Paper 2026/1653

Lumora: A Family of Permutation-Based Wide-Block Ciphers for Post-Quantum zkSNARK Applications

Abstract

The deployment of advanced cryptographic protocols such as zero-knowledge proofs (ZKPs) requires symmetric primitives optimized for fast verification inside proof systems. In frameworks based on Rank-1 Constraint Systems (R1CS), prover performance and proof size are dominated by the cost of arithmetization, specifically, by the number of nonlinear multiplication constraints. Traditional bit-oriented designs are typically inefficient under this metric. In this paper, we introduce Lumora, a family of arithmetization-oriented, permutation-based wide-block ciphers designed for efficient use inside zkSNARK circuits and for applications in post-quantum digital signatures. Each instance of Lumora follows a unified AES-like SPN structure defined over the binary extension field $\mathbb{F}_{2^n}$ for $n \in \{16,32,64\}$. The underlying permutation is instantiated as a block cipher via the Even-Mansour paradigm, which eliminates the R1CS constraint overhead of a separate key schedule, ensuring the prover's workload remains strictly focused on evaluating the public permutation. Finally, we provide a detailed security analysis of the Lumora family, together with implementation results and a comparison within the FAEST-EM-256 framework.