An apparatus for generating a physical random number sequence, comprising: a physical random number generating circuit configured to generate physical random numbers of a predetermined number of bits; a health test circuit configured to perform a test process to check the randomness of each physical random number by generating statistical information as a number of subsequent bits having the same value as a first bit in the physical random number and by generating an indication whether or not the physical random number has satisfactory randomness based on this statistical information; a control circuit configured to retain, in the case of results of the test process indicating satisfactory randomness, the physical random number generated by the physical random number generating circuit, and to discard, in the case of the results of the test process failing to indicate satisfactory randomness, the physical random number generated by the physical random number generating circuit; a minimum entropy estimating circuit configured to estimate a minimum entropy of each physical random number based on the statistical information generated as a byproduct of the test process; an entropy compressing apparatus configured to perform an entropy compression process using retained physical random numbers as an input, and to output the physical random number sequence; and an entropy-estimation-based control circuit configured to control the input into the entropy compression process performed by the entropy compressing apparatus, the entropy compressing apparatus is configured to accumulate the physical random numbers as a plurality of sets, each of which is constituted by those of the retained physical random numbers, which have a minimum entropy larger than or equal to a predetermined value, and the entropy-estimation-based control circuit is configured to send a signal to the entropy compressing apparatus to start the entropy compressing process when the number of accumulated sets exceeds a predetermined number. a physical random number generating circuit configured to generate physical random numbers of a predetermined number of bits; a health test circuit configured to perform a test process to check the randomness of each physical random number by generating statistical information as a number of subsequent bits having the same value as a first bit in the physical random number and by generating an indication whether or not the physical random number has satisfactory randomness based on this statistical information; a control circuit configured to retain, in the case of results of the test process indicating satisfactory randomness, the physical random number generated by the physical random number generating circuit, and to discard, in the case of the results of the test process failing to indicate satisfactory randomness, the physical random number generated by the physical random number generating circuit; a minimum entropy estimating circuit configured to estimate a minimum entropy of each physical random number based on the statistical information generated as a byproduct of the test process; an entropy compressing apparatus configured to perform an entropy compression process using retained physical random numbers as an input, and to output the physical random number sequence; and an entropy-estimation-based control circuit configured to control the input into the entropy compression process performed by the entropy compressing apparatus, the entropy compressing apparatus is configured to accumulate the physical random numbers as a plurality of sets, each of which is constituted by those of the retained physical random numbers, which have a minimum entropy larger than or equal to a predetermined value, and the entropy-estimation-based control circuit is configured to send a signal to the entropy compressing apparatus to start the entropy compressing process when the number of accumulated sets exceeds a predetermined number. <EOS>