Optimized Non-Linear DNA Cryptosystem with Quantum-Secured Key Synthesis

Abstract

Medical imaging systems are moving quickly to cloud-based picture archiving and communication systems (PACS), while rapidly shifting to cloud-based PACS networks requires encryption standards that offer cryptographic strength, clinical fidelity and clinical workflow compatibility. The existing approaches cater to some of these requirements, but there is no published system that meets all requirements simultaneously. This paper presents the Efficient Data Masking (EDM) framework, a three-phase chaotic-DNA encryption pipeline that addresses this gap through three integrated components. First, a Nested Chaotic System (NCS) coupling a logistic map with a sine map through bidirectional parameter exchange yields a maximum Lyapunov exponent λ = 0.87, guaranteeing exponential sensitivity to initial conditions. Second, a SHA-256-based key derivation module (termed quantum-inspired because key material is augmented with NCS-derived entropy to resist Grover-class exhaustive search) generates a 256-bit session key with effective entropy exceeding 2²⁵⁶. Third, an eight-rule dynamic DNA encoding layer with XOR diffusion implemented over GF(4) provides invertible nucleotide-level confusion and diffusion. Formal security analysis is conducted under the IND-CPA game, with a structured argument linking ciphertext indistinguishability to the computational hardness of distinguishing NCS output from a truly random sequence. We explicitly acknowledge that the NCS pseudorandomness assumption is non-standard and identify reduction to an established hard problem as future work. Experiments on six medical imaging modalities demonstrate that all fifteen NIST SP 800-22 randomness tests pass (minimum p-value 0.213; minimum pass rate 98/100), Shannon entropy reaches 7.942–7.999 bits, pixel correlation coefficients fall within ±0.003 of zero, NPCR spans 98.36–99.27%, and UACI spans 33.42–33.62% (both within theoretically optimal bounds). Zero recoverable information was obtained under known-plaintext (up to 1,000 pairs) and chosen-plaintext (seven structured patterns) attacks. Throughput ranges from 39 MB/s (ARM Cortex-A72) to 264 MB/s (Xilinx Artix-7 FPGA), with ROI-selective encryption reducing overhead to 2–5% relative to AES-256-CTR. Bit-perfect lossless decryption (PSNR = ∞, SSIM = 1.000) is verified for all tested modalities, and a Hadoop/Spark pipeline achieves 100% reconstruction accuracy from 1 KB to 1 TB.