Hadamard-transform on-line randomness test

A method for testing the randomness of a stream of random numbers, the method comprising the steps of:

• (a) generating a continuous stream of random binary bits;
• (b) applying a predefined block of said random binary bits to a Hadamard-transform calculation;
• (c) assigning an array of accumulators having a predetermined range of values to each output of said Hadamard-transform calculation to count a number of times that each output of said Hadamard-transform calculation falls into one of said predetermined range of values in the respective said accumulator;
• (d) applying the values of said array of accumulators to an exponential-frequency calculation (Z) to update the average number of times that each output of said Hadamard-transform calculation falls into one of said predetermined range of values in the respective said accumulator over a predetermined time period;
• and,
• (e) comparing the output of said exponential-frequency calculation (Z) to a predetermined acceptance range;
• wherein said exponential-frequency calculation (Z) is updated according to the following equation:
• Znew=α·Zold+h(t), wherein α falls between 0 and 1 (0<α<1), Zold is initially assigned by an operator;
• and, h(t) represents the number of times that the output of said Hadamard-transform falls into the corresponding said predetermined range of values in the respective said accumulator.

A system for testing randomness, comprising:

• a random-number generator for generating a random sequence comprising binary bits;
• a detector for detecting whether said generated random sequence is sufficiently random based on an exponential frequency operation;
• and,
• a switch for controlling the flow of said generated random sequences for a subsequent application based on the outcome of said exponential-frequency operation,
• wherein a predefined block of said random binary bits undergoes a Hadamard-transform calculation and thereafter undergoes an exponential frequency calculation (Z) to update an average number of times that each output of said Hadamard-transform calculation falls into one of predetermined range of values over a predetermined time period and wherein, if any output of said exponential-frequency calculation outputs repeatedly falls outside a predetermined acceptance range more than a predefined number of times, determining that said generated random sequences are insufficiently random;
• and wherein said exponential-frequency calculation (Z) is counted according to the following equation:
• Znew=α·Zold+h(t), wherein a falls between 0 and 1 (0<α<1), Zold is initially assigned by an operator;
• and, h(t) represents the number of times that the output of said Hadamard-transform falls into the corresponding said predetermined range of values during said predetermined time period.

A machine-readable medium having stored thereon data representing sequences of instructions, and the sequences of instructions which, when executed by a processor, cause the processor to:

• process a continuous stream of random binary bits;
• apply a predefined block of said random binary bits to a Hadamard-transform calculation;
• perform an exponential-frequency calculation (Z) to the output of said Hadamard-transform calculation to update an average number of times that each said Hadamard-transform output falls into one of predetermined range of values over a predetermined time period;
• and, determine whether said generated random binary bits are sufficiently random by comparing the output of said exponential-frequency calculation to a predetermined acceptance range;
• wherein said exponential-frequency calculation (Z) is undated according to the following equation:
• Znew=α·Zold+h(t), wherein α falls between 0 and 1 (0<α<1), Zold is initially assigned by an operator;
• and, h(t) represents the number of times that each output of said Hadamard-transform falls into the corresponding range of values during said predetermined time period.