Secret-Sharing

Under secret sharing ( shared secret ) or Secret sharing is a technique ( usually a number ) to share a secret among a certain number of so-called players. None of the people can reconstruct the secret without the other. Depending on the system, only a subset of the player is required to determine the secret. As a dealer of one who is called, which performs the division.

A typical secret is the secret key of the RSA cryptosystem. If it is split among several people, no person alone can create a signature. Even the compromise of a participant (and its partial key ) does not lead to the compromise of the entire key. Such a division is in high security areas (eg military, certification companies, banks, ... ) is useful.

Method

Simple secret sharing

A simple sharing method looks like this:

  • Be the secret
  • Select the part secrets so that:
  • Reconstructing only possible if all combined

This process is a ( n, n) - threshold scheme (pronounced n- of-n threshold scheme ), since all n partial secrets are needed for reconstruction. The need to be selected at random. is selected such that the condition is satisfied. Since the random, is also random.

A second possibility may be realized by the addition is replaced with the exclusive OR operation ():

  • Be the secret (binary number represented )
  • Select the part secrets as follows:
  • Reconstructing only possible if all combined

This method is again a (n, n ) - threshold scheme. The conditions for which are as in the previously described method.

Advanced secret sharing method

Two well-known secret sharing procedures submitted by Adi Shamir: Shamir 's Secret Sharing and Visual Cryptography.

Another method is the Verifiable Secret Sharing, in which there is the dealer is not possible to distribute false shares to the players. In order to ensure this security, commitments are used with which the Dealer irrevocably stipulates to the shares.

Areas of application

Secret sharing (particularly VSS) is used in many variants of the distributed key generation needs to distribute the key among the participants.

XOR gate Organizational commitment
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