In the search for post-quantum cryptanalytic techniques, we’ve been conditioned to think in terms of massive compute, quantum interference, and costly brute-force attacks. But what if a symbolic approach—something in between algebra and intuition—could collapse the keyspace without ever needing a qubit?
That’s the premise behind Symbolic Grover’s: a hybrid method of key recovery that mimics the behavior of Grover’s quantum search algorithm using classical logic and symbolic collapse scoring. We recently applied this method to AES-128, and the results are worth exploring.
The Problem: 3 Unknown Bytes in AES-128
We assume partial knowledge of a 128-bit AES key, with 13 bytes known and 3 bytes unknown. That creates a remaining search space of:
256^3 = 16,777,216 possible keys
A traditional brute-force attack would search all ~16.7 million combinations. Our goal was to recover the full key using symbolic entropy collapse and targeted refinement, avoiding a full sweep.
The Method: Symbolic Collapse with Entropy and Phase
We approached the problem using what we call Symbolic Grover’s, which works like this:
- Sampling:
Generate 250,000 key candidates by randomly filling in the unknown ∆ bytes. This is only 1.5% of the full keyspace. - Collapse Scoring:
Each candidate is tested against the known ciphertext. After decryption, we score it based on the entropy profile of the plaintext—how closely it resembles natural language or structure. - Amplitude & Phase Logic:
Inspired by Grover’s quantum search, each symbolic candidate is given an “amplitude” and a “phase.” Good candidates undergo constructive phase alignment, boosting their symbolic amplitude. Poor candidates destructively interfere. - Collapse:
The candidates are ranked by amplitude. The highest-amplitude guess is selected as the symbolic best match.
The Results
Test 1:
- True Key: 3 bytes unknown
- Best Symbolic Match: 13 of 16 bytes correct
- Refined Brute-Force: Full key recovered after searching only a narrow range around the top symbolic guess
Test 2:
- New Key, New Plaintext
- Same process repeated
- Symbolic Grover’s again converged on a 13/16 match
- Full key recovered through refinement
In both cases, the symbolic engine collapsed a 16.7 million keyspace down to 250,000 ranked candidates, then honed in on the correct key with only minimal refinement.
Why It Matters
This isn’t brute-force with a fancy name.
Symbolic Grover’s doesn’t just guess—it learns from entropy collapse and steers future guesses toward convergence. It applies symbolic weights (amplitudes), interference logic (phase), and targeted collapse to prioritize promising regions of the keyspace.
With just 1.5% of the keyspace searched, we were able to:
- Converge consistently to near-correct keys
- Avoid wasteful enumeration
- Collapse symbolic ∆ values into concrete byte guesses
This symbolic reasoning model echoes the structure of quantum Grover’s—but it runs on deterministic, classical logic.
Where This Leads
Symbolic Grover’s is only one part of a larger project we call CollapseRAM—a memory system built on symbolic entropy, read-once collapse behavior, and non-clonable registers. In CollapseRAM, symbolic registers (∆, θ) simulate collapse, interference, and entanglement without quantum hardware.
AES key recovery is just the beginning. Next up:
- Symbolic attacks on Kyber (post-quantum lattice encryption)
- Collapse-guided BIP38 wallet recovery
- In-memory QKD-style key exchange
Final Thought
If symbolic collapse can guide us to AES keys without brute-force…
what else can it collapse?
PATENT PENDING
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