Galois extension field-based block cipher

A Galois Extension Field-based block decryption process, comprising:

• synchronizing a random number generator (RNG), wherein the RNG is a pseudo-random number generator (PRNG);
• forming an output from the PRNG into a key matrix, wherein the key matrix is formatted as an invertible square matrix;
• applying a Galois Extension Field (GEF) operation to the key matrix, to map elements of the key matrix from a Galois field space order GF(pk), where p is a prime number, to a closed subset in a higher-order Galois extension field space;
• inverting the key matrix to an inverted key matrix;
• extending a vector of ciphertext from the order GF(pk) to the higher-order Galois extension field space using the GEF operation;
• combining the vector of ciphertext and the inverted key matrix using extension field matrix multiplication, to produce a vector of plaintext in the higher-order Galois extension field space;
• and
• reducing the vector of plaintext from the higher-order Galois extension field space to the order GF(pk) using an inverse GEF operation.

A Galois Extension Field-based block encryption system, comprising:

• at least one processing device;
• and
• at least one memory device that stores computer-readable instructions thereon that, when executed by the at least one processing device, direct the at least one processing device to:
• synchronize a random number generator (RNG), wherein the RNG is a pseudo-random number generator (PRNG);
• form an output from the PRNG into a key matrix, wherein the key matrix is formatted as an invertible square matrix;
• apply a Galois Extension Field (GEF) operation to the key matrix, to map elements of the key matrix from a Galois field space order GF(pk), where p is a prime number, to a closed subset in a higher-order Galois extension field space;
• map plaintext to a plaintext matrix;
• apply a GEF operation to the plaintext matrix, to map elements of the plaintext matrix from the order GF(pk) to the higher-order Galois extension field space;
• combine the plaintext matrix and the key matrix using extension field matrix multiplication, to produce a vector of ciphertext in the higher-order Galois extension field space;
• reduce the vector of ciphertext from the higher-order Galois extension field space to a reduced vector of ciphertext in the order GF(pk) using an inverse of the GEF operation;
• and
• during the reduction of the vector of ciphertext, apply a ceiling operation to bijectively map elements in the reduced vector of ciphertext to a closed subset in the order GF(pk).

A Galois Extension Field-based block decryption system, comprising:

• at least one processing device;
• and
• at least one memory device that stores computer-readable instructions thereon that, when executed by the at least one processing device, direct the at least one processing device to:
• synchronize a random number generator (RNG), wherein the RNG is a pseudo-random number generator (PRNG);
• form an output from the PRNG into a key matrix, wherein the key matrix is formatted as an invertible square matrix;
• apply a Galois Extension Field (GEF) operation to the key matrix, to map elements of the key matrix from a Galois field space order GF(pk), where p is a prime number, to a closed subset in a higher-order Galois extension field space;
• invert the key matrix to an inverted key matrix;
• extend a vector of ciphertext from the order GF(pk) to the higher-order Galois extension field space using the GEF operation;
• combine the vector of ciphertext and the inverted key matrix using extension field matrix multiplication, to produce a vector of plaintext in the higher-order Galois extension field space;
• and
• reduce the vector of plaintext from the higher-order Galois extension field space to the order GF(pk) using an inverse GEF operation.