Reduce MD5 - Using a different base - php

Question

My client generates promotional coupon codes which are nothing but 32 char MD5 hashes.
My job is to reduce the MD5 string from 32 chars to less than 10 chars in a way that the hash can be recreated from the reduced string.
The reduction is important as it would be easier for users to reproduce the reduced hash.
For e.g.: 719bedacf2e560b27f39d80accc67ffd => ZjKa1Gh (not mathematically true)
I came across this: How to reduce hash value's length?
It suggests: Using a different base
I am clueless as to how to do this in PHP, can we decode a string to its ASCII and re-encode it?
Are there any in-built functions in PHP that I can use in this case?
Update using https://packagist.org/packages/aza/math
$original = '719bedacf2e560b27f39d80accc67ffd';
$long1 = NumeralSystem::convert($original, 16, 10);
$short = NumeralSystem::convertTo($long1, 62);
$long2 = NumeralSystem::convertFrom($short, 62);
$recovered = NumeralSystem::convert($long2, 10, 16);
var_dump($long1);
var_dump($short);
var_dump($long2);
var_dump($recovered);
// output
string(39) "151012390170261082849236619706853916669"
string(22) "3SNOKWefotgnnCmWnYkTOf"
string(39) "151012390170261082849236619706853916669"
string(32) "719bedacf2e560b27f39d80accc67ffd"
Seems like the lowest I can reach from 32 chars MD5 is 22 chars this way. I am still looking for ways in which I can further reduce it to 10 chars.
Update: Using first half of MD5
$original = '719bedacf2e560b';
$coupon = NumeralSystem::convert($original, 16, 62);
$recovered = NumeralSystem::convert($coupon, 62, 16);
var_dump($coupon);
var_dump($recovered);
// output
string(10) "bnMR3RjZil"
string(15) "719bedacf2e560b"
If the user is providing bnMR3RjZil I can use that to recreate 719bedacf2e560b and then do a MySQL LIKE search to get the full MD5. If it returns a row I can then get forward with the promotional activity.

Answer 1

My job is to reduce the MD5 string from 32 chars to less than 10 chars in a way that the hash can be recreated from the reduced string.
That isn't possible. A MD5 hash is 128 bits; an ASCII character is 7 bits. There's no way to store an MD5 hash in any less than 128÷7 = 18.2 (round up to 19) ASCII characters, and even that would include nonprintable control characters.

Answer 2

A cryptographic hash is in fact a sequence of bits but it can be interpreted as a number. As such, you could theoretically use good old base_convert() to express is in a large base. Unfortunately, this function only works up to base 36 and it's restricted to actual numbers (i.e. short integers that fit into PHP_INT_MAX)—otherwise data loss happens.
Here's where third-party libraries come to the rescue. The only problem is that they tend to be difficult to find because they normally address very specific use cases (Bitcoin, ID obfuscation, etc.).
I found e.g. aza/math, which is probably overkill but should get the job done. I haven't had the chance of testing it but it should go like this:
$original = '719bedacf2e560b27f39d80accc67ffd';
$short = NumeralSystem::convert($original, 16, 62);
$recovered = NumeralSystem::convert($short, 62, 16);

Answer 3

The method of using a different base could proceed as follows. Note that the code below is just to illustrate the method, in order to implement it efficiently, one would need to work directly with the binary representation.
The idea is that you interpret your input string as a sequence of 128 bits. Now, if you specify that your new alphabet (characters of the new base system) is A-Za-z0-9+-, you have 64 characters which means that you need 6 bits to encode each one of them. Therefore you can first convert your input string to binary representation, split this representation into chunks of 6 bits, and express each chunk within the specified character set A-Za-z0-9+-:
<?php
$s = "719bedacf2e560b27f39d80accc67ffd";
function conv($s){
$ret = base_convert($s, 16, 2);
return str_repeat("0", 8 - strlen($ret)) . $ret;
}
$binary_repr = implode(array_map(conv, str_split($s, 2)), '');
$items = str_split($binary_repr, 6);
function item2char($str){
$code = base_convert($str, 2, 10);
$alphabet = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+-';
return $alphabet[$code];
}
$result = implode(array_map(item2char, $items), '');
echo $result;
?>
As noted in the comments, this is basically the idea behind:
<?php
$s = "719bedacf2e560b27f39d80accc67ffd";
echo base64_encode(hex2bin($s));
//cZvtrPLlYLJ/OdgKzMZ//Q==
echo bin2hex(base64_decode("cZvtrPLlYLJ/OdgKzMZ//Q=="));
//719bedacf2e560b27f39d80accc67ffd
?>