Domain-Informed Representation for Evolutionary Sieving in Integral and Module Lattices

The Lenstra-Lenstra-Lovász (LLL) algorithm is a seminal contribution to computer science used for lattice basis reduction, yet its polynomial-time outputs produce bases that are far from optimal as the dimension grows. We show that deep reinforcement learning can discover strictly superior, generalizable reduction strategies by interacting with the primitive action space of LLL. We formulate lattice reduction as a single-player Markov Decision Process (MDP) and train a deep residual network using an AlphaZero-style self-play pipeline augmented with adaptive-horizon MCTS (Monte Carlo Tree Search), which couples multi-step network predictions with an entropy-gated expansion mechanism. The resulting policy, DeltaStar, is trained exclusively on small $8$-dimensional $q$-ary lattices and requires fewer primitive row operations than LLL. Crucially, it generalizes zero-shot to unseen moduli and higher dimensions up to $n=32$ without retraining.

Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

We report genuine-un-compiled, textbook-faithful-quantum cryptanalysis of symmetric-cipher structures executed on real IBM quantum hardware (ibm_kingston, Heron generation). Using Simon's algorithm we recover the hidden period of the Even-Mansour cipher up to security parameter N = 10 on real hardware, beyond the largest previously reported real-hardware key recovery of N = 4, and we cleanly recover the periods of a 3-round Feistel (DES-family) construction at block sizes 6 and 8; a 21-qubit block-10 instance is verified in simulation and submitted to hardware. We further provide a breadth-first benchmark of five genuine quantum attacks spanning four symmetric-cipher design paradigms -- Bernstein-Vazirani (linear structure, single query), Grover (SPN key search, quadratic), and Simon (Even-Mansour, CBC-MAC forgery, and Feistel; exponential-to-polynomial in query complexity) -- validated to the classical-simulation ceiling of 25 qubits. We are deliberately explicit about scope: these attacks target reduced or structured constructions in the Q2 (quantum-query) model, asymptotically follow the birthday bound and therefore do not constitute quantum advantage over classical collision-finding, do not break full AES/RSA or 16-round DES, and rely on error mitigation rather than fault-tolerant error correction. Our contribution is the real-hardware demonstration at record structure sizes, the breadth of genuine algorithmic coverage across four paradigms, and an honest, reproducible benchmark with public artifacts.