The Alaniz Cipher: Encryption from Nonlinear Sheaf Morphisms over Graphs (SPN Fix)

This record contains the preprint of the paper:“The Alaniz Cipher: Encryption from Nonlinear Sheaf Morphisms over Graphs” (Lucas Damian Alaniz Pintos, 2026). The Alaniz cipher is a new post-quantum public-key encryption scheme whose security is based on the Nonlinear Sheaf Morphism Inversion Problem (NL‑SMIP), a hardness assumption that combines polynomial systems with secret coefficients and the cohomology of cellular sheaves over graphs. Messages are encoded as global sections H0(G,F0)H0(G,F0) and encrypted viacv=Avsv+Bvσ(Avsv)cv=Avsv+Bvσ(Avsv), with secret linear maps (Av,Bv)(Av,Bv) per node and a public nonlinear map σσ. The paper: defines NL‑SMIP and proves it is at least NP‑hard via a reduction from the Multivariate Quadratic (MQ) problem; proves decryption correctness and a uniqueness bound using a cohomological tree‑propagation argument; analyzes security against Gröbner basis, XL, MinRank, linearization, and known quantum attacks (Shor, Grover, HHL, quantum walks); discusses variants, limitations, and open problems, and compares the scheme with existing post‑quantum proposals such as Kyber and multivariate schemes like Rainbow and UOV. The goal of this preprint is to introduce the Alaniz cipher and NL‑SMIP to the cryptographic community and to facilitate independent cryptanalysis and further research on sheaf‑based post‑quantum cryptography.