Paper 2025/213

An Innovative Lightweight Symmetric Encryption Algorithm Integrating Little OaldresPuzzle\_Cryptic

Abstract

Little OaldresPuzzle_Cryptic (LOPC) is specified as a parameterized 128-bit keyed block-transformation core built from three internal components: the NeoAlzette 64-bit ARX-box layer, the XorConstantRotation (XCR) Hybrid8–Shadow round-material generator, and a reversible Key Switch Layer. For every 128-bit data block, the core is invoked with a 128-bit key and a one-time public input number_once; the implementation supports counter-indexed block processing by assigning distinct number_once values to successive blocks. Authentication is not implemented inside the LOPC core: authenticated encryption must be obtained by composing the core with an external MAC or AEAD wrapper. The paper gives a code-faithful specification of the current construction, including the diagonal NeoAlzette placement, XCR-derived round material, keyed switching, and the keyed bit-position tweak. For the NeoAlzette component, it provides local differential and linear MILP boxes, fixed-public arithmetic oracle interfaces, and a mathematical oracle-to-MILP backbone for MEDCP/MELCC-style single-characteristic searches. The current artifact additionally reports one-round 12-hour SCIP incumbent campaigns for differential and linear NeoAlzette characteristics; these are trace/oracle-consistent incumbents, not solver-certified optima. For XCR, it specifies the Hybrid8 byte layer, the zero-fill Shadow arithmetic operators, the non-padded polynomial-Weyl constant stream, and the exact component-oracle boundary; full pseudorandom-generator security of XCR is not claimed. The manuscript separates component-local evidence from composition-level security claims. It proves round invertibility of the specified core and records the current component-analysis infrastructure, but it does not claim a complete AEAD mode, a full PRP/PRG proof for the LOPC composition, or complete endpoint differential/linear hull bounds unless the corresponding endpoint enumeration is explicitly complete. The repository also contains a separate OPC companion block-cipher artifact; Appendix B records its artifact boundary, but OPC is not analyzed as part of the LOPC security claims. Keywords: ARX cryptography, lightweight symmetric encryption, NeoAlzette ARX-box, XorConstantRotation, round-material generation, counter-indexed block processing, keyed switching, shadow-boxed arithmetic, Hybrid8, MEDCP, MELCC, MILP trail search, endpoint HULL, implementation artifact

Note: The Current Revision and Ongoing Research Trajectory This manuscript and its accompanying artifacts represent a development snapshot as of mid-2026. While the underlying implementations—the LOPC core, the NeoAlzette V6.5 ARX-box, and the XCR Hybrid8-Shadow generator—are considered stable and are specified in a code-faithful manner, the associated cryptanalytic evidence must be understood within its current, well-defined boundaries. The active research track is maintained in the public repository, which integrates increasingly rigorous ARX-based automated evaluation tools. Established Foundations: Component Specifications & Reversibility: We provide complete executable specifications and formal proofs of invertibility for NeoAlzette and the Key Switch Layer, establishing the correctness of the implemented round functions. Exact Local Oracles & MILP Models: The paper defines precise mathematical oracles (DP and LC) for all four arithmetic cases (two-variable and fixed-public) and for the joint Boolean-arithmetic injection. These are translated into exact MILP constraint models for single-characteristic search. Resource-Limited Single-Characteristic Incumbents: We report the results of 12-hour SCIP campaigns, providing the best-known single-characteristic differential (80.43) and linear (16.62) weights for a one-round NeoAlzette. These are verified incumbents, as all local traces are oracle-consistent. Current Boundaries and Active Areas of Investigation: The Optimality Gap: The reported NeoAlzette MILP results are resource-limited incumbents, not solver-proven global optima. The SCIP runs ended by time limit with significant optimality gaps (e.g., >185% for the linear case). Ongoing work is focused on extending computation time and deploying complete semantic no-good cuts to either close this gap and achieve solver-verified optima or to prove completeness for specific endpoints. Multi-Round Extension: The current MILP analysis is strictly limited to a single round of the NeoAlzette component. Extending this framework to cover the full multi-round LOPC construction—and analyzing the resulting trail probabilities—is a primary objective of the ongoing evaluation. XCR Formal Security: While XCR is fully specified and its Hybrid8/Shadow component oracles are defined, a full, unconditional proof of its pseudorandomness (PRG security) remains an open theoretical challenge. The current analysis treats its security as a well-defined assumption (as per Section 38.4 of the specification). Complete Endpoint Enumeration and Compositional Security: Neither a complete endpoint differential/linear HULL for NeoAlzette nor a full pseudorandom permutation (PRP) security proof for the composed LOPC cipher has been established. These require exhaustive enumeration and further analysis of the interaction between the XCR-derived key schedule and the NeoAlzette/Key Switch layers. In summary, this paper provides a rigorous, executable foundation for the LOPC cipher and its components, backed by verified MILP models and a clear, honest assessment of the evidence level. The results reported here are the strongest findings from the first phase of this automated cryptanalytic campaign, and they serve as the benchmark for the ongoing, more exhaustive second phase. The repository continues to evolve, integrating the stricter evaluation methods necessary to address the open questions outlined above. The current implementation and research track are maintained here: https://github.com/Twilight-Dream-Of-Magic/NeoAlzette_ARX_CryptoAnalysis_MILP/