Current run
Choose exact identity bytes
The profile accepts 1–96 printable ASCII characters without spaces. It does not normalize case, aliases, or Unicode; those enrollment questions sit outside the construction.
1 · Public address
Identity → SHA-256 → syndrome
GPV §7.2 models this map as a random oracle. This bounded profile instead uses a named SHA-256 domain and unbiased 16-bit rejection sampling; that is executable, deterministic, and not a proof-preserving random-oracle instantiation.
- Exact UTF-8 bytes
- First SHA-256 block
- Syndrome u
- Rejected 16-bit words
2 · Central extraction
SampleISIS finds e with A e = u mod q
The authority solves for one coset representative, then runs GPV's randomized nearest-plane SampleD over the secret short basis. Repeated extraction returns the cached key, as the stateful extractor in GPV §7.2 requires.
A · e = u (mod 4093)
Public matrix A
Omniscient teaching view: master trapdoor T
The public-search control below does not receive this basis.
- Arbitrary representative t
- Sampled kernel vector v
- Extracted private key e=t+v
- Independent relation
- Key norm
- Second request
| Row | ||b*|| | c′ | r′ | z | tries |
|---|
3 · Dual-LWE encryption
One bit, current-run arithmetic
The sender uses only public A and u. The error samples here are centered-binomial teaching values, not the paper's discretized normal distribution.
p = Aᵀs + x · c = uᵀs + x′ + b⌊q/2⌋
- Uniform secret s
- Error x; scalar x′
- Ciphertext p; c
- c − eᵀp mod q
- Residual, two routes
4 · Failure and boundary controls
What the successful round trip does not prove
Changed identity
One-coordinate key mutation
Wrong identity key
Oversized error
5 · Parameter boundary
The theorem hypotheses are not decorative
Exact algebraic invariants can pass while security prerequisites fail. “Post-quantum” applies to the source construction under its LWE/SIS assumptions and parameters, not automatically to this four-dimensional run.
| Check | Current value | Verdict |
|---|
Deployment status.
NIST's current PQC portfolio standardizes/selects KEM and signature algorithms. This
GPV IBE profile is not an approved deployment scheme, and ML-KEM does not replace an
authority that extracts keys from identities or policies. NIST's FIPS 203 page carries
a November 17, 2025 potential-update notice; this lesson relies only on its classification
of ML-KEM as a KEM, not on an affected algorithm detail.
6 · Interface comparison
Same escrow question, different algebra
| System | Address | Extraction | Encryption | Trust and status |
|---|
Sources and retained limits
Read the construction, then read the caveats
- GPV 2008 full paper: §§4, 5.3 and 7 are the implemented source.
- Agrawal–Boneh–Boyen 2010 full paper: the unimplemented standard-model comparison.
- Post-quantum IBE and ABE encyclopedia entry.
- NIST PQC selected algorithms and FIPS 203, including its potential-updates notice.
- GGH Trapdoor for good-basis intuition.
Not implemented: secure TrapGen, production dimensions, a concrete estimator, QROM or CCA security, authenticated encryption, ABE policies, key enrollment, revocation, constant-time arithmetic, or a deployment profile. The deterministic seed is for reproducibility only.