Cryptompress, a new 128-bit (initial) private-key cryptography algorithm is proposed. It uses a block size of at least 30 bits and increments prior key size to additional 32 bits on each unsuccessful attempt of any means, including bruteforcing, further changing a specific portion of the cyphertext using the reformed Feistel network. Encryption process results from a proposed compression sequence developed using lookup table and shift operations followed by key generation. Eventually, four matrixes named add-sub matrix, reduced matrix, sequence matrix and term matrix are obtained which ultimately forms a cyphertext.
To start with encryption process, we follow a compression methodology which is mostly applicable for data comprising of consecutive similar binary pairs. The compression methodology has been presented along with the encryption phase. We consider 30 bits block code and lay down a mapping function for two consecutive bits i.e. 00, 01, 10 and 11 mapped to first four positive integer prime numbers i.e. 2, 3, 5 and 7. One can express such mapping function M as: M = { 00 ⟺ 2 01 ⟺ 3 10 ⟺ 5 11 ⟺ 7 (1) This will transform the block code of 30 bits into 15 integers (15 bytes). Next off, the compression sequence initiates deploying three main operations, right shift operation, lookup table corresponding to Add-Sub Matrix (ASM) and simpler addition/subtraction. Compression sequence has a rigid boundary in a sense that it will begin its procedure by choosing the first occurring prime integer (target integer) of the block. Once, first occurring prime integer is done with, the next occurring integer becomes target integer and so on up till the last integer available in the block code is finished.
Once a target integer is acquired, next operation is to perform right shifting the target integer and follow two rules. First, add similar integer(s) together and feed the sequence serial number (S n ) along with the number of redundant integers (R n ) summed up into a matrix, known as Sequence Matrix (SM). Second, whenever a different integer is crossed, perform a certain addition/subtraction operation in the target number by looking in the ASM. Execution takes place until the target number reaches the end of the block, finally ending up as target number outcome. This outcome is stored in a new matrix called Reduced Matrix (RM). Similar operations are performed for the rest of the available target prime integers resulting in a transformed data only available in RM, SM and new matrix called Term Matrix (TM) which holds the information of the last sequence serial number corresponding to each target number.
Overall, compression sequence results into three matrixes whose total size may be bigger than the original block code depending upon the occurrence of the consecutive similar binary pairs. For instance, if similar binary pairs occur consecutively for a bigger block size then the resultant sequence matrix will contain less information, hence compressing the data effectively.
To obtain data back in its original form (decompression), first off, refer to the last occurring target integer highest sequence number from the TM and assign its respective outcome from RM. Proceed with left shifting using the ASM (which in this case replaces add/sub with sub/add operations) and fetching number of known redundant integers from the SM.
As aforementioned, there are four main matrixes which need to be dealt with during the Cryptompress. Let us describe them here with their structures and significance.
Add-Sum Matrix (ASM): An Add-Sum Matrix (ASM) works like a lookup table during both compression and decompression sequences. It has a major impact on the Reduced Matrix (RM) data as it works like a channel between block code data and Reduced Matrix data. It is so relevant because it depicts the type of operation to be performed on a target number when it right/left shifts any distinct integer. It solely determines whether there would be 1 bit addition or 1 bit subtraction to the target number. Table 1 elucidates the structure of ASM, here Order depicts the range of values from 0000-1111 which means that for every “0” there would occur 1 bit subtraction (-1) from the target number and for every “1” there would occur 1 bit addition (+1) to the target number. The process inverts during left shifts. Here, “X” denotes addition of the target number by itself and has no relevance to ASM. Refer section IV for illustration learning. Description of the keys:
ASM Key: With the virtue of ASM key, the complete Add-Sub Matrix (ASM) can be reformed. Using initial 16 bits it defines the type of order to be used during the compression-decompression mechanism. Next 16 bits decides the sequential arrangements of the horizontal target numbers assigned in ASM according to the mapping function N. Similarly, last 16 bits decides the vertical target numbers sequence according to N.
The mapping function N distributes all possible combinations of binary values (2 4 ) to each target numbers for their final arrangements in the cyphertext. It works in a cyclic process and transforms the arrangement of target numbers for each matrix as follows:
Horizontal ASM → Vertical ASM → RM → SM → TM → back to Hort. ASM
The target numbers swaps their arrangement with the next matrix at a position equal to the decimal equivalent of defined binary combination in the key.
The 16 bits of the RM key define the new position of each target numbers arrangements by abiding the cyclic rule of mapping function N.
First 16 bits of SM key works same as RM key for Sequence Matrix.
This content is AI-processed based on open access ArXiv data.
