BMM-Certified RNG

Certification Chain

The Math Engine uses a BMM-certified random number generator for all game-determining randomness. The certification chain is preserved through an isolated PHP microservice:

+---------------+       HTTP POST /rng       +----------------------+
|  Game Engine  | -------------------------> | PHP RNG Microservice |
+---------------+                            |      (Certified)     |
                                             +----------+-----------+
                                                        |
                                                        v
                                             +-----------------------+
                                             | Certified RNG Wrapper |
                                             +----------+------------+
                                                        |
                                                        v
                                             +----------------------+
                                             | PHP random_int(...)  |
                                             +----------+-----------+
                                                        |
                                                        v
                                             +----------------------+
                                             |      OS CSPRNG       |
                                             |    /dev/urandom,     |
                                             |      getrandom       |
                                             +----------------------+

Why This Architecture

Concern	Solution
BMM Certification	The PHP RNG wrapper is pre-certified by BMM Testlabs
Audit Trail	Every random number passes through the certified class path, no shortcuts
Performance	The gateway calls the PHP service via HTTP; the PHP process is persistent (no cold start)
Isolation	The RNG service runs as a separate container, independent scaling and monitoring

HTTP Bridge Specification

Property	Value
Protocol	HTTP/1.1 POST
Endpoint	/rng
Content-Type	application/json
Request Format	{"method":"getInteger","min":10000,"max":99999}
Response Format	{"number":42781}
Retry Strategy	3 attempts with exponential backoff (100ms, 200ms, 400ms)
Timeout	5000ms

What the RNG Is Used For

The certified RNG generates the client_seed, a single integer in the range [10000, 99999], once per game round. This seed is one of three inputs to the provably fair hash chain.

The engine never generates its own random numbers for game outcomes. The Fisher-Yates shuffle used during deterministic replay verification is seeded from known values, not from OS entropy.

Statistical Verification

The RNG was internally re-verified on June 1, 2026. A batch of 1,000,000 random numbers was generated and subjected to 29 statistical tests across 3 standard suites. The results matched the original BMM Testlabs certification values, with all tests returning a p-value ≥ 0.01 (99% confidence interval).

Empirical Tests (7)

#	Test	What It Measures
1	Frequency (Monobit)	Proportion of 0s vs 1s in bitstream
2	Serial Correlation	Correlation between consecutive values
3	Runs (Wald-Wolfowitz)	Runs of consecutive identical bits
4	Gap	Distance between occurrences of a target digit
5	Coupon Collector	Draws until all values in a range appear
6	Subsequences	Uniformity within blocks
7	Poker	Chi-square test on k-tuple patterns

Diehard Tests (7)

#	Test	What It Measures
1	Binary Rank 32×32	Rank of 32×32 binary matrices over GF(2)
2	Binary Rank 6×8	Rank of 6×8 binary matrices
3	Birthday Spacings	Clustering detection (birthday paradox)
4	Bitstream	Overlapping 20-bit word counts
5	Count The 1's	Distribution of 1s in bytes
6	Runs (Diehard)	Ascending and descending runs
7	Squeeze	Overlapping sums uniformity

NIST SP 800-22 Tests (15)

#	Test	NIST Section	What It Measures
1	Approximate Entropy	§2.2	Frequency of overlapping m-bit patterns
2	Block Frequency	§2.2	Proportion of 1s within M-bit blocks
3	Cumulative Sums	§2.13	Random walk maximum excursion
4	Discrete Fourier Transform	§2.6	Periodic features in bit sequence
5	Frequency (Monobit)	§2.1	NIST variant of monobit test
6	Linear Complexity	§2.10	LFSR length needed to generate sequence
7	Longest Run of Ones	§2.4	Longest run of 1s within M-bit blocks
8	Non-Overlapping Template	§2.7	Occurrences of non-periodic patterns
9	Overlapping Template	§2.8	Occurrences of patterns (allows overlap)
10	Random Excursions	§2.14	Visits to states in cumulative sum walk
11	Random Excursions Variant	§2.15	Variant of excursions test
12	Binary Matrix Rank	§2.5	Rank of disjoint sub-matrices
13	Serial	§2.11	Frequency of overlapping m-bit patterns
14	Runs	§2.3	NIST variant of runs test
15	Universal (Maurer's)	§2.12	Compressibility of sequence

Threshold

All tests use p-value ≥ 0.01 as the passing criterion, per NIST SP 800-22 §1.1.2 and BMM Testlabs standards. A p-value below 0.01 indicates the sequence is non-random with 99% confidence.

Certification Documents

The official BMM Testlabs Certification Report (which includes the Certificate of Compliance and the full Statistical Analysis Report) is available upon request.