Tests and Results
The quantum security technologies used in ozone chain have undergone various standardized tests and have passed all of them. The tests have been conducted by TÜV Rheinland which is an agency that provides testing and certification services to ensure the safety, quality, and performance of cybersecurity products and services, including quantum security solutions.
The following tests were conducted and the results shown below.
Entropy test
The entropy of a random variable is the average level of uncertainty inherent to the variable's possible outcomes.
Diehard tests
The diehard tests are a battery of statistical tests for measuring the quality of a random number generator. The diehard test suite conducted by TÜV Rheinland consisted of several individual tests like
Birthday spacings test Choose random points on a large interval. The spacings between the points should be asymptotically exponentially distributed.
Overlapping 5-permutations test Analyze sequences of five consecutive random numbers. The 120 possible orderings should occur with statistically equal probability.
Binary rank test for 31x31 matrices Select some number of bits from some number of random numbers to form a matrix over {0,1}, then determine the rank of the matrix. Count the ranks.
Binary rank test for 32x32 matrices
Binary rank test for 6x8 matrices
Bitstream test The test uses simulation to check if it is possible to interpret the integer output of a QRNG as a sequence of random bits.
OPSO, OQSO and DNA tests
Count the 1's test Count the 1 bits in each of either successive or chosen bytes. Convert the counts to "letters", and count the occurrences of five-letter "words".
Minimum distance test Randomly place 8000 points in a 10000×10000 square, then find the minimum distance between the pairs. The square of this distance should be exponentially distributed with a certain mean.
3D spheres test Randomly choose 4000 points in a cube of edge 1000. Center a sphere on each point, whose radius is the minimum distance to another point. The smallest sphere's volume should be exponentially distributed with a certain mean.
Squeeze test Multiply 2^31 by random floats on (0,1) until you reach 1. Repeat this 100000 times. The number of floats needed to reach 1 should follow a certain distribution.
Overlapping sums test Generate a long sequence of random floats on (0,1). Add sequences of 100 consecutive floats. The sums should be normally distributed with characteristic mean and variance.
Runs test Generate a long sequence of random floats on (0,1). Count ascending and descending runs. The counts should follow a certain distribution.
Craps test Play 200000 games of craps, counting the wins and the number of throws per game. Each count should follow a certain distribution.
NIST tests
Ozone's QRNG has also passed the NIST SP 800-22 tests, which is a test suite standards by National Institute of Standards and Technology. NIST SP 800-22 is a statistical test suite for random and pseudorandom number generators for cryptographic applications.
Frequency (monobit) test
Frequency test within a block
Runs test
Longest run of ones in a block
Binary matrix rank test
Discrete Fourier Transform (Spectral) test
Non-overlapping template matching test
Overlapping template matching test
Maurer's "Universal Statistical" test
Linear complexity test
Serial test
Approximate entropy test
Cumulative sums (Cusums) test
Random excursions test
Random excursions variant test
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