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    <p>I suggest a very simple algorithm.</p> <ol> <li>Feed the password into a hash function.</li> <li>Initialize a random number generator with the hash or something you derived from the hash.</li> <li>Generate a 12 digit random number.</li> <li>Add this random number to the input digit by digit modulo 10 to encrypt.</li> </ol> <p>To decrypt subtract the random number modulo 10. <strike>This is actually a form of <a href="http://en.wikipedia.org/wiki/One-time_pad" rel="nofollow noreferrer">One Time Pad</a>.</strike> Because of the comments on this answer I realized that refering to <a href="http://en.wikipedia.org/wiki/One-time_pad" rel="nofollow noreferrer">One Time Pad</a> was a bad choice. A better reference is <a href="http://en.wikipedia.org/wiki/Polyalphabetic_substitution" rel="nofollow noreferrer">Polyalphabetic cipher</a> - while One Time Pad uses polyalphabetic substitution its main characteristic is not to use any key bit twice.</p> <pre> Input 1234 1234 1234 Random number 6710 3987 2154 Output 7944 4111 3388 </pre> <p>There is one remaining problem with that - the algorithm might create leading zeros. To solve this problem one could use <code>XOR</code> instead of addition and substraction. Just transform the digits with <code>XOR</code>. If the first digit turns into a zero, don't encrypt the first digit. When you decrypt with <code>XOR</code> again, the first digit will turn into zero and you know that the first digit was not enrcypted.</p> <p><strong>UPDATE</strong></p> <p>A simple <code>XOR</code> is not the solution because it will produce to large numbers - <code>2 XOR 9 = 11</code> for example. Going to rethinks this...</p> <p><strong>UPDATE</strong></p> <p>The nice propoerties of <code>XOR</code> are <code>XOR(a, b) = XOR(b, a)</code> and <code>XOR(XOR(a, b), b) = a</code>. This makes encryption and decryption the same and allows to detect the unencrypted leading digit. But it is further required that our function only returns values in the range from 0 to 9 what <code>XOR</code> doesn't do.<br> But maybe we can build a custom function with all required properties. So we create an array <code>FUNC</code> with 10 columns and 10 rows and use it as a lookup table for our function. What values to but in? I actually don't know - I am not even sure that it is possible. But if we pick three number from the range 0 to 9 we have to make the following six entries. (It is a symmetric matrix.)</p> <pre> FUNC[x,y] = z FUNC[x,z] = y FUNC[y,z] = x FUNC[y,x] = z FUNC[z,x] = y FUNC[z,y] = x </pre> <p>So maybe it is possible to create such a function by repeatedly choosing random numbers and filling the six entries if there is no conflict. Maybe it is not. I would like to see the table if one finds a solution.</p>
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    1. POHow can I encrypt/decrypt 12-digit decimal numbers to other ones, using a password and Java?
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    1. USDaniel Brückner
    1. USDaniel Brückner
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    1. CODrat, you beat me to it. I don't think the RNG is necessary, though.
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      1. USTadmas
    2. COExcept... you never want to reuse a one time pad (that would be the one time part). Given the encrypted numbers (A + K) and (B + K) I can take (A + K) - (B + K) and get (A - B). That doesn't look that scary because the values X0 - Xn still seem random, except for the fact that each digit it defines a line Ai - Bi = Xi which substantially reduces the search space and makes your encrypted numbers much more susceptible to attack particularly if I have more than one encrypted number or the numbers have any recognizable format.
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      1. USAaron Maenpaa
    3. COThe problem is when the algorithm is run multiple times, the key becomes easily "guessable". I apologise I did not add a constraint that "There must not be a pattern between the numbers". My 12 digit output is going to be presented to a user as a identifier. So a user who can do like 30-40 registrations should not be able to guess what the applications key is :( and thereby guess a valid output
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      1. USKannan Ekanath
 

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