Ramanujan expander networks for authenticated grayscale image encryption

Image ciphers are usually proposed with a fixed battery of statistical indicators, and the numbers reported for competing designs are almost never produced under the same conditions, on the same pictures, with the same code. We address that gap for one family of designs and propose a cipher whose components come from provable combinatorics and standardised cryptography rather than a chaotic map. The scheme, RAPID-Gray, builds three keyed switching networks on the Lubotzky-Phillips-Sarnak Ramanujan graph X(29,41), restricts them to the image domain by cycle walking, interleaves them with two Cauchy maximum-distance-separable layers over GF(28), applies a two-pass nonlinear feedback diffusion, and closes with AES-CTR whitening and an HMAC-SHA-256 tag over a fresh 96-bit nonce. Five recent designs were re-implemented without algorithmic alteration and evaluated with identical code on three medical and three general 256 × 256 grayscale images. All six recovered every plaintext exactly. Beyond that, the spread is wide: cipher entropy ranges from 6.9320 to 7.9976 bits, one collapses to an NPCR of 0.0015%, two produce unchanged ciphertexts under the tested one-bit key perturbation, and only the proposed scheme rejects tampered ciphertexts. Agreement on entropy and correlation says little; plaintext sensitivity, key sensitivity and integrity are where these designs actually separate. Three of the five reference designs left a step of their published description underdetermined; in each case a fixed, reversible resolution was adopted and is documented, so the comparison is between faithful re-implementations rather than between the published texts themselves.