Phase 2: analytic Renyi divergence certification - #3
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Certification layer (certification.py):
- Computes R_a(P_spec || P_ideal) exactly from the RCDT table and
BerExp quantization, without sampling
- Base sampler: R_128-1 ~ 9.1e-23 (informational; CDT quantization)
- Full sampler: R_128-1 ~ 1.3e-29 at typical (mu,sigma), 6 orders
of magnitude below the 2^{-75} target — BerExp rejection tightens
the distribution dramatically
- Tested at hostile fractional mu (0.0, 0.25, 0.5) and across sigma
range; all pass with large margin
- Finding: sigma=1.8 (near sigma0=1.8205 boundary) marginally fails
at R_128-1 = 3.94e-23 vs 2.65e-23 target — genuine BerExp
quantization effect at extreme sigma values
Effect-size diagnostics (saga.py):
- effect_sizes() method on UnivariateSamples: TV distance with
null-expected bias floor, R_2 divergence (= log(1 + chi2/n)),
resolution floor 1/sqrt(N)
- Framed as diagnostics, not security certification
Seeded determinism (test_sampler_determinism.py):
- Same seed produces identical output stream
- Different seeds produce different streams
README scope paragraph:
- Statistical layer detects bugs at delta ~ 1/sqrt(N)
- Certification layer certifies proof-level RD bounds
- Neither detects trace-level side-channel leakage
Test suite: 104 passed, 12 skipped (known blind spots), 0 failed
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Adds
certification.py— analytic Renyi divergence computation for the base sampler and full sampler chain. This is the missing piece between statistical testing (which tops out at ~1/sqrt(N) sensitivity) and the proof-level guarantees (R_128 - 1 < 2^{-75}).Key results at default params:
Uses mpmath for arbitrary-precision arithmetic. Tests verify the computation at 6 (mu, sigma) pairs against known bounds.
Also updates the README with scope/install instructions.