Real‑World Example: 1EXXGnGN98yEEx48fhAMPt8DuzwaG5Lh8h
7.1 Initial data of compromise
Target Wallet Profile
Bitcoin address: 1EXXGnGN98yEEx48fhAMPt8DuzwaG5Lh8h
Address type: P2PKH legacy address used by an embedded BLE wallet.
Balance at recovery: $188,775 USD in BTC equivalent.
Hardware & Crypto Stack
Platform: Nordic nRF5340 (ARM Cortex‑M33 with TrustZone and TFM).
Crypto library: PSA Crypto with variable‑time ECDSA scalar multiplication.
Isolation model: Secure World (keys, ECDSA) vs Normal World (BLE wallet app).
Attacker Capabilities
Normal‑World code was allowed to request ECDSA signatures and timestamp each operation with microsecond resolution hardware timers.
Over 100,000 signing operations were collected for correlation analysis.
The ChronoForge methodology applied here follows exactly the architecture described in
CryptoDeepTech's article on the Chronoforge Attack on ARM TrustZone – Critical Timing Side‑Channel
Vulnerability in Bitcoin Private Key Extraction via Nordic nRF52/nRF53. The Normal World becomes a timing oracle,
while VulnCipher acts as a scientific cryptanalytic engine that transforms raw timing traces into a usable
private key candidate for the address 1EXXGnGN98yEEx48fhAMPt8DuzwaG5Lh8h.
Mathematical Core of the ChronoForge Attack
ECDSA secp256k1 parameters
Both the CryptoDeepTech and KEYHUNTERS research papers begin by fixing the standard Bitcoin secp256k1 domain parameters:
Curve equation: y² = x³ + 7 (mod p)
Prime field p = 2²⁵⁶ - 2³² - 977
Order n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
Base point G = (Gx, Gy)
Gx = 0x79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
Gy = 0x483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
Vulnerable double‑and‑add scalar multiplication
The vulnerable implementation on nRF5340 uses a classic left‑to‑right double‑and‑add algorithm.
The key problem is that pointadd() executes only when the processed key bit is 1,
and its execution time differs significantly from pointdouble(). This turns every bit of
the private key into a timing‑dependent random variable.
void ecdsa_scalar_multiply_vulnerable(const uint8_t *d, point_t *Q) {
point_t acc = G; // accumulator
for (int i = 255; i >= 0; --i) {
point_double(&acc, &acc); // T_double ≈ 3.2 µs
int bit = (d[i / 8] >> (i % 8)) & 1;
if (bit) {
point_add(&acc, &acc, &G); // T_add ≈ 5.8 µs
}
}
*Q = acc;
}
Ti = T_double + di · T_add + εi
// Total time for 256‑bit scalar multiplication
T_total = 256 · T_double + H(d) · T_add + noise
// H(d) – Hamming weight of the private key
In the dedicated mathematical paper "ChronoForge Attack – Mathematical Formalization of Bitcoin Private Key Extraction via Timing Side‑Channels", CryptoDeepTech shows that this model is sufficient to recover most bits of the 256‑bit private key by correlation analysis, assuming access to N ≈ 10⁵ timing samples.
Correlation Power Analysis (CPA) for each key bit
For each bit position k, VulnCipher builds two hypothesis timing vectors: one assuming
d_k = 0 and one assuming d_k = 1. The observed timing vector
T = (T₁, …, T_N) is then correlated against both hypotheses.
T = (T₁, T₂, …, T_N)
// Hypothesis vectors for bit k
H₀(k) = (h₀,₁(k), h₀,₂(k), …, h₀,N(k)) // expected timings if d_k = 0
H₁(k) = (h₁,₁(k), h₁,₂(k), …, h₁,N(k)) // expected timings if d_k = 1
// Pearson correlation for each hypothesis
r₀(k) = corr(T, H₀(k))
r₁(k) = corr(T, H₁(k))
// Bit decision rule
d̂_k = 1, if r₁(k) > r₀(k); otherwise 0
C(k) = ( rd̂_k(k) − r1−d̂_k(k) ) / ( |rd̂_k(k)| + |r1−d̂_k(k)| )
// Bits with C(k) < 0.5 are marked as "weak" and delegated to brute‑force correction.
For the 1EXXG... wallet, the VulnCipher‑style analysis yielded an average correlation
of about 0.842 across bits and an overall recovery accuracy of
≈94.5%, leaving only 18 weak bits to be corrected via constrained
brute‑force search.
VulnCipher Application Workflow
From timing traces to a usable private key
The VulnCipher framework, as described in the VulnCipher cryptotools article and integrated into the ChronoForge scientific ecosystem, is built as a modular scientific platform. It transforms raw side‑channel data into a verified private key through a chain of algorithmic stages:
- Timing Collection Module (TCM) – collects N precise timing samples using hardware timers.
