chaotic permutation with nonlinear S-box driven diffusion, although both proposed designs achieve a level of decorrelation that is clearly superior or at least comparable to the best existing techniques. Let denote K pairs of adjacent pixel values (e.g., horizontal, vertical, or diagonal neighbours) extracted from an image. The sample correlation coefficient between and is calculated using ( 33 ). 33 where 34 are the sample means of and , respectively. Table 5. Horizontal correlation comparison for existing and proposed techniques. Images Existing techniques Proposed techniques 4 5 8 12 16 17 Proposed technique-I Proposed technique-II Gray_1 0.0212 − 0.0088 0.0156 − 0.0112 0.0053 0.0008 − 0.0013 0.0024 Gray_2 0.0163 0.1035 − 0.0436 − 0.0844 − 0.0032 0.0022 0.0007 0.0007 Gray_3 0.0169 0.0009 0.0016 − 0.0702 0.0001 0.0036 0.0010 0.0001 Gray_4 0.0021 0.1060 − 0.0901 − 0.0296 − 0.0008 − 0.0256 − 0.0008 − 0.0009 Gray_5 − 0.0179 − 0.0037 0.0044 0.0027 0.0025 − 0.0012 0.0011 0.0011 Colour_1 0.0636 − 0.0113 − 0.0414 − 0.0242 0.0069 0.0022 0.0011 0.0018 Colour_2 0.0266 0.0138 0.0724 0.0312 0.0036 0.0218 0.0009 0.0003 Colour_3 0.0246 0.0095 0.0270 0.0257 0.0011 0.0025 0.0012 − 0.0018 Colour_4 0.0011 − 0.0018 0.0027 0.0159 − 0.0001 − 0.0312 − 0.0010 − 0.0006 Colour_5 − 0.0633 0.0050 0.0535 0.0381 0.0009 0.0155 0.0015 0.0001 Open in a new tab Table 6. Vertical correlation comparison for existing and proposed techniques. Images Existing techniques Proposed techniques 4 5 8 12 16 17 Proposed technique-I Proposed technique-II Gray_1 0.0078 − 0.0110 0.00219 0.0332 0.0018 0.0046 0.0038 − 0.0008 Gray_2 0.0045 0.0020 − 0.022633 − 0.0305 0.0013 0.0055 0.0021 0.0003 Gray_3 − 0.0077 − 0.0040 0.066955 0.0262 − 0.0006 0.0006 − 0.0024 − 0.0018 Gray_4 0.0023 − 0.0110 0.008894 0.0301 − 0.0020 0.0026 − 0.0020 − 0.0006 Gray_5 0.0100 − 0.0030 0.00965 0.0342 − 0.0053 − 0.0104 − 0.0012 0.0007 Colour_1 − 0.0452 − 0.0010 − 0.0066969 0.0469 − 0.0062 − 0.0014 − 0.0004 − 0.0014 Colour_2 0.0034 − 0.0240 0.004451 0.0155 0.0022 0.0266 0.0009 − 0.0003 Colour_3 − 0.0334 − 0.0060 − 0.000899 − 0.0324 − 0.0038 − 0.2144 − 0.0007 0.0003 Colour_4 0.0336 − 0.0010 0.001477 0.0247 − 0.0004 0.0228 − 0.0001 − 0.0004 Colour_5 0.0055 0.0080 0.0055698 − 0.0286 0.0005 0.0751 − 0.0010 0.0000 Open in a new tab Table 7. Diagonal correlation comparison for existing and proposed techniques. Images Existing techniques Proposed techniques 4 5 8 12 16 17 Proposed technique-I Proposed technique-II Gray_1 0.0336 − 0.0087 0.0087 − 0.0422 0.0057 0.0032 − 0.0016 − 0.0007 Gray_2 0.0965 − 0.0130 0.0130 0.0352 0.0083 0.0066 0.0001 − 0.0018 Gray_3 0.0446 − 0.0103 − 0.0336 0.0005 0.0076 0.0028 − 0.0016 0.0000 Gray_4 0.0663 0.0073 0.0044 0.0239 0.0096 0.0045 0.0001 − 0.0004 Gray_5 − 0.0224 − 0.0036 0.0045 − 0.0332 0.0135 − 0.0056 − 0.0030 − 0.0006 Colour_1 0.0445 − 0.0001 0.0001 − 0.0441 0.0116 0.0067 0.0021 − 0.0022 Colour_2 0.0026 − 0.0240 0.0664 0.0056 0.0019 − 0.0109 0.0004 − 0.0017 Colour_3 − 0.0033 0.0001 0.0055 0.0007 0.0090 − 0.0097 0.0016 0.0004 Colour_4 0.0667 0.0016 − 0.0045 0.0216 0.0012 − 0.0468 0.0008 − 0.0011 Colour_5 0.0038 − 0.0134 − 0.0147 − 0.0122 0.0091 0.0034 0.0004 0.0005 Open in a new tab Parameter definitions for correlation coefficients In ( 33 ) and ( 34 ), the parameters are defined as: K total number of pixel pairs sampled from the image, gray-level (or colour-channel) value of the first pixel in the k -th pair, gray-level (or colour-channel) value of the second pixel in the k -th pair (adjacent to ), sample mean of , sample mean of , sample correlation coefficient between and , with indicating very low correlation. Threat model analysis We consider a realistic deployment setting for medical-image storage and transmission where the adversary is assumed to know the full encryption algorithm (Kerckhoffs’ principle) but not the secret key(s). We explicitly evaluate (i) known-plaintext attacks (KPA), in which the adversary may observe a limited number of plaintext–ciphertext pairs, and (ii) chosen-plaintext attacks (CPA), in which the adversary can submit inputs to the encryption pipeline and observe the resulting ciphertexts. We do not claim resistance to a full chosen-ciphertext attack (CCA) model because that would require a decryption-oracle setting and typically an authenticated encryption design; instead, our goal is confidentiality under KPA/CPA, which matches the target imaging workflow. Purely statistical indicators such as entropy, correlation, NPCR/UACI on natural images can be misleading because they may not reveal structural leakage under adversarially structured inputs. Therefore, under CPA we encrypt a small set of worst-case plaintext patterns such as all-zero, all-255, checkerboard, and impulse to verify that the ciphertexts remain near-ideal: (i) entropy stays close to 8 bits/pixel and (ii) horizontal correlation , vertical correlation , and diagonal correlation remain close to zero, indicating that neither SPiRAL nor CHRONEX preserves exploitable structure even for highly regular CPA queries. Tables 9 and 10 report the CPA-sanity results for grayscale and color images. Table 9. CPA sanity-test results for SPiRAL: entropy , horizontal correlation , vertical correlation , and diagonal correlation computed on ciphertexts generated from adversarially chosen plaintext patterns. Chosen plaintext Grayscale ciphertext Color ciphertext (bits) (bits) All-zero 7.999290 − 0.000056 0.001168 0.001110 7.999290 − 0.000056 0.001168 0.001110 All-255 7.999324 − 0.001594 0.003036 − 0.002309 7.999324 − 0.001594 0.003036 − 0.002309 Checkerboard (0/255) 7.999280 − 0.001580 − 0.001786 − 0.002145 7.999280 − 0.001580 − 0.001786 − 0.002145 Impulse (1-pixel) 7.999293 0.000185 0.000898 0.000812 7.999293 0.000185 0.000898 0.000812 Open in a new tab Table 10. CPA sanity-test results for CHRONEX: entropy , horizontal correlation , vertical correlation , and diagonal correlation computed on ciphertexts generated from adversarially chosen plaintext patterns. Chosen plaintext Grayscale ciphertext Color ciphertext (bits) (bits) All-zero 7.999268 − 0.000543 − 0.002655 0.000467 7.999268 − 0.000543 − 0.002655 0.000467 All-255 7.999257 − 0.001940 0.002199 − 0.000889 7.999257 − 0.001940 0.002199 − 0.000889 Checkerboard (0/255) 7.999336 0.000477 − 0.002358 0.000555 7.999336 0.000477 − 0.002358 0.000555 Impulse (1-pixel) 7.999333 − 0.000250 0.000155 0.000394 7.999333 − 0.000250 0.000155 0.000394 Open in a new tab To substantiate resistance against structured chosen-plaintext manipulation beyond histogram/entropy on natural images, we evaluate the avalanche effect by encrypting an image I and its minimally perturbed version which is obtained by flipping exactly one pixel and then computing NPCR/UACI between the ciphertext pair E ( I ) and . High NPCR (close to 100%) indicates that a one-pixel plaintext change spreads to almost all ciphertext pixels, and UACI near the theoretical ideal for 8-bit images ( ) indicates strong average intensity variation. As shown in Table 11 , both ciphers produce near-ideal diffusion for grayscale and color images; in particular, SPiRAL achieves mean NPCR (gray) and (color), while CHRONEX (strong) yields even higher mean NPCR (gray) and (color), with UACI consistently near to . These results confirm that the proposed designs exhibit strong plaintext sensitivity and rapid error propagation, which is essential for confidentiality under KPA/CPA settings. Table 11. Avalanche effect comparison for SPiRAL and CHRONEX: NPCR and UACI computed between ciphertext pairs E ( I ) and , where differs from I by flipping exactly one pixel. Images SPiRAL CHRONEX NPCR (%) UACI (%) NPCR (%) UACI (%) Gray_1 99.30 33.38 99.60 33.43 Gray_2 99.31 33.35 99.69 33.49 Gray_3 99.29 33.38 99.61 33.45 Gray_4 99.29 33.42 99.64 33.36 Gray_5 99.23 33.41 99.57 33.48 Colour_1 99.26 33.34 99.62 33.43 Colour_2 99.28 33.34 99.59 33.43 Colour_3 99.24 33.34 99.63 33.50 Colour_4 99.28 33.40 99.59 33.44 Colour_5 99.29 33.33 99.59 33.45 Open in a new tab Key-sensitivity, key space, and latency analysis: Table 11 evaluates plaintext sensitivity by computing NPCR/UACI between E ( I ) and , where differs from I by flipping exactly one pixel, whereas Table 12 evaluates key sensitivity by computing NPCR/UACI between and with obtained via a 1-bit perturbation of K . The results confirm that both SPiRAL and CHRONEX exhibit strong key sensitivity (NPCR close to