algorithm - String to unique integer hashing

Question

I'm trying to develop a system that can change my string into a unique integral value, meaning say for example the word "account" has an encrypted numerical value of 0891 and no other word can possibly be converted to 0891 with the same conversion process, it does not however need to be able to be converted back the generated integer to string.

At the same time it will be dependent on the word structure rules, meaning words such as "accuracy" and "announcement" will have a generated number greater than 0891 and words such as "a", "abacus" and "abbreviation" will have a generated number less than 0891.

The purpose of this application is to serve similar to an index or primary key. The reason why I'm not using an increment index is for security purposes and is due to the indexes dependency to the number of data in the set

(e.g.)

[0] A, [1] B, [2] C, [3] D, [4] E, [5] F

The above letters has each corresponding index, E has the index of 4

However if the data is suddenly increased or decreased then sorted

[0] A, [1] AA, [2] AAB, [3] C, [4] D, [5] DA, [6] DZ, [7] E, [8] F

E now has the index of 7

Each word must have a unique independent integral equivalent and has the corresponding weights.

I need to know if there exist an algorithm that can do the above.

Any help will be appreciated.

Answer 1

This is not possible with the constraints you have given, unless you impose a maximum length.

Assume that k("a") and k("b") are the codes of these two strings.

With your constraints, you are looking for a unique integer number that falls inbetween these two values, but k("a") < k("a....a") < k("b"). As there is an infinite number of strings of style "a....a" (and "akjhdsfkjhs") that would need to fit inbetween the two codes, such an order preserving general, unique, fixed-length code cannot exist for strings of arbitrary length. Because you would need as many integers as strings, and since strings are not bounded by length this cannot work.

Drop either general (so don't allow inserting new strings), unique (allow collissions - e.g. use the first four letters as code!), the unbounded length (to e.g. 3 characters) or the order-preserving property.