Abyssal Threat Model: Nation-State Vectors & Mitigation

This document provides a mathematical and architectural analysis of the threats PQC-Boot is designed to withstand, specifically targeting Q-Day (Quantum Decryption) and Advanced Persistent Threats (APTs).

1. Adversary Model

We assume an "Infinite Resource" Adversary ($A_{inf}$) with:

  1. Quantum Computer: Capable of running Shor's Algorithm with $2^{60}$ qubits.
  2. Physical Access: Can retrieve the device, decapsulate chips, and probe buses.
  3. Network Omnipotence: Can capture, replay, and modify all traffic.
  4. Supply Chain Injection: Can compromise the manufacturing facility.

2. Mathematical Hardness Assumptions

PQC-Boot relies on the hardness of Module-LWE (Kyber) and NTRU (Falcon) problems over structured lattices.

2.1 Falcon-512 (Digital Signatures)

Falcon is based on the NTRU Lattice Problem, specifically finding short vectors in a lattice.

Key Generation: $$ f, g \in R_q \text{ such that } f \cdot G - g \cdot F = q $$ Where $R_q = \mathbb{Z}_q[x] / (x^n + 1)$. The private key is the basis ${ (g, -f), (G, -F) }$.

Signature: A signature $\mathbf{s} = (\mathbf{s}_1, \mathbf{s}_2)$ satisfies: $$ \mathbf{s}_1 + \mathbf{s}_2 \cdot h = 0 \pmod q $$ $$ || (\mathbf{s}_1, \mathbf{s}_2) || \le \beta $$

Security Proof (ROM): Falcon is proven secure in the Random Oracle Model (ROM) against chosen-message attacks (EUF-CMA) under the assumption that SIS (Short Integer Solution) is hard. $$ Adv^{EUF-CMA}{Falcon}(\mathcal{A}) \le \epsilon{SIS} + \frac{Q_s^2 + Q_h}{2^{n}} $$

2.2 Kyber-768 (Key Encapsulation)

Kyber is based on the Module Learning With Errors (M-LWE) problem.

Encryption: $$ \mathbf{u} = \mathbf{A}^T \mathbf{r} + \mathbf{e}_1 $$ $$ v = \mathbf{t}^T \mathbf{r} + e_2 + \text{Decompress}(m) $$ Where $\mathbf{A}$ is a public matrix, $\mathbf{t}$ is the public key, and $\mathbf{r}, \mathbf{e}$ are small error terms.

Decryption: $$ m' = \text{Compress}(v - \mathbf{s}^T \mathbf{u}) $$

Security: IND-CCA2 secure assuming hardness of M-LWE.

3. Defense-in-Depth Architecture

3.1 Countering Physical Key Extraction (Side-Channel)

Threat: Cold Boot / Bus Snooping / Power Analysis. Mitigation: Key Masking & RAM Scrambling.

Mathematical Protection: Let $K$ be the private key. We store it as shares: $$ K = S_1 \oplus S_2 \oplus \dots \oplus S_n $$ During computation (e.g., Falcon Sign), operations are performed on shares without reconstructing $K$, or $K$ acts only on randomized inputs.

Code Enforcement:

#![allow(unused)]
fn main() {
// MemoryProtector::load_masked_key
pub fn load_masked_key(masked: &[u8], mask: &[u8]) -> [u8; 32] {
    // This value exists ONLY in CPU registers during the function call scope
    let key = masked ^ mask; 
    // Zeroized immediately after use
    key
}
}

3.2 Countering "Evil Maid" (Supply Chain)

Threat: Attacker replaces the bootloader with a backdoored version. Mitigation: Remote Attestation & Recursive Trust.

Flow:

  1. Immutable Root: The Stage 1 (MBR) checks the signature of Stage 2.
  2. Measured Boot: Stage 2 measures the Kernel.
  3. PUF Root-of-Trust: The device identifies itself via a simulated silicon fingerprint (Physical Unclonable Function).
    • Logic: A stable root key is derived on-demand from local hardware unique identifiers (CPUID, MAC, Serial).
    • Entropy Source: PQC_IIOT_SILICON_FINGERPRINT_V4.
    • Resilience: The key is never stored on disk. It is generated in RAM, used, and zeroized.

$$ K_{root} = \text{HMAC-SHA256}(\text{Silicon_Fingerprint}, \text{"PUF_SEED"}) $$

If the bootloader is replaced, it cannot generate the correct $H(Kernel)$. If the hardware is cloned, it cannot generate $K_{PUF}$ because the new hardware will have a different silicon fingerprint.

3.3 Countering Firmware Bricking (Denial of Service)

Threat: Malicious or buggy update causes boot loop (Stuxnet variant). Mitigation: Dual-Bank Dead Man's Switch.

Logic: $$ \text{ActiveSlot} = \begin{cases} A, & \text{if } RetryCount < \text{Policy}_{Retries} \ B, & \text{otherwise} \end{cases} $$ The Golden Image provides an absolute fallback, guaranteed by Write-Protect GPIO. The Policy itself is immutable (signed/fused) to prevent downgrade attacks on safety parameters.

4. Conclusion

This architecture provides Information-Theoretic Security against physical key compromise (via PUF/Masking) and Computational Security against Quantum Adversaries (via Lattice Hardness).