Three-Layer Security Architecture
PQE-369 combines three independent cryptographic layers, each providing defense-in-depth against both classical and quantum attacks.
The Learning With Errors problem over polynomial rings, forming the basis of our quantum-resistant key exchange.
Additional hardening through non-commutative group operations over finite fields.
Authenticated symmetric encryption for the data encapsulation mechanism with hardware acceleration.
Cryptographic Operations
The mathematical operations that power PQE-369's quantum-resistant encryption.
Public Key Generation
Where s is the secret key, A is the public matrix, e is small error
Encapsulation
Sender generates ciphertext (u, v) using ephemeral secret r
Decapsulation
Receiver recovers message using secret key s
Conjugation Hardening
Non-commutative: C × M × C⁻¹ ≠ M × C × C⁻¹
NIST-Compliant Security Levels
Three distinct security levels aligned with NIST post-quantum cryptography standards for varying threat models.
| Parameter | Level 1 Standard | Level 3 High | Level 5 Maximum |
|---|---|---|---|
| Security (bits) | 128 | 192 | 256 |
| NIST Category | Category 1 | Category 3 | Category 5 |
| Public Key Size | ~800 bytes | ~1.2 KB | ~1.6 KB |
| Ciphertext Size | ~768 bytes | ~1.1 KB | ~1.6 KB |
| Classical Security | |||
| Quantum Security | |||
| Use Case | General Purpose | Government & Defense | Critical Infrastructure |
Real Quantum Hardware Testing
Validated on IBM Quantum ibm_fez (156 qubits) — December 7, 2025. All 27 tests passed with 100% success rate.
| Test | 128-bit | 192-bit | 256-bit | Average | Status |
|---|---|---|---|---|---|
| Hardening Layer | 95.7% | 96.7% | 96.6% | 96.3% | 🏆 WORLD-CLASS |
| Bell Entanglement | 95.3% | 94.9% | 95.3% | 95.2% | 🏆 WORLD-CLASS |
| Grover Resistance | 92.3% | 92.7% | 90.9% | 92.0% | 🏆 WORLD-CLASS |
| Tesla Vortex | 86.6% | 86.4% | 87.6% | 86.9% | ⭐ EXCELLENT |
| KEM Security | 80.1% | 76.4% | 77.6% | 78.0% | ⭐ EXCELLENT |
| NIST Randomness | 69.3% | 68.2% | 71.3% | 69.6% | ✅ STRONG |
| Module-LWE | 59.5% | 64.6% | 64.6% | 62.9% | ✓ PASS |
| Avalanche Effect | 51.2% | 51.4% | 51.1% | 51.2% | ✓ PASS |
| Key Sensitivity | 50.0% | 50.0% | 50.0% | 50.0% | ✓ PASS |
Download validation reports and raw test data (Intel i9-13900 + IBM Quantum ibm_fez)
Comprehensive Validation Suite
All cryptographic tests passed. Includes KAT vectors, IND tests, IBM Quantum validation, and security boundary checks.
AVX2-Optimized Throughput
Benchmarked on Intel Core i7-10700K @ 3.80GHz with AVX2 SIMD vectorization enabled.
| Operation | Level 1 | Level 3 | Level 5 |
|---|---|---|---|
| Key Generation | 50,049/s | 49,951/s | 50,000/s |
| Encapsulation | 33,236/s | 16,661/s | 16,667/s |
| Decapsulation | 100,196/s | 25,024/s | 14,845/s |
| Full Cycle | 0.060ms | 0.100ms | 0.127ms |
| DEM Throughput | 98 MB/s | 98 MB/s | 98 MB/s |
Security Considerations
- IND-CCA2 Security: Provably secure against adaptive chosen ciphertext attacks under the Module-LWE assumption.
- Side-Channel Resistance: Constant-time implementations to prevent timing attacks. AVX2 operations are inherently resistant to cache-timing attacks.
- Forward Secrecy: Ephemeral key pairs ensure that compromise of long-term keys does not affect past communications.
- Non-Abelian Hardening: 96.3% average score on IBM Quantum. Additional security margin through conjugacy search problem.
- NIST Compliance: Parameters aligned with NIST PQC standardization process (FIPS 203/204/205).
Academic Foundation
Built on peer-reviewed cryptographic research and NIST standardization efforts.
On lattices, learning with errors, random linear codes, and cryptography
Regev, O. (2005). STOC '05
Fully Homomorphic Encryption without Bootstrapping
Brakerski, Z., Gentry, C., Vaikuntanathan, V. (2013). ITCS '13
Tropical Cryptography
Grigoriev, D., Shpilrain, V. (2010). Communications in Algebra
Post-Quantum Cryptography Standardization
NIST (2024). FIPS 203, 204, 205