Preprint / Version 1

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

Applications in Cryptography


  • Peter Lablans LabCipher



n-state involutions, bitwise XOR, 2-operand involutions, self-reversing, n-state commutative involution, n=2^k, self-reversing n-state inverters, finite fields, GF(n=2^k), Finite Lab-Transform, FLT, encryption, hashing, AES-GCM, ChaCha20, SHA-256, LabCipher


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.


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