1. An order-preserving encryption system, comprising: an encryption device which encrypts an inputted plaintext and outputs an encrypted text; and a decryption device which decrypts the inputted encrypted text and outputs the plaintext, wherein the encryption device comprises: a storage module which stores in advance an encryption key required for encryption processing; a pre-processing function unit which applies, on the inputted plaintext, a pre-processing function to convert input values of the inputted plaintext that are not distributed uniformly to output values that are distributed uniformly, wherein the pre-processing function comprises of a cumulative probability distribution function; and an encryption unit which outputs the encrypted text that is acquired by encrypting the uniformly distributed output values obtained from the pre-processing function unit with order-preserving encryption by using the encryption key; wherein the pre-processing function acquires an output value by adding an arbitrarily selected random number to a value acquired by inputting an input value of the inputted plaintext to the cumulative probability distribution function of an integer set to which the input value belongs.