Superposition as a Means of Data Encryption in N-Dimensional Value Spaces

Abstract

The objective of this study was to provide a new method for creating quantum-proof encryption algorithms. I accomplished this by designing a symmetric 2-key cryptosystem that exploits the superposition principle to encrypt data in multi-dimensional value spaces.    The proposed cryptosystem substitutes characters for frequencies, as determined by two private keys: component wave order key (CWOK) and character transmission order key (CTOK). A CWOK defines the values and theoretical spatial arrangement of frequencies in a complex wave. A CTOK defines the unique arrangement of system characters (i.e., characters in an encoding scheme such as ASCII), determined by a hash function, to identify a user. Combining the CWOK and CTOK, we construct a character-lookup table (CLT), which defines the character-frequency relationships used to generate a substitution cipher. A cipher’s frequency values must be superimposed in accordance with the CWOK. Fast Fourier Transforms are used during the decryption stage to perform complex wave analysis.    Complex waves can have n! frequency configurations, where n = the number of component frequencies; each CTOK can have a! character configurations, where a = the number of characters defined in an encoding scheme. Therefore, by requiring n ≥128 and using the ASCII encoding scheme (a = 128), there are n!+a!=128!+128!=2*128! possible key configurations for any given cipher. This is approximately 3.330284e+138 times as many key configurations possible with AES 256.    Exploiting the multi-dimensional nature of complex waves, and combining these techniques with other powerful encryption algorithms used today, it appears likely that we can create a quantum-proof cryptosystem.