1. An encryption device, comprising: at least one processor; and a memory in communication with the at least one processor, the memory storing computer-executable instructions, wherein when executed the computer-executable instructions cause the at least one processor to at least: generate two non-commutative matrices A1, A2 based on a d×d matrix A and two prime numbers p1, p2, wherein the d×d matrix A is private data that is set in common with a decryption device; derive a vector v i 1 by performing a plurality of matrix operations between the non-commutative matrix A1 and at least one of a d dimensional initial vector v 0 that is set in common with the encryption device or a previously derived d dimensional vector v i−1 1 , and derive a vector v i 2 by performing the plurality of matrix operations between the non-commutative matrix A2 and at least one of the initial vector v 0 or a previously derived d dimensional vector v i−1 2 , wherein the plurality of matrix operations comprises at least one of a sum calculation or a product calculation; derive a bit sequence W1 by performing non-linear transformation to transform the vector v i 1 into a current bit sequence of W1 and by joining the current bit sequence of W1 to at least one previously derived bit sequence of W1, and derive a bit sequence W2 by performing non-linear transformation to transform the vector v i 2 into a current bit sequence of W2 and by joining the current bit sequence of W2 to at least one previously derived bit sequence of W2; repeat the deriving and the joining of the bit sequences of W1 and the bit sequences of W2 until a number of bits of each of the bit sequence W1 and the bit sequence W2 is equal to a number of bits of a bit sequence expressing encryption target data; derive a pseudo-random number bit sequence by computing an exclusive logical sum between the bit sequence W1 and the bit sequence W2; and encrypt the encryption target data by computing an exclusive logical sum between the pseudo-random number bit sequence and the bit sequence expressing the encryption target data.