H4-U16 Cryptographic Algorithm by Roth C. Paxton 10/21/2013 Abstract The purpose of this paper is to describe a powerful new cryptographic algorithm that utilizes stacked blocks of data to encrypt and decrypt information. H4-U16 is an abstract symmetric block cipher that relies on the homomorphic properties of linear sets in three dimensional vector space to create large numbers of indeterminate polysymbolic substitutions for each letter of the alphabet. Each letter of the alphabet is essentially a superset or "set of sets" in which each set has the property of being homomorphic to each and every other set that is generated for that letter. Every set generated for any letter has equal probability of being syntactically equivalent but semanticaly different from any other set for any other letter. Due to this property it is virtually impossible to discern any encrypted letter from any other encrypted letter as the encryption changes for each additional letter encrypted. H4-U16 is information theoretic security and is immune to brute force attacks drawing its strength from the complexity of its key. Introduction H4-U16 is based loosely on the design of a rubicks cube. If you will please discard the traditional construction of a rubicks cube and focus more on a construction like SHA3. H4-U16 is constructed from five four by four grids that are then stacked to form a three dimensional cube. Each part of this cube can be shifted by dividing each grid (block) of data into four quadrants of four squares apiece. Now , each quadrant can rotate four times and each block can rotate four times. This serves to shift each constituent part of the cube (80 Squares) an innumerable number of times. Data or plaintext can be encrypted by selecting a pattern of highlighted squares that fits over the face of the cube and stands for a letter. H4-U16 uses what I call homomorphic linear sets to accomplish the task of encryption. As far as I know no such thing as a homomorphic linear set exists in the literature anywhere. A homomorphic linear set is a concept that I have come up with that is based on the concept of a linear homomorphism and applied to cryptography. In my mind I picture a set of five different objects situated equidistantly on a line in three dimensional vector space. The only relationship that these five very dissimilar objects share with one another is the fact that they are all situated on a line. The concept of homomorphic linear set comes into play when one views the line of objects from the front so that they are overlapped. Now imagine that there is a lightbulb situated at the front of the line and that all of the very dissimilar objects are perfectly in line with one another still situated at equidistant points and overlapping. Now when I select any one of these objects imagine that the lightbulb lights up. What I have done by adding the lightbulb is to create a homomorphic linear set. All of the objects are different but are related to each other by having the property of lighting the lightbulb any time that one of them is selected. That as far as I know is a homomorphism. Now imagine that I design some pattern of these homomorphic linear sets by selecting patterns of lightbulbs that light up any time one of the objects that is contained within my sets are selected. As it stands right now if I have five sets of these linear sets that are in a circle or a square or any other pattern that is recognizable when one object is highlighted from each set then I have a pool of data that can be used to generate sequences of objects (five letter sets) that are all equivalent semantically but completely different syntactically. Imagine that these five sets are as follows- 1- A,B,C,D,E 2-F,G,H,I,J,K 3-L,M,N,O,P 4-Q,R,S,T,U 5-V,W,X,Y,Z. This should generate or form the superset (1,2,3,4,5) If I were to select A from 1, H from 2, P from 3, R from 4, and Z from 5 it would be the same as selecting any other sequence of one letter from each set as they would all fall into the superset (1,2,3,4,5). By selecting sets of letters in this way I can generate 3,125 sets of five characters (5^5). Each and every one of these sets are equivalent as they are essentially substitutions that are linked by the homomorphic property of the linear sets (each set chosen lights all five lightbulbs that are situated in a pattern that signifies a letter or number). Now imagine that I have some way of taking the sets themselves and changing their ordering and also changing the actual sets themselves to include members of other sets in a random fashion. This is what the cube accomplishes. By arranging eighty unique characters in a cube and then rotating parts of the cube it allows the characters to change positions and exist in other sets. By shuffeling the blocks it allows the characters to shift their order in each set. If each encrypted letter consists of five characters that are encrypted in this fashion then there are more than a nonillion ways to encrypt each letter of the alphabet. Furthermore each encryption of the letter A always changes each time it is encrypted and all encryptions of the letter A are unique but equivalent (they are all substitutions). I propose using a random number generator to shuffle and rotate the quadrants and blocks. Each time a letter is encrypted the cube must be set in an encryption/decryption sequence that must be recorded and stored with each letter. This generates a lot of data but is secure as the ciphertext cannot be decrypted without knowledge of the order of the 80 symbols of ASCII that make up the key. The constituent parts of the key can be discerned with enough ciphertext but the order that they are in cannot. In a brute force attack a factorial of 80! Keys would need to be checked to discern the key (realistically half of that). I believe that this would still be a rather high bit strength. I am only an amatuer cryptographer. Any input would be appreciated. Sent from Yahoo Mail on Android
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