[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85760-en":3,"doc-seo-85760-105":29,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85760,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","A Hybrid Quantum-Chaos Theory Approach to Image Encryption Using Reservoir Computing","Research presents a hybrid image encryption system combining quantum cryptography, chaos theory, and reservoir computing to overcome weaknesses of conventional encryption under quantum threats. It uses the E91 quantum cryptographic protocol to generate secure, eavesdropping-resistant keys via quantum entanglement. The Lorenz hyper-chaotic system adds sensitivity to initial conditions and unpredictability, improving resistance to classical and quantum attacks. Reservoir computing boosts computational efficiency for faster encryption and decryption. Reported results include encryption as low as 0.0296s and decryption as low as 0.0164s for 128×128 images, with strong MAE, NPCR, and UACI performance across configurations.","arXiv :2607 .09923v 1 [ cs .CR] 10 Jul 2026  \nA Hybrid Quantum-Chaos Theory Approach to Image Encryption Using Reservoir Computing  \nNaheen Mohd. Kadir  \n[naheen.kadir@gmail.com](naheen.kadir@gmail.com)  \nDepartment of Computer Science & Engineering  \nRUET, Rajshahi, Bangladesh June, 2025 (Undergrad Thesis)  \nAbstract  \nThis research presents a novel hybrid image encryption system that combines quantum cryptography, chaos theory and reservoir computing to address the limitations of conventional encryption methods. With the rapid advancements in quantum computing, traditional systems like RSA, DHKE (related to prime number factorization) are vulnerable to quantum attacks i.e. Shor’s algorithm, Grover’s algorithm. In response, this study proposes a hybrid solution that uses quantum cryptographic protocols, particularly the E91 protocol, to generate secure, eavesdrop-proof keys through quantum entanglement. The integration of chaos theory, specifically the Lorenz hyper-chaotic system, enhances the encryption system by adding unpredictability and sensitivity to initial conditions, making it more resistant to both classical and quantum-based attacks. Reservoir computing is used to improve computational efficiency, enabling faster and more effective encryption and decryption processes. The system achieved encryption times as low as 0.0296sand decryption times as low as 0.0164s for 128 × 128 images, with MAE reduced for 300–600 node networks, and NPCR and UACI above 99.6% and 0.49, respectively, across various image sizes and configurations. By combining quantum cryptography, chaos theory and reservoir computing, this approach offers both enhanced security and practical feasibility for image encryption in the age of quantum computing.  \nKeywords: Quantum cryptography, Quantum computing, E91 protocol, Image encryption, SHA-256, Chaos theory, Lorenz system, Reservoir computing, Hybrid encryption system  \n1 Introduction  \nThe rapid development of quantum computing [1] and chaos theory [2] has introduced paradigm-shifting in cryptography and data security. Encrypting images is a very impor-  \ntant way to keep private visual data safe from people who want to access them illegally over a network. Traditional encryption methods, on the other hand, have a lot of issues [3], mostly because they rely on formulas that are easy to figure out [4] by quantum computer. Classical types of encryption are simple to get around. We can see two examples, RSA [5] and DHKE [6] . They are safe because it is hard to factor big prime numbers. If we have a powerful enough quantum computer, Shor’s algorithm [7] can de-touch prime numbers from multiplication of big prime numbers in a very short amount of time. In other words, it can get around RSA cryptography. In the same way, Grover’s algorithm [8] can weaken traditional encryption methods, making it easier for brute-force attacks to find valid keys. Keys that are safe and can’t be read by anyone else are made with quantum encryption protocols [9], such as the E91 protocol [10] . On the other hand, chaos theory has done a great job of making cryptography safer [11] . This is because it is usually unpredictable and depends a lot on how it initiates. This convergence of quantum and chaotic systems may offer a feasible pathway toward quantum-resistant image encryption methodologies.  \nThe main objective of this research is to find ways to fix the problems with current image encryption methods. As quantum computing gets better, encryption methods that rely on breaking down prime numbers are becoming less secure. Chaotic dynamical systems, especially the Lorenz attractor model [12], are a very interesting option because they can create complex, non-linear patterns that are very sensitive to initial conditions. Because they are so unpredictable, these systems are very hard to break with regular cryptanalysis methods. They are also more secure against both classical and quantum attacks. Reservoir Computing [13][14] a","cbCainHHlHnGDXBc","https://ap.wps.com/l/cbCainHHlHnGDXBc","pdf",2214127,1,21,"English","en",105,"# Introduction\n# Existing Research and Developments","[{\"question\":\"Why is chaos theory included, and which chaotic model is used?\",\"answer\":\"Chaos theory is used to introduce unpredictability and high sensitivity to initial conditions; the Lorenz hyper-chaotic system drives the chaotic sequences to strengthen encryption.\"}]",1784206067,53,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":27},"a-hybrid-quantum-chaos-theory-approach-to-image-encryption-using-reservoir-computing","",{"@graph":35,"@context":77},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/a-hybrid-quantum-chaos-theory-approach-to-image-encryption-using-reservoir-computing/85760/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"Why is chaos theory included, and which chaotic model is used?","Question",{"text":75,"@type":76},"Chaos theory is used to introduce unpredictability and high sensitivity to initial conditions; the Lorenz hyper-chaotic system drives the chaotic sequences to strengthen encryption.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]