1. An encryption device, comprising: a matrix generation section that generates 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; a matrix operation section that derives a vector v i 1 by operating the non-commutative matrix A1 on a d dimensional initial vector v 0 that is set in common with the decryption device or on a d dimensional vector v i−1 1 derived the previous time, and that derives a vector v i 2 by operating the non-commutative matrix A2 on the initial vector v 0 or on a d dimensional vector v i−1 2 derived the previous time, wherein at least one out of a sum calculation or a product calculation of operations of the non-commutative matrices A1, A2 is substituted into a predetermined calculation method combining a plurality of operator types, and operations of the non-commutative matrices A1, A2 are performed; a bit sequence transformation section that derives a bit sequence W1 by performing non-linear transformation to transform the vector v i 1 derived by the matrix operation section into a bit sequence and by joining the transformed bit sequence to the bit sequence W1 derived the previous time, and that derives a bit sequence W2 by performing non-linear transformation to transform the vector v i 2 into a bit sequence and by joining the transformed bit sequence to the bit sequence W2 derived the previous time; a bit number determination section that repeats the operation by the matrix operation section and the transformation and joining of the bit sequence transformation section until the respective numbers of bits of the bit sequence W1 and the bit sequence W2 derived by the bit sequence transformation section have reached a number of bits of a bit sequence expressing encryption target data; a pseudo-random number sequence generation section that derives a pseudo-random number bit sequence by computing an exclusive logical sum between the bit sequence W1 and the bit sequence W2; and an encryption section that encrypts encryption target data by computing an exclusive logical sum between the pseudo-random number bit sequence derived by the pseudo-random number sequence generation section and the bit sequence expressing the encryption target data.