CyCity CQWS | Post-Quantum Cryptographic Shield

The Mathematics of RSA/ECC

The entire modern internet is built on one premise: it is easy to multiply two large prime numbers, but extremely difficult to factor the result.

For classical computers, factoring a 2048-bit RSA key would take millions of years.

Classical Supercomputer (General Number Field Sieve)Time: ~300 Trillion YearsExponential Complexity: O(exp(c · (log N)^(1/3) · (log log N)^(2/3)))

Quantum Computer (Shor's Algorithm on 4096 Qubits)Time: ~2 to 8 HoursPolynomial Complexity: O((log N)³)

Shor's Algorithm Mechanics

In 1994, Peter Shor formulated a quantum algorithm that uses quantum superposition and entanglement to factor in polynomial time.

A quantum computer with 4,000 to 10,000 qubits will execute Shor's algorithm in a matter of hours.

Critical Threat Window (Store-Now-Decrypt-Later):Adversaries are archiving unencrypted or RSA-encrypted telemetry from fiber lines today. Once CRQCs achieve quantum coherence, all archived RSA-2048 keys will be factored simultaneously.

Hybrid Key Exchange (ML-KEM + X25519)

CQWS uses a double-locked hybrid key exchange combining ML-KEM-768 (NIST FIPS 203) with classical X25519 Elliptic Curve (RFC 7748).

ML-KEM is based on Learning With Errors (LWE) over module lattices, while X25519 relies on elliptic curve Diffie-Hellman.

This hybrid framework ensures that even if an AI discovers a shortcut in lattice math, the channel is still fully secured by classical math.

Lock 1: Post-Quantum LatticeNIST FIPS 203

Module-Lattice (ML-KEM-768)

Hardness derived from Short Integer Solution (SIS) and Learning With Errors (LWE) across $k$-dimensional polynomial rings. Resistant to both classical and quantum Fourier analysis.

Lock 2: Classical CurveRFC 7748

Curve25519 (X25519 ECDH)

Decades of rigorous classical cryptanalysis. Protects against unknown future algebraic shortcuts in lattice schemes, ensuring complete defense-in-depth.

The Migration Timeline

The NSA and NIST mandate that all critical infrastructure migrate immediately toward post-quantum cryptography.

CQWS allows an instant migration to ML-KEM without modifying a single line of application code.

Phase 1 (2024-2026)

Cryptographic Discovery

Catalog all vulnerable RSA/ECC certs and endpoints across enterprise assets.

Phase 2 (Immediate)

CQWS Ring-0 Injection

Deploy kernel-level ML-KEM encapsulation without touching existing application code.

Phase 3 (2030 Mandate)

Full PQC Sovereignty

Complete compliance with NSA CNSA 2.0 and NIST FIPS 203/204 mandates.