# Tests and Results

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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.

Given a discrete random variable , which takes values in the alphabet and is distributed according to

where denotes the sum over the variable's possible values.

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**