1. A computer-readable recording medium that stores therein a computer program for digital signature authentication, the computer program causing a computer to execute: dividing streaming data into a plurality of pieces of partial data in a predetermined unit; creating a hash value string including a plurality of hash values corresponding to the pieces of partial data; creating a first binary tree using the hash value string; creating a digital signature of a signer using a root value of the first binary tree; extracting partial data from the streaming data; deleting remaining partial data from the streaming data; creating a second binary tree using hash values corresponding to the remaining partial data; outputting the partial data extracted and a root value of the second binary tree; obtaining a root random number; and creating a third binary tree using the root random number such that number of leaves of the third binary tree is identical to number of the pieces of partial data, wherein the creating the first binary tree includes creating the first binary tree based on the leaves and the hash value string.