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

A decryption 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 an encryption 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 decryption 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
• decrypt the decryption target data by computing an exclusive logical sum between the pseudo-random number bit sequence and the bit sequence expressing the decryption target data.

A non-transitory computer readable medium storing an encryption program executable in a computing device, wherein when executed the encryption program causes the computing device 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 decryption 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 a 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 a 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.

A non-transitory computer readable medium storing a decryption program executable in a computing device, wherein when executed the decryption program causes the computing device 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 decryption 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 a 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 a 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 decryption 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
• decrypt the decryption target data by computing an exclusive logical sum between the pseudo-random number bit sequence and the bit sequence expressing the decryption target data.

An encryption method, comprising:

• generating, via a computing device, 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;
• deriving, via the computing device, 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 decryption device or a previously derived d dimensional vector vi−11, and deriving 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;
• deriving, via the computing device, 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 a previously derived bit sequence of W1, and deriving 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 a previously derived bit sequence of W2;
• repeating 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;
• deriving a pseudo-random number bit sequence by computing an exclusive logical sum between the bit sequence W1 and the bit sequence W2;
• and
• encrypting 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.

A decryption method, comprising:

• generating, via a computing device, 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;
• deriving, via the computing device, 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 decryption device or a previously derived d dimensional vector vi−11, and deriving 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;
• deriving, via the computing device, 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 a previously derived bit sequence of W1, and deriving 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 a previously derived bit sequence of W2;
• repeating 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 decryption target data;
• deriving a pseudo-random number bit sequence by computing an exclusive logical sum between the bit sequence W1 and the bit sequence W2;
• and
• decrypting the decryption target data by computing an exclusive logical sum between the pseudo-random number bit sequence and the bit sequence expressing the decryption target data.