Date of Publication : June 2026

Abstract: The advent of large-scale quantum computing threatens the public-key primitives that secure today’s digital communication. Code-based cryptography, and in particular the McEliece and Niederreiter families, is a leading candidate for post-quantum security because no efficient quantum algorithm is known against the general decoding problem. This paper proposes a hybrid security scheme that couples a Hexi (GF(2⁴)) code-based Niederreiter cryptosystem with an integer discrete wavelet transform (DWT) image steganographic channel. The plaintext is first mapped to a bounded-weight error vector over the hexi field and encrypted into a compact syndrome using the public parity-check matrix H′ = M • H • P. The resulting ciphertext bitstream is then embedded into the high-frequency wavelet sub-bands (HH, HL, LH) of the red, green and blue channels of a cover image through a reversible integer Haar lifting transform, so that the stego image is visually indistinguishable from the cover and the payload is recovered without loss. A fully worked example over the hexi field is presented, and the embedding stage is evaluated on six 512 × 512 colour cover images. Carrying 24,576 bits per image (0.094 bits per pixel), the scheme attains an average peak signal-to-noise ratio of 66.6 dB and a structural similarity index of 0.9999, while extraction is bit-exact for every image. The combination delivers confidentiality (post-quantum encryption) and undetectability (steganographic concealment) in a single pipeline.

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