Dialog Secret Sharing by CRT: Solving a secret with k of n keys

This dialog window can be called via the menu path Individual procedures \ Applications of the Chinese Remainder Theorem (CRT) \ Secret Sharing by CRT

With this application, you'll be able to try out and understand a (n, k)-Secret Sharing-Threshold Scheme, which distributes a secret on several parties. Here (number-) keys are generated from a secret and distributed on a number of n parties. These keys are public. To rebuilt this secret, you don't need to have all keys, but a number of k (which has to be smaller than or equal to n), which is specified before. The Chinese Remainder Theorem is used in this procedure to calculate the keys.


By clicking Calculate a secret is generated and distributed to a predefined number of n parties (Default for n is 5). This happens by random-generating of primes and using them in specific way.

 


By clicking Options you get the sub-dialog to view and vary the basic conditions for the distribution of the secret to the n keys.

Here, you can specify, how many parties shall get a personal key, how many will be necessary to rebuild the secret, and the range of the prime numbers, which are used.


The field 'Number of parties given (n)' specifies, how many parties are involved in the distribution. The minimum number is '2', because with a smaller number there wouldn't be a distribution anymore. The biggest number is '7'. This upper limit is not set by the algorithm, but by the dialog gui, because we only want to show the exemplary use of this scheme.

The field 'Number of parties needed (k)' specifies, as it says, the number of parties, which are needed to rebuild the secret. This number has to be bigger than 0 and smaller than or equal to the number of parties given (n).

The third option to influence the calculation and distribution is to vary the range for the prime numbers, which are used as identifiers.  Here, you're able to set upper and lower limits. To make sure, everything works all right, set the left number (which is the lower limit) smaller than the right one (the upper limit). In this example, the upper limit is set on 2^109 (a 33-digit number). By exceeding this value, the numbers are no more shown completely in the displayed fields.

The range of values can be entered as a decimal number or as a power of two ( 2^x ).

 


By clicking Calc. Steps (Calculation Method) you'll see a sub-dialog, showing all the steps, made to distribute the secret. Every step and every result is shown in here.


If you want to reconstruct this distribution by yourself, try it by using small numbers and a simple calculator. It'll work.

All steps and results can also be seen in the  Log-File .

 


Clicking the button Reset in the main dialog, you can reset the dialog to the initial conditions. This contains deleting all textfields in the main dialog and the log-file as well as setting the basic conditions for the distribution of the secret (parties given = 5, parties needed = 3, lower limit = 2^108, upper limit = 2^109).

 


To have the secret rebuilt, click button Rebuilt secret. Depending on how many and which keys have been provided, the secret can be rebuilt or not. In any case, this procedure will try and a specific event message appears.

 


Clicking the button Help will lead you to the beginning of this document.

 


After clicking Log file a window appears, where all steps, events and results, starting with the distribution of the secret up to the reconstruction, are shown. This contains successful as well as failed reconstructions. If Reset is clicked, the log file will be emptied.

 


If you click the button Exit, the dialog will be closed and you will be brought back to the CrypTool main window.

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