Abstract: Providing an encryption scheme which is invulnerable to the low-density attack based on the LLL algorithm and capable of improving the security. Ciphertext is obtained by a product-sum operation of the components of a composite vector, which is obtained by adding a random number vector whose components are arbitrarily selected random numbers to a plaintext vector obtained by dividing plaintext to be encrypted, and the components of a public-key vector modulo-transformed based on one or a plurality of base vectors which, are set such that Vi=(d/di)·vi (where d=d1d2 . . . dK) by using one or a plurality of sets of integers di(1≦i≦K). The positions of the components of the plaintext vector or random number vector in the composite vector are arbitrarily set by an entity as the sender or an entity as the receiver.

Abstract: After converting each of characters in a plaintext into binary data, the respective binary data are sequentially connected to form a block of a predetermined number of bits. When binary data can not be inserted in the end portion of each block due to a shortage of the number of bits, dummy data as the digit “0” is added to that portion in a length corresponding to a necessary number of bits so as to form a block consisting of a predetermined number of bits in total. Information indicating the number of bits of this dummy data is added to the end of the plaintext or ciphertext.