Need an maths algorithm to encode number in big integer to integer

I want to convert a number value of 100 digits into lessthan 10 digits and vice versa. So I pass that encoded number to mobile user and on getting back can make 100 digits number again. I want to use it in PHP, .NET or JS.

But before that I need an algorithm for that.

I have some idea t开发者_JAVA百科o use simple divide-subtract and add-multiply options in my mind to implement. But need some more secure than that.

What you're asking for is impossible. You are trying to pigeonhole 10^100 items into 10^10 boxes. Some box will get more than one item and so it's impossible to invert back to "the" original item.

You could encode the 100-digit base-10 numbers as a 56-digit base-62 number (use uppercase and lowercase Roman alphabet and digits 0-9). The math here is 100 * log(10) / log(62).

To encode using less than ten characters from some alphabet, you need an alphabet with ~2^34 symbols. The math here is 100 * log(10) / log(number of symbols). Good luck with that.

If you have more than 10 000 000 000 different possible values in the 100 digit number you can not possibly map that to a 10 digit number and reliably map back to the original number.

A 100 digit number, I assume this is a base ten number, When talking about numbers on computers talk of 'digits' is almost meaningless.

If you actually mean a 100bit integer, then this wont easily fit into a single 64bit integer ( range +/- 9,223,372,036,854,775,808 ) then you have not phrased your question all that well. And no amount of compression or encoding will let you represent 100bits using no more than 10bits.

If you mean 100 figures in base ten, then you are dealing with bignums so should probably just treat them as bytes and use a bignum library.

100 base ten figures is still less than 512 bits.

Assuming that the 100-digit number is base 10, then if my math is not wrong you'll need 10 base 100 digits to represent the same number. So instead of using just characters from 0-9, you'll need to expand the characters to include other glyphs, including upper-case and lower-case letters, etc., to complete a 100 character alphabet. OK, my math is wrong, so disregard this, but consider the next paragraph.

Another thought is to use a hashing algorithm to derive a 10-byte hash from your 100-digit number and use that as key in a server-side database (hash-table). No encoding/decoding, just send the key to the mobile client, the mobile client uses the key to fetch the 100-digit number from the server.