A quantum-key distributing method for a quantum cryptographic system including a transmission-side communication apparatus that transmits a random number sequence forming a basis of an encryption key in a predetermined quantum state on a quantum communication path and a reception-side communication apparatus that measures a photon on the quantum communication path, the quantum-key distributing method comprising: a check matrix generating step (S1, S11) at which the transmission-side communication apparatus and the reception-side communication apparatus generate an identical parity check matrix of which elements are "0" or "1"; a cyclic code generating step at which the transmission-side communication apparatus generates a cyclic code for error detection; transmitting and receiving (S3, S4, S12, S13) including the reception-side communication apparatus maintaining reception data with probability information obtained as a result of measuring a light direction with a measuring device capable of correctly identifying the light direction, and the transmission-side communication apparatus maintaining transmission data corresponding to the reception data, that are part of the random number sequence; information notifying (S5, S14) including the transmission-side communication apparatus notifying, via a public communication path, the reception-side communication apparatus of error correction information generated based on the parity check matrix and the transmission data (m A), and error detection information (S C) generated based on the cyclic code and the transmission data (m A); transmission-data estimating including the reception-side communication apparatus obtaining a temporary estimated word (m C ') in an estimation process based on the parity check matrix, the reception data (m B) with probability information, and the error correction information (S A), generating estimated error correction information based on the temporary estimated word (m C ') and the parity check matrix, completing the estimation process and setting the temporary estimated word to estimated transmission data when a condition that the error correction information equals the estimated error correction information is satisfied (S36-Yes), then performing error detection of the estimated transmission data based on the error detection information (S C), and when there is no error, determining the estimated transmission data to be original transmission data (m A), or when there is an error, discarding the estimated transmission data; and encryption-key generating (S6, S16) including the transmission-side communication apparatus and the reception-side communication apparatus discarding a part of the transmission data according to an amount of information laid open to the public and generating an encryption key using rest of the transmission data. a check matrix generating step (S1, S11) at which the transmission-side communication apparatus and the reception-side communication apparatus generate an identical parity check matrix of which elements are "0" or "1"; a cyclic code generating step at which the transmission-side communication apparatus generates a cyclic code for error detection; transmitting and receiving (S3, S4, S12, S13) including the reception-side communication apparatus maintaining reception data with probability information obtained as a result of measuring a light direction with a measuring device capable of correctly identifying the light direction, and the transmission-side communication apparatus maintaining transmission data corresponding to the reception data, that are part of the random number sequence; information notifying (S5, S14) including the transmission-side communication apparatus notifying, via a public communication path, the reception-side communication apparatus of error correction information generated based on the parity check matrix and the transmission data (m A), and error detection information (S C) generated based on the cyclic code and the transmission data (m A); transmission-data estimating including the reception-side communication apparatus obtaining a temporary estimated word (m C ') in an estimation process based on the parity check matrix, the reception data (m B) with probability information, and the error correction information (S A), generating estimated error correction information based on the temporary estimated word (m C ') and the parity check matrix, completing the estimation process and setting the temporary estimated word to estimated transmission data when a condition that the error correction information equals the estimated error correction information is satisfied (S36-Yes), then performing error detection of the estimated transmission data based on the error detection information (S C), and when there is no error, determining the estimated transmission data to be original transmission data (m A), or when there is an error, discarding the estimated transmission data; and encryption-key generating (S6, S16) including the transmission-side communication apparatus and the reception-side communication apparatus discarding a part of the transmission data according to an amount of information laid open to the public and generating an encryption key using rest of the transmission data.