cim-lwe-qubo-cryptanalysis

name

cim-lwe-qubo-cryptanalysis

description

CIM-BDD methodology for LWE cryptanalysis via penalty-free QUBO reduction on Coherent Ising Machines. Use when: analyzing Learning With Errors (LWE) problem security, reducing lattice problems to QUBO for quantum annealing/Ising machines, performing penalty-free mapping of cryptanalytic problems, designing hybrid quantum-classical cryptanalysis workflows, evaluating post-quantum cryptography parameter security. Core insight: algebraic elimination of the secret + nearest-plane decomposition yields compact QUBO without penalty terms.

CIM-BDD: LWE Cryptanalysis via Penalty-Free QUBO

Overview (arXiv:2606.22843)

CIM-BDD is a hybrid Bounded-Distance-Decoding solver for the LWE problem:

• LWE is the mathematical foundation of post-quantum cryptography (NIST standards)
• Reduces LWE to QUBO via strictly penalty-free mapping
• Uses Coherent Ising Machine (CIM) hardware for solving

Key Innovation: Penalty-Free Mapping

Traditional QUBO reductions use penalty terms to enforce constraints:

• Penalties increase energy landscape complexity
• Require careful parameter tuning
• Often dominate the objective function

CIM-BDD avoids this through:

1. Algebraic elimination of the secret: embeds LWE into q-ary lattice directly
2. Nearest-plane decomposition (Babai): yields compact binary representation
3. No penalty terms needed: constraints are structurally satisfied

Pipeline

Step 1: LWE Instance → BDD Problem

LWE: A·s + e = b (mod q)
→ Find closest lattice point in q-ary lattice Λ_q(A)
→ This is a Bounded-Distance-Decoding (BDD) problem

Step 2: BDD → QUBO (Penalty-Free)

BDD instance → Nearest-plane algorithm (Babai rounding)
→ Binary expansion of coefficients
→ Direct QUBO formulation: min x^T Q x

Step 3: QUBO → CIM

QUBO matrix Q → Ising Hamiltonian H = Σ J_ij σ_i^z σ_j^z
→ Run on Coherent Ising Machine
→ Read optimal binary solution → Decode lattice point

Applications

Post-Quantum Security Analysis

• Evaluate NIST PQC parameter choices (Kyber, Dilithium)
• Find weakest parameter sets for CIM-based attacks
• Compare classical vs quantum-classical hybrid attack complexity

Cryptographic Parameter Selection

• Use CIM-BDD as oracle during parameter selection
• Ensure q-ary lattice instances resist BDD at target security level

Hybrid Attack Design

• Combine with lattice reduction (BKZ) as preprocessing
• Use CIM-BDD for the final SVP/BDD step
• Classical-quantum division of labor

Implementation Notes

• QUBO size scales with lattice dimension and basis quality
• Preprocessing with BKZ reduction significantly improves results
• CIM hardware availability limits practical attack scale
• Penalty-free structure is critical: penalties would make QUBO landscape too rugged for CIM convergence

Activation

cim, coherent ising machine, LWE cryptanalysis, QUBO reduction, penalty-free mapping, post-quantum security, bounded distance decoding, lattice attacks, q-ary lattice