Encryption device, decryption device, encryption method, decryption method, and program

摘要

An encryption device generates non-commutative matrices A1, A2 based on private data A and prime numbers p1, p2, and operates the non-commutative matrices A1, A2 on vectors vi1, vi−12. The encryption device performs non-linear transformation to transform the vectors vi1, vi2 into bit sequences, and joins these to the bit sequences W1, W2. The encryption device repeats the operation of the non-convertible matrices and the non-linear transformation until the respective numbers of bits of the bit sequence W1 and the bit sequence W2 have reached a number of bits of a bit sequence expressing encryption target data. The encryption device derives a pseudo-random number bit sequence by computing the exclusive logical sum between the bit sequence W1 and the bit sequence W2, and performs encryption using the pseudo-random number bit sequence. The encryption device is thereby able to increase the speed of encryption processing and to increase the cryptographic strength in cases in which the number of bits of the encryption target data is modifiable.

主权项

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 vi1 by performing a plurality of matrix operations between the non-commutative matrix A1 and at least one of a d dimensional initial vector v0 that is set in common with the encryption device or a previously derived d dimensional vector vi−11, and derive a vector vi2 by performing the plurality of matrix operations between the non-commutative matrix A2 and at least one of the initial vector v0 or a previously derived d dimensional vector vi−12, 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 vi1 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 vi2 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; andencrypt 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.