ARITHMETIC GEOMETRY FINGERPRINTS: COMPRESSED INVARIANTS FOR DIGEST AND STREAM CLASSIFICATION

This record contains the full manuscript Arithmetic Geometry Fingerprints: Compressed Invariants for Digest and Stream Classification, together with an executable implementation and empirical results. The paper introduces a deterministic feature-extraction framework for fixed-length cryptographic digests based on arithmetic and algebraic invariants. Rather than testing digests solely through direct bit-level statistics, each digest is mapped to a small algebraic or combinatorial model over a finite field, and only stable invariants of that model are retained. These “fingerprints” act as a lossy but informative compression designed for large-scale audit, clustering, anomaly detection, and regression testing. Three classes of fingerprints are developed. The first two are distributional and Boolean-function-based summaries derived from classical cryptographic criteria, including Walsh spectra and algebraic-degree proxies. The third class introduces a tractable arithmetic construction in which each digest is deterministically associated with a genus-one model over a finite field, and Frobenius trace and point-count invariants are used as a compact arithmetic signature. This construction is motivated by standard ideas from arithmetic geometry and zeta-function theory, but is applied here strictly as a feature extractor rather than as a cryptanalytic tool. Empirically, the framework reliably detects known weak generators and reduced-strength constructions, such as linear feedback shift registers and RC4-derived outputs, while full SHA-256 behaves as a robust negative control. Apparent deviations observed at small sample sizes disappear at larger scales, consistent with the design goals of SHA-256 and the Secure Hash Standard. No inversion, key recovery, or distinguishing attack on SHA-256 is claimed; demonstrating robustness against this class of arithmetic tests is itself treated as a validation outcome. The intended use cases are cryptographic auditing, implementation health checks, large-corpus forensics, and mathematical data science. The method complements existing statistical batteries such as NIST SP 800-22 and TestU01 by probing induced arithmetic invariants rather than direct bit-pattern symptoms. All code and data provided here are released for transparency, reproducibility, and independent verification.