cim-bdd-penalty-free-lwe-cryptanalysis

name	cim-bdd-penalty-free-lwe-cryptanalysis
description	CIM-BDD methodology — hybrid Bounded-Distance-Decoding solver that reduces LWE to QUBO via penalty-free mapping, using algebraic elimination and adaptive mixed-radix encoding for NISQ devices.
trigger	cim-bdd, penalty-free qubo, lwe cryptanalysis, coherent ising machine, bounded distance decoding, lwe to qubo mapping, post-quantum cryptanalysis hardware
category	quantum

CIM-BDD: Penalty-Free LWE Cryptanalysis via Coherent Ising Machine

Description

Hybrid BDD solver reducing LWE to QUBO through strictly penalty-free mapping. Algebraic elimination embeds LWE into a q-ary lattice, absorbing modular arithmetic and recasting as CVP. Squared error norm used directly as QUBO energy — cryptographic noise is minimized rather than penalized. CR-BNP projection drives adaptive mixed-radix encoder reducing qubit count and coefficient range. Validated on 40-dimensional LWE Challenge instances on CPQC-550.

Activation Keywords

• cim-bdd
• penalty-free qubo
• lwe cryptanalysis
• coherent ising machine
• bounded distance decoding
• lwe to qubo mapping
• post-quantum cryptanalysis hardware
• cr-bnp encoding

Core Methodology

Step 1: Algebraic Elimination of Secret

1. Embed LWE instance into q-ary lattice
2. Absorb modular arithmetic into lattice structure
3. Recast as Closest Vector Problem (CVP)
4. Squared error norm becomes the QUBO energy directly (no penalty terms)

Step 2: CR-BNP Encoding

1. Apply Continuous Relaxed Babai's Nearest Plane (CR-BNP) projection
2. Drive adaptive mixed-radix encoder
3. Reduce both qubit count and QUBO coefficient range
4. Enable single batched hardware submission

Step 3: Early-Stopping Certificate

1. Derive statistically bounded early-stopping threshold (T_early)
2. Use as one-sided certificate for solution quality
3. Double as Decision-LWE distinguisher

Step 4: Hardware Execution

1. Map reduced QUBO to Coherent Ising Machine (CPQC-550)
2. Execute single batched submission
3. Apply T_early threshold for convergence detection

Key Innovations

• Penalty-Free Mapping: Eliminates penalty coefficients that plague standard QUBO formulations
• Mixed-Radix Encoding: Dramatically reduces qubit requirements vs. binary encoding
• CR-BNP Projection: Bridges lattice reduction with quantum optimization
• Early-Stopping Certificate: Statistical bound eliminates need for convergence heuristics

When to Use

• LWE cryptanalysis on NISQ devices
• Constrained optimization requiring penalty-free formulation
• Post-quantum cryptography security assessment
• Algorithm-hardware co-design for quantum-classical hybrids

Related Papers

• arXiv:2606.22843 — When the Learning With Errors Problem Meets the Coherent Ising Machine

Resources

• arXiv: https://arxiv.org/abs/2606.22843