# chapter8-1 - Secret sharing It is often useful to divide a...

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1 • It is often useful to divide a secret into many pieces, and distribute shares amongst many parties • The parties can later join together to reconstruct the secret Secret sharing

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2 Motivation 1. Reliability : In case the original key is lost, it can be reconstructed from the distributed pieces 2. Confidentiality : Only all parties together can use the key (separation of privilege)
3 Examples Nuclear weapons: Two or more different key are needed to launch a nuclear rocket. This prevents a misuse of the weapon by a single person and also an accidental launch of the rocket Top secret information: The information can be accessed only if more than one person is present Bank vault access: The vault can be opened only during certain time slots. Two or more managers are needed to open the door to the critical area. Each of them has his/her own key The problems of secret sharing and secret splitting can be solved mechanically (a real key) or with use of cryptography

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4 Secret Splitting • We have a secret key K that we want to split in two pieces and distribute it between two people: Alice and Bob • Our goal – We want Alice or Bob to be able to learn nothing about the key K using only their shares respectively – We also want Alice and Bob to be able reconstruct the secret K together
5 Bad example of splitting • Let K be a 256-bit secret key • We split it as follows: Alice gets the first half of the bit representation of the key – and Bob gets the second one • Why is this a bad idea? – Each party does learn something about the key, namely, half of the key – But we want each party to know nothing about the key without the other shares

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6 Possible Attacks • Brute Force attack is possible – Amount of work : O(2 256 ) (ideally for our goal)
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chapter8-1 - Secret sharing It is often useful to divide a...

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