# A Quantum-Resistant FHE Framework for Privacy-Preserving Image Processing in the Cloud
## 1 Introduction  
The emergence of practical quantum computing represents perhaps the most significant cryptographic paradigm shift since the inception of public key cryptography [1]. [PERSON]'s algorithm [2] poses an existential threat to the mathematical foundations underlying RSA and elliptic curve cryptography--the bedrock of today's secure communications [3]. This vulnerability extends beyond theoretical concerns; the mere prospect of quantum computers capable of breaking current encryption standards demands immediate action to protect data that must remain confidential for decades to come [4]. Furthermore, the explosive growth of cloud-based image processing services across critical domains, from medical diagnostics to autonomous vehicle perception, has created an urgent need for privacy-preserving computational techniques [5, 6, 7]. Healthcare providers uploading radiological images, surveillance systems processing sensitive footage, and personal photo management services all require solutions that enable computation on encrypted data without exposing the underlying content [8, 9, 10, 11]. Traditional approaches force an uncomfortable choice: either sacrifice privacy by processing data in plaintext or accept severe performance penalties that render the solutions impractical [12]. Fully homomorphic encryption emerged as a theoretical breakthrough that promised to resolve this dilemma by enabling arbitrary computations on encrypted data [13]. Homomorphic encryption itself is a cryptographic paradigm that allows computation to be performed directly on encrypted data, generating an encrypted result that, when decrypted, matches the result of the same operation performed on the plaintext. This eliminates the need to expose sensitive data to an untrusted server, providing a powerful tool for cloud privacy. Our work focuses on fully homomorphic encryption (FHE), which supports arbitrary computations. Early FHE implementations suffered from crippling performance overhead that relegated them to academic curiosity rather than practical deployment [14]. Recent advances, particularly in approximate FHE schemes like CKKS optimized for real-number arithmetic [15], have begun to narrow this gap. Yet a critical challenge persists: existing solutions fail to simultaneously address both quantum resistance and computational efficiency [16]. In selecting a post-quantum scheme, we chose CRYSTALS-Kyber due to its strong security profile, high efficiency, and status as a primary standard selected by the U.S. National Institute of Standards and Technology (NIST). Its small key and ciphertext sizes, combined with sub-millisecond operational latencies, make it an ideal choice for the key exchange phase of an interactive protocol, minimizing the performance overhead of securing the communication channel. Contemporary secure image processing architectures exhibit a troubling dichotomy [5]. Systems prioritizing performance typically rely on cryptographic primitives vulnerable to quantum attack [2], while quantum-resistant implementations impose computational costs that preclude real-world deployment [16]. This research addresses this fundamental gap by demonstrating that quantum security and practical performance need not be mutually exclusive. This research addresses the existing gap by proposing a framework that carefully fuses two state-of-the-art cryptographic components: CRYSTALS-Kyber and the CKKS FHE scheme. The methodological advantage of this specific pairing is its unique balance of security, efficiency, and functionality. By leveraging Kyber, a highly efficient and NIST-standardized PQC KEM, and integrating it with CKKS, a powerful FHE scheme optimized for real-number arithmetic, our framework can support complex image processing operations often beyond the scope of other hybrid systems. This fusion allows us to achieve end-to-end post-quantum security without sacrificing functional versatility.