Novel N-state Commutative (Full) Involutions NOT Being Additions Over GF(2^k)

Applications of full commutative n-state involutions are ubiquitous in standard cryptographic operations in current encryption and hashing. The full involutions are generally implemented as bitwise XOR of words of k bits and may be generally described as additions over GF(2^k). Novel n-state full involutions are described herein, including methods how to generate them. The novel n-state full involutions can NOT be described as additions over GF(2^k). Application of these n-state involutions creates a level of uncertainty for attackers and increases security of encryption and hashing when replacing conventional involutions. Application of the Finite Lab-Transform (FLT) on these novel involutions maintains their self-reversing properties and further increases security. Examples of use of novel involutions in encryption (AES-GCM,) and hashing (SHA-256) are provided.