FractalShield: Oracle-Free Verification with Geometric Cost Escalation for Offline Brute-Force Resistance

We present FractalShield, a novel layered file-encryption construction that simultaneously achieves:

• (i) Oracle-Free Verification (OFV): The attacker cannot determine password correctness without spending the full key-derivation cost per layer.

• (ii) Geometric Cost Escalation: Protection levels escalate at 3.5×, 7.5×, and 15.5× the baseline.

• (iii) Statistical Indistinguishability: Real versus decoy ciphertext layers are indistinguishable to an adversary.

• (iv) Serverless Operation: Fully functional for offline environments.

Standard MAC-protected encryption grants an attacker instant oracle access to key correctness, converting offline brute-force into a pure throughput problem. While memory-hard KDFs slow each attempt, they do not eliminate this oracle. FractalShield eliminates it entirely via internal magic-prefix detection across layers of escalating KDF cost, where decoy layers remain statistically identical to the real payload.

Security Validation & Formal Results

We provide four formal security theorems:

1. Integrity.

2. Two-time-pad resistance.

3. OFV (Oracle-Free Verification).

4. IND-CCA2 under the Random Oracle Model (ROM).

The framework includes a resolved min-entropy bound (H∞≥128 bits via a four-lemma chain) and full empirical validation through the NIST SP 800-22 battery:

• Tests 01–13: 13/13 pass (n=2×106 bits, 10 independent pairs).

• Tests 14–15: 6/8 eligible pairs pass.

Technical Advances (v2.0)

This version introduces cumulative advances over v1.0, transforming previous conjectures into proven results:

• Theorem 5.7: PRG under ROM (formerly Conjecture 4.5).

• Theorem 5.11: IND-CCA2 under ROM (formerly Open Problem 1.3).

• Theorem 6.5: H∞≥128 (formerly Open Problem 1.1).

• NIST STS Execution: Substantial resolution of Open Problem 1.4.

• Refinements: Correction of normalization in Eq. (8'), raw-field χ2 adjusted from 1752 to $\approx 245$ ($p=0.66$), and honest reporting of the Lyapunov spectrum (DKY≈9, indicating weak chaos and entropy derived from injectivity).

The construction remains KDF-agnostic. All security results are stated with explicit assumptions and open residuals.

Full implementation available at: https://github.com/Fracta-Axis/Fractalyx