with UACI near the 8-bit ideal), while Table 13 shows that encryption/decryption latency remains practical for lightweight deployment; CHRONEX incurs a modest additional cost due to chaos-driven permutation and S-box-based nonlinear mixing. Table 12. Key-sensitivity (1-bit key perturbation): NPCR and UACI between ciphertexts and , where differs from K by flipping exactly one key bit. Images SPiRAL CHRONEX NPCR (%) UACI (%) NPCR (%) UACI (%) Gray_1 99.61 33.40 99.62 33.44 Gray_2 99.59 33.43 99.60 33.42 Gray_3 99.60 33.48 99.61 33.47 Gray_4 99.60 33.51 99.60 33.46 Gray_5 99.60 33.44 99.61 33.53 Colour_1 99.60 33.45 99.61 33.49 Colour_2 99.61 33.41 99.60 33.45 Colour_3 99.60 33.46 99.59 33.43 Colour_4 99.60 33.50 99.60 33.47 Colour_5 99.61 33.44 99.61 33.48 Open in a new tab Table 13. Latency (in seconds) comparison for encryption and decryption of the proposed SPiRAL and CHRONEX techniques. Images SPiRAL CHRONEX Encryption Latency (s) Decryption Latency (s) Encryption Latency (s) Decryption Latency (s) Gray_1 0.112 0.119 0.117 0.112 Gray_2 0.208 0.205 0.243 0.222 Gray_3 0.213 0.205 0.245 0.210 Gray_4 0.205 0.215 0.244 0.213 Gray_5 0.207 0.214 0.252 0.239 Colour_1 0.613 0.634 0.733 0.713 Colour_2 0.632 0.651 0.713 0.694 Colour_3 0.620 0.647 0.698 0.701 Colour_4 0.657 0.647 0.771 0.743 Colour_5 0.661 0.666 0.754 0.730 Gray avg. 0.189 0.192 0.220 0.199 Colour avg. 0.637 0.649 0.734 0.716 Open in a new tab Key-space (conservative lower bound): In our implementation, SPiRAL uses a secret key K to seed the PRNG that generates the permutation and keystream, yielding a key space of at least (e.g., for a 32-bit seed). CHRONEX uses two independent secret keys , giving a conservative lower bound of at least (e.g., for two 32-bit keys), in addition to key-dependent chaotic initialization via . For completeness, we also report AES as a throughput reference on serialized image bytes; however, AES is not a reversible pixel-domain permutation and diffusion construction and is therefore not treated as a structure-equivalent baseline. Memory footprint (practical estimate). Let be the number of pixels. In our implementation, SPiRAL stores the working image and one temporary buffer (both 8-bit) and generates a permutation and an 8-bit keystream of length M . Using 32-bit indices for the permutation, the dominant memory is approximately M bytes (image) bytes (buffer) bytes (permutation) bytes (keystream), i.e., about 7 M bytes in total. For CHRONEX, we additionally store the chaotic sequence used for sorting and an extra keystream/S-box, leading to roughly 7 M bytes bytes, i.e., about 15 M bytes overall (implementation-dependent). For a image ( ), this corresponds to approximately 1.8 MB for SPiRAL and 3.9 MB for CHRONEX. Statistical analysis The overall robustness of the proposed schemes was further validated through a statistical analysis of Entropy, NPCR, and UACI across multiple medical images. Table 8 first summarizes the mean and standard deviation of these metrics for six representative existing techniques. Extensive evaluation shows entropy stays at least 7.999 bits/pixel, neighbour correlations are driven near zero, NPCR remains near-ideal across tests about 99.2–99.7% in avalanche and about 99.6% in key-sensitivity, and UACI is in the range 33.3–33.5% while reaching higher deviations in natural-image differential tests. To rigorously assess whether the improvements achieved by the proposed SPiRAL and CHRONEX techniques are statistically meaningful rather than incidental, paired t -tests with a significance level of were conducted, and the corresponding t -statistics and p -values are reported in Tables 14 and 15 . For SPiRAL, the entropy values are statistically different (and closer to the ideal 8 bits) compared to most existing methods (significant in 5 out of 6 cases), while NPCR shows significant gains over several baselines and at least comparable behaviour (non-significant p -values) to the strongest competing techniques. UACI for SPiRAL is also statistically higher than that of the existing methods [5], [12], [16], and 17 , indicating stronger average intensity variation under small plaintext changes. CHRONEX exhibits an even clearer advantage: