A system and a method for encoding sequence preservation numerical data using beta expansion are provided to perform the search of the encoded numerical data by performing the encoding, the searching, and the decoding by preserving the order of the size of the numerical data. A secret key generator(11) produces the encryption key of the secret key method. A numerical data encoding unit(12) encodes the numerical data by using the beta expansion with the encoded key generated by the secret key generator. The numerical data is stored in a server. If a search unit(13) searches for data with an arbitrary number of n, the search unit receives the encoded numerical data searched by the result of the beta expansion from the server by transmitting the result of the beta expansion to the server after beta-expanding the arbitrary number of n by using the secret key. A numerical data decoder(14) decodes the numerical data by a decoding key using the beta expansion.
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