- Preprocessing Engine (PE) – cleans, normalizes and filters timing traces (z‑score, 3σ rule, drift removal).
- Hypothesis Generation Module (HGM) – models expected timing for each key bit and branch pattern.
- Statistical Analysis Engine (SAE) – performs correlation analysis, SNR estimation and guessing entropy.
- Key Recovery Module (KRM) – assembles a key candidate, marks weak bits and performs local enumeration.
- Validation & Verification Module (VVM) – recomputes public key and Bitcoin address to prove correctness.
Brute‑force correction of weak bits
After CPA, VulnCipher marks a small set E of weak bits (here, |E| = 18) whose
confidence is below the threshold. Instead of searching the full 2²⁵⁶ space, the algorithm
restricts enumeration to 2^|E| = 262,144 candidates – a task solvable in seconds on commodity hardware.
E = { k | C(k) < 0.5 } // weak bit positions, |E| = 18
for each x in [0, 2|E| − 1]:
d_candidate ← d̂ with bits in E replaced by bits of x
Q_candidate = d_candidate · G
if Address(Q_candidate) == 1EXXGnGN98yEEx48fhAMPt8DuzwaG5Lh8h:
return d_candidate
In the case study, the expected search time is on the order of a few dozen seconds for a test rig capable of performing around 10,000 key verification operations per second – a trivial cost compared to the recovered $188,775.
Recovered key material
Following the formal description in the mathematical paper, the recovered key and its cryptographic bindings are:
| Parameter | Value (documented in research) |
|---|---|
| Bitcoin address | 1EXXGnGN98yEEx48fhAMPt8DuzwaG5Lh8h |
| Recovered private key (HEX) | F2E242938B92DA39A50AC0057D7DCFEDFDD58F7750BC06A72B11F1B821760A4A |
| Recovered private key (WIF, compressed) | L5MqyroFa1pcprty2vXc5xBJWdDfuicetxoQB4PZVMqQgqRVfnMB |
| Recovered public key (compressed) | 02658AC78A3526CFC47533E7C6C66DFA97E1C74EBCDA6B8F49C9EB4E2CC7A95710 |
| Verification relation | Q = d · G, Address(Q) = 1EXXGnGN98yEEx48fhAMPt8DuzwaG5Lh8h |
| Funds recovered (USD) | $188,775 at the time of operation |
The research explicitly warns that such key material must never be reused or published in raw form in production environments; it serves only as a controlled demonstration of the attack's feasibility.
Scientific Context: CryptoDeepTech & KEYHUNTERS Research
ChronoForge in embedded wallets and Bitcoin Core
The CryptoDeepTech chronicle of the ChronoForge Attack focuses on ARM TrustZone‑based microcontrollers (Nordic nRF52/nRF53/nRF5340) and PSA Crypto / ECDSA implementations, while the KEYHUNTERS article analyzes similar variable‑time issues in the Bitcoin Core BIP324 ECDH code and the ellswift decoding path. Both streams converge on a common scientific conclusion:
- Mathematical strength of secp256k1 is intact – the problem lies in implementation‑level timing leaks.
- Non‑constant‑time scalar multiplication and decoding create a measurable side‑channel.
- With enough samples, an attacker can reconstruct private keys bit by bit.
- VulnCipher generalizes this process into a reusable tool for both offense (audit, recovery) and defense.
Formal classification and CVE landscape
KEYHUNTERS situate ChronoForge within the broader taxonomy of Elliptic Curve Side‑Channel Timing Attacks, referencing public CVEs such as:
- CVE‑2019‑25003 – variable‑time scalar operations in libsecp256k1 enabling timing attacks.
- CVE‑2024‑48930 – side‑channel leakage in EC‑DH implementation related to ellswift decoding.
The CryptoDeepTech ChronoForge papers complement this with concrete attack timelines, from initial device compromise through timing data collection, CPA analysis, limited brute‑force, all the way to Bitcoin transaction creation and fund extraction. Together, they provide a scientifically rigorous blueprint for how a $188,775 recovery can be both reproducible and defensible as a research result.
T+00 min – attacker gains Normal‑World access to nRF5340 BLE wallet
T+02 min – malicious app starts collecting ECDSA signing timings
T+35 min – ≈100,000 timing samples collected and exfiltrated
T+50 min – CPA recovers ≈94.5% of key bits; 16–18 bits uncertain
T+52 min – constrained brute‑force fixes weak bits
T+52+ – private key verified; funds (~$188,775) transferred from 1EXXG...
Both articles emphasize that the same methodologies can – and should – be used in a defensive context: security audits, formal verification of constant‑time implementations, and controlled recovery of legitimately lost wallets where vulnerable libraries were historically deployed.