its entropy is statistically superior to all existing techniques (all ), NPCR again matches or exceeds the best baselines (with non-significant differences only where the existing methods already attain very high NPCR), and its UACI improvements are statistically significant against every compared method. Taken together, these results confirm that both proposed ciphers provide consistently higher or comparable randomness and differential robustness across the tested dataset, with CHRONEX in particular delivering statistically significant gains in entropy and UACI over all state-of-the-art baselines, thereby offering a stronger level of security for medical image protection. Although our evaluation uses 115 images (100 color + 15 grayscale), we still interpret significance-test results cautiously and report effect trends alongside p -values. Table 8. Mean and standard deviation of entropy, NPCR and UACI for different medical images. Parameters 4 5 8 12 16 17 Entropy Mean 8.00 7.97 7.53 8.00 7.99 8.00 Standard deviation 0.00 0.04 0.25 0.00 0.01 0.00 NPCR Mean 99.66 99.82 99.86 99.58 99.61 99.68 Standard deviation 0.06 0.20 0.06 0.05 0.01 0.10 UACI Mean 34.00 33.47 34.85 33.51 33.41 33.53 Standard deviation 0.61 0.00 0.35 0.26 0.10 0.14 Open in a new tab Table 14. T-test and p -value based statistical significance analysis for different medical images for proposed technique-I (SPiRAL). Existing techniques Parameters Tests 4 5 8 12 16 17 Entropy T-Test − 5.1387 − 2.7739 − 5.7854 − 0.8257 − 2.5310 − 5.9060 P-values 0.0004 0.0197 0.0002 0.4282 0.0298 0.0001 Statistical significance testing with error rate Statistically significant Statistically significant Statistically significant Not statistically significant Statistically significant Statistically significant Npcr T-Test 2.8315 3.1963 12.0144 − 2.0231 − 0.6544 2.3421 P-Values 0.0178 0.0096 0.0000 0.0706 0.5276 0.0412 Statistical significance testing with error rate Statistically significant Statistically significant Statistically significant Not statistically significant Not statistically significant Statistically significant Uaci T-Test − 1.8433 − 2.9179 − 0.3863 − 2.8109 − 3.0143 − 2.7987 P-values 0.0951 0.0154 0.7074 0.0184 0.0130 0.0188 Statistical significance testing with error rate Not statistically significant Statistically significant Not statistically significant Statistically significant Statistically significant Statistically significant Open in a new tab Table 15. T-test and p -value based statistical significance analysis for different medical images for proposed technique-II (CHRONEX). Existing techniques Parameters Tests 4 5 8 12 16 17 Entropy T-Test − 7.0622 − 2.6494 − 5.4912 − 5.3610 − 2.4838 − 6.6930 P-values 0.0000 0.0243 0.0003 0.0003 0.0323 0.0001 Statistical significance testing with error rate Statistically significant Statistically significant Statistically significant Statistically significant Statistically significant Statistically significant Npcr T-Test 2.5880 2.9992 11.3696 − 2.1023 − 1.2020 2.1551 P-values 0.0270 0.0134 0.0000 0.0618 0.2571 0.0566 Statistical significance testing with error rate Statistically significant Statistically significant Statistically significant Not statistically significant Not statistically significant Not statistically significant Uaci T-Test − 5.4928 − 6.3835 − 4.5043 − 6.2876 − 6.4505 − 6.2916 P-values 0.0003 0.0001 0.0011 0.0001 0.0001 0.0001 Statistical significance testing with error rate Statistically significant Statistically significant Statistically significant Statistically significant Statistically significant Statistically significant Open in a new tab Descriptive statistics Group 1 Let denote the performance scores for the existing technique: 35 36 37 38 39 Group 2 Let denote the scores for the proposed technique: 40 41 42 43 44 Pooled variance and standard error Pooled variance by assuming equal-variance: 45 Standard error of the mean difference: 46 Total degrees of freedom: 47 Test statistic We test the null hypothesis , where and are the population means of the existing and proposed techniques, respectively. The independent-samples t -statistic is 48 Under , the statistic t follows a Student t -distribution with df degrees of freedom. p -value computation Let be a random variable with a t -distribution with df degrees of freedom, and let denote its cumulative distribution function. Two-tailed test: Testing whether the proposed technique differs from the existing technique in either direction is carried out using two-tailed test. The null hypothesis is rejected if the corresponding p -value is smaller than the chosen significance level (e.g., ). 