A Biometric‐Algebraic Block Cipher Framework Using Fingerprint Minutiae, Ridge Orientation Fields, and GL(8,GF(2))$$ GL\left(8, GF(2)\right) $$ Transformations for Dynamic S‐Box Generation

Abstract

The security of symmetric‐key block ciphers depends critically on the strength and structural unpredictability of their substitution boxes (S‐boxes). Existing constructions rely on fixed mathematical structures, such as finite field inversion, chaotic maps, or elliptic curves that are entirely independent of the encrypting user's identity, creating a fundamental separation between authentication and encryption layers. This article presents a formally analyzed framework that derives all cryptographic parameters of a block cipher directly and systematically from the five biometric feature classes of a fingerprint image: minutiae points, ridge orientation fields, singular points (cores and deltas), ridge frequency maps, and local block entropy. Each feature class is mapped, through a novel algebraic procedure, to a distinct cipher parameter: (i) minutiae coordinates and angles seed a Fisher‐Yates permutation that whitens the output of the S‐box permutation layer; (ii) the 8×8$$ 8\times 8 $$ ridge orientation field is binarized and corrected to generate an invertible matrix M∈GL(8,GF(2))$$ M\in GL\left(8, GF(2)\right) $$ for the affine diffusion transform; (iii) singular point topology determines the biometric‐adaptive round count R∈{8,…,32}$$ R\in \left\{8,\dots, 32\right\} $$ ; (iv) the mean ridge frequency selects the GF(28)$$ GF\left({2}^8\right) $$ irreducible polynomial from a set of four valid polynomials; and (v) the block entropy map calibrates the per‐round diffusion strength parameter δ∈{1,2,3}$$ \delta \in \left\{1,2,3\right\} $$ . Three multi‐round block encryption algorithms of increasing complexity are built upon this five‐parameter biometric cipher core, evaluated with a full Python reference implementation that reproduces every reported figure. The primary scheme (Algorithm II) achieves a plaintext avalanche effect of 49.6%±4.5%$$ 49.6\%\pm 4.5\% $$ and a key sensitivity of 50.3%±4.2%$$ 50.3\%\pm 4.2\% $$ (16 rounds, n=500$$ n=500 $$ trials), reaching within 1%$$ 1\% $$ of the ideal from round 1. The fingerprint S‐boxes exhibit nonlinearity values in the range [96,110]$$ \left[96,110\right] $$ with mean 103.8, differential uniformity Δ∈{10,12}$$ \Delta \in \left\{10,12\right\} $$ , SAC mean ≈0.500$$ \approx 0.500 $$ , BIC‐NL average ≈103.6$$ \approx 103.6 $$ , and algebraic degree 7 on all eight output bits. A critical cross‐user security property is demonstrated: encrypting identical plaintext with an identical conventional key but different fingerprint templates produces ciphertexts whose pairwise Hamming distance averages ≈50%$$ \approx 50\% $$ (range 46%$$ 46\% $$ – 58%$$ 58\% $$ per trial, 49.7%$$ 49.7\% $$ – 51.9%$$ 51.9\% $$ averaged over 30 trials per pair), confirming that the biometric parameter functions as a genuine second key factor. A parameter‐stability experiment under simulated repeated‐acquisition noise (translation, rotation, minutiae dropout and spurious detections) further shows that the coarse, quantized cipher parameters (round count, field polynomial, diffusion strength) remain stable, while the fine‐grained minutiae‐derived permutation does not—a scope limitation discussed openly alongside the reliance on synthetic ISO/IEC 19794‐2‐format templates.