GB2401443A

GB2401443A - Data compression using the index of a string of digits in the expansion of an irrational number

Info

Publication number: GB2401443A
Application number: GB0310429A
Authority: GB
Inventors: David Vincent Broadway
Original assignee: Individual
Current assignee: Individual
Priority date: 2003-05-07
Filing date: 2003-05-07
Publication date: 2004-11-10
Also published as: GB0310429D0

Abstract

A computer program for compressing an arbitrary string of digits (in any base, e.g. binary, decimal, octal or hexadecimal) by locating that string of digits in the expansion of an irrational number and providing the position index and length of the string to be compressed. Expansion is effected by expanded the relevant irrational (e.g Pi or the square root of two), locating the position indexed and reading out the digits up to the required length. Also disclosed is an encryption method using the above compression algorithm whereby the particular irrational number is a shared secret and the position or length fields are encoded in a non-disclosed way. Reduction in bandwidth requirements is the only stated application.

Description

2401 443 Data compression and encryption software Efficient computer data

storage and communications can require compression of data. Existing compression algorithms are limited in their ability to compress data. Computer speed is increasing rapidly, but data transfer between computers is limited by the bandwidth and compression available. Increasing bandwidth currently requires large investment. Increased data compression can be achieved by more efficient software.

This invention describes a computer program that utilises the characteristics of certain irrational numbers to achieve theoretically almost infinite compression.

All data held on computers may be represented as numbers. These numbers may be in binary, octal, hexadecimal or decimal format, but all can be converted to any of the other forms. Certain irrational numbers such as pi, the square root of 2 and others have a decimal portion that is infinitely long. It is possible to calculate this decimal to any number of places. The occurrence of the digits 0 to 9 within this decimal have no fixed sequence. It is therefore possible to find any sequence of numbers within the decimal portion of any of these irrational numbers. It is therefore possible to describe any sequence of numbers by stating it's starting position and it's length (in characters) within the decimal portion of an irrational number.

This invention is a computer program that converts any data into a numeric string, and then generates the decimal portion of a chosen irrational number until a sequence of numbers is fauna that matches all or part of the numeric string of data. The program continues to generate the decimal portion of the irrational number until a chosen level of compression is reached. The chosen level of compression is reached by searching for a suitable length of numeric string that matches a portion of the data numeric string. The level of compression may range from none, up to a single position and length to describe the whole data string. If only partial compression is chosen, then the data string will be described by a series of positions and lengths for each portion of the data.

On reaching its destination, the recipient need only know the irrational number used to decompress the data using the computer program and the reverse of the method outlined above. It should be noted that if the irrational number used is not known, and if the position or length fields are encoded, then this method of compression also offers a secure method of encryption. i

A key feature of this inventions compression method is that it may be used upon data that has already been compressed using other compression algorithms, and in addition, the simple numeric sequence produced may be further compressed by utilising other compression algorithms upon it. This means that by combination with existing data compression software, data may be repeatedly compressed to any desired level, even if the level of compression from the use of this invention is relatively low each time.

A specific example of the operation of the program is given below.

Data represented as the 40 character number sequence 8850387534 3276415727 3501384623 0912297024 is to be compressed. The decimal portion of the square root of 2 is calculated and compared until the same sequence of numbers is found. This is found to occur starting at the 90th decimal so the above number could be represented by the length, 40 and the position 90 hence in this example 40 characters are compressed to 4 characters.

A further example of the level of compression possible is given below.

If a piece of data consisting of 10,000,000 numeric characters is found to occur after 1,000,000,000,000,000 decimals of an irrational number. The full 10,000,000 characters can be described by their starting position (1,000,000,000,000,000) and their length (10,000,000) so ten million characters are compressed to just 24 characters a compression of 99. 99976%.

Claims

1. A computer program that utilises the features of irrational numbers with infinite length to compress data.

2. A computer program as claimed in Claim 1 above that can compress data by a chosen amount or percentage.

3. A computer program as claimed in Claim 1 and Claim 2 that can compress data to an almost infinitely small percentage of it's original size.

4. A computer program as claimed in Claim 1, 2 and 3 that can be used repeatedly in conjunction with other compression algorithms either on the programs input data, output data, or both.

5. A computer program as claimed in Claim 1 that can be easily utilised for secure encryption in addition to compression.