49 The proposed SPiRAL and CHRONEX schemes jointly provide a flexible encryption framework that is specifically tailored for medical imaging workflows, offering lossless reconstruction so that no diagnostically relevant information is degraded after decryption. Extensive evaluation shows entropy with a minimum of 7.999 bits/pixel, NPCR is in the range 99.2–99.7%, neighbour correlations are driven near zero, and UACI is in the ideal range of 33.3–33.5%. These results demonstrate that both ciphers produce encrypted images with randomness and diffusion on par with, or superior to, state-of-the-art techniques. This strongly limits information leakage and resists statistical and differential attacks. SPiRAL achieves this level of security with a lightweight, purely spatial design and linear-time complexity, making it particularly suitable for real-time, resource-constrained applications such as wearable devices, point-of-care scanners, and edge-based telemedicine systems where low latency and low power consumption are critical. CHRONEX further strengthens security by combining key-driven chaotic permutations with nonlinear S-box-based XOR diffusion, which is ideal for high-risk environments such as cloud-based archives, multi-institutional image sharing, and long-term encrypted storage where stronger adversarial models must be considered. Taken together, the two proposed techniques offer a practical and robust toolbox for secure medical image protection across a wide range of application scenarios, from embedded acquisition hardware to large-scale hospital information systems, while consistently outperforming or matching existing methods in both security metrics and computational efficiency. Using the statistics of the existing (Group 1) and proposed (Group 2) techniques, the independent-samples t values were computed from ( 48 ) with the pooled variance and standard error defined in ( 45 ) to ( 46 ), and the corresponding two-tailed p -values were obtained according to ( 49 ). Threat model and qualitative security discussion Threat model: We consider a strong, standard adversary for medical-image confidentiality in transmission and storage. The attacker is assumed to have full access to encrypted images and the encryption algorithm, and may also know the image dimensions and file format. We explicitly evaluate security under the following capabilities: Ciphertext-only attack (COA): the attacker observes encrypted medical images and attempts to recover visual structure or diagnostic content. Known-plaintext attack (KPA): the attacker may know some plaintext–ciphertext pairs, such as publicly available test images or repeated acquisition patterns. Chosen-plaintext attack (CPA): the attacker may query the encryption oracle on adversarially structured inputs such as all-zero, checkerboard, impulse patterns, which is realistic in shared clinical pipelines if the endpoint is compromised. We do not claim resistance to chosen-ciphertext attacks (CCA), since the schemes are designed for lightweight reversible encryption rather than authenticated encryption. The integrity and tamper detection can be added by pairing the cipher with a standard MAC or authenticated channel. Key reuse and session assumptions: The primary deployment assumption is that the secret key is not disclosed and that encryption uses either (a) a fresh session key for each encryption process, or (b) a per-image public nonce/identifier combined with the long-term key via a key-derivation step. This avoids deterministic reuse patterns across repeated encryptions of similar content. In our implementation, the keyed PRNG and all derived sequences, such as permutation, keystream, and S-box are deterministically regenerated during decryption from the same seed. This ensures strict reversibility while still permitting safe per-image diversification through a nonce-derived seed. The proposed techniques resist common attacks, beyond experimental metrics: Resistance to differential/CPA structure probing: Both ciphers deliberately couple confusion with multi-stage diffusion such that a minimal plaintext change propagates broadly in the ciphertext. SPiRAL establishes tight local coupling by iterative XOR propagation along selected rows/columns, followed by index-adaptive circular rotations, and then applies a key-controlled permutation and masking stage. CHRONEX adds a global, key-dependent chaotic permutation and nonlinear diffusion using a keyed S-box with ciphertext feedback, which further amplifies the disruption of structured inputs. Consequently, adversarially chosen inputs such as uniform, checkerboard, and impulse do not preserve visible artifacts after encryption, and one-pixel perturbations in the plaintext produce near-ideal ciphertext sensitivity (NPCR/UACI), supporting resistance to differential probing under CPA/KPA. Resistance to KPA under key secrecy: Given a fixed key, the encryption pipeline is nonlinear and mixing, combining (i) key-controlled permutation and keystream masking (SPiRAL) and (ii) key-dependent chaotic permutation plus S-box-based nonlinear diffusion (CHRONEX). These operations prevent straightforward linear reconstruction of keystreams or permutations from a small number of known pairs, especially when session diversification (fresh key or nonce-derived seed) is used. Importantly, the keyed permutation breaks spatial alignment, and nonlinear diffusion breaks simple XOR-cancellation attacks that typically exploit deterministic additive masks. Key sensitivity: A one-bit change in the secret key produces statistically independent derived sequences (permutation/keystream and S-box, where applicable), yielding ciphertexts that differ across nearly all pixels. This behavior supports robustness against key-guessing and near-key attacks. Parameter constraints and key-space: All secret parameters are chosen from validated ranges that keep the underlying chaotic maps in their fully chaotic regime and avoid degenerate cases such as fixed points, short cycles, or near-periodic behavior. In practice, this means the control parameters and initial states are constrained so that the generated sequences remain highly sensitive to small perturbations and do not collapse into predictable patterns under finite precision. In addition, we report an explicit conservative lower bound on the effective key space. Specifically, even after accounting for any parameter constraints and implementation details, the number of distinct secret configurations that an attacker would have to exhaustively search is at least . Accordingly, the effective key space is conservatively lower-bounded by (with for SPiRAL and for CHRONEX), which is sufficient to preclude brute-force search under realistic computational limits. Conclusion In this manuscript, we introduce two fully reversible, pixel-domain medical image ciphers SPiRAL and CHRONEX built for lightweight deployment while preserving strictly lossless reconstruction. SPiRAL prioritizes efficiency by tightening local pixel coupling through iterative XOR propagation across rows and columns, followed by index-adaptive circular rotations and a compact key-controlled permutation and masking step. The CHRONEX complements this with a more global, chaos-driven design in which coupled logistic maps generate a key-dependent permutation of pixel indices, followed by nonlinear diffusion using a keyed S-box and cumulative XOR chaining. Across the evaluated images, both schemes consistently produce ciphertext whose entropy stays extremely close to the 8-bit ideal, typically at least 7.999 bits, while horizontal, vertical, and diagonal correlations are reduced to values near zero, indicating that spatial redundancy is effectively removed. The avalanche analysis further supports strong plaintext sensitivity: flipping exactly one pixel in the input causes widespread changes in the ciphertext, with NPCR typically between and and UACI concentrating around 33.3% to 33.5%. To move beyond purely statistical evidence, we also include a threat-model-oriented evaluation: chosen-plaintext sanity tests on highly structured patterns and one-bit key-sensitivity checks confirm that the ciphertext remains well mixed and strongly dependent on the secret key. From a deployment perspective, SPiRAL is a natural choice when latency and energy dominate, such as point-of-care devices and edge gateways, while CHRONEX is better suited to higher-exposure settings such as telemedicine back-ends and long-term encrypted repositories where extra computation is acceptable for a stronger security margin. Finally, we provide a realistic complexity discussion, noting that CHRONEX is mainly governed by permutation construction through sorting, whereas the remaining stages scale linearly with the number of pixels. Future work Future work will investigate hardware-oriented realizations of SPiRAL and CHRONEX on FPGA and SoC platforms, co-design with medical image compression standards, and extensions to volumetric and multi-modal datasets. Another promising direction is the integration of the proposed ciphers into end-to-end e-health architectures that jointly manage key distribution, access control, and auditability. By demonstrating that lightweight, fully reversible pixel-domain cryptography can satisfy both clinical and cryptographic constraints, this study lays the groundwork for practical, standards-compatible protection of medical imagery in next-generation healthcare systems. Supplementary Information Supplementary Information 1. (793.3MB, rar) Supplementary Information 2. (129.1MB, rar) Author contributions D.S: Conceptualization (equal); data curation (lead); formal analysis (lead); investigation (equal); methodology (equal); writing-original draft (lead); writing-review and editing (equal). K.U: Conceptualization (equal); methodology (equal); formal analysis (lead); investigation (equal); writing and editing (equal). B.B: Conceptualization (equal); methodology (equal); formal analysis (lead); investigation (equal); writing and editing (equal). C.C.S.: Conceptualization (equal); methodology (equal); formal analysis (lead); investigation (equal); writing and editing (lead). S.S: Formal analysis (lead); investigation (equal); methodology (equal); writing-original draft (lead); writing and editing (equal). R.C: Formal analysis (lead); investigation (equal); methodology (equal); writing-original draft (lead); writing and editing (equal). Funding This article was co-funded by the European Union under the REFRESH-Research Excellence for Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition and has been done in connection with project Students Grant Competition SP2024/087 Specific Research of Sustainable Manufacturing Technologies “financed by the Ministry of Education, Youth and Sports and Faculty of Mechanical Engineering VŠB-TUO. The article has been done in connection with the project Students Grant Competition SP2024/087”, Specific Research of Sustainable Manufacturing Technologies “financed by the Ministry of Education, Youth and Sports and Faculty of Mechanical Engineering VŠB-TUO”. Data availability All the data and material used in this study is available in the supplementary material, and further details if required, the corresponding author will provide the same, through proper requisition. Declarations Ethics declarations The authors declare that the manuscript is prepared by obeying the Ethical Standards as described in the Committee on Publication Ethics (COPE). Human and animal rights and informed consent This article does not contain any studies with human or animal subjects performed by any of the authors. Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary Information The online version contains supplementary material available at 10.1038/s41598-026-41579-z. References 1. D. Jeni Jeba Seeli, K. K. Thanammal,. A comparative review and analysis of medical image encryption and compression techniques. Multimed. Tools Appl. 84 , 4457–4473. 10.1007/s11042-024-18745-4 (2025). 2. Tajudeen, Kafayat Odunayo, Ameen, Ahmed Oloduowo & Adeniyi, Abidemi Emmanuel. 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