密码算法与协议6_阈值加密算法分析

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10 5
0
-1.5
-1
-0.5
0
0.5
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1.5
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2.5
-5
-10
-15
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Secret sharing schemes
With t users communicating, we can solve the function for the initial secret, f(0). The problem is that once t individuals communicate, a
Message requires a certain number of individuals to sign it before it can be verified
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Threshold cryptography
Threshold cryptography, or more generally group-oriented cryptography, comprises techniques to distribute basic cryptographic schemes among a number of parties. For example, in a threshold version of a digital signature scheme
Finding f(0) requires t+1 distinct points on the line, where
t is the order of function f 25源自Equations20
f(x) = 5x - 2 f(x) = 4x2 + 3x + 1 f(x) = 3x3 - 2x2 + 4x - 3 f(x) = 2x4 - 3x3 + 4x2 + 6
Chapter 6.
Threshold Cryptography
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Motivation
In many situations it is undesirable that access to valuable items is controlled by a single party only. For example, opening a personal safe at a bank requires the use of two keys, one kept by the owner of the safe and one kept by a bank employee. Similarly, in many cryptographic schemes it is undesirable that ownership of a secret key is limited to a single party only. Instead, the ownership (i.e., knowledge) of a secret key needs to be distributed among a number of parties.
signatures.
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Secret sharing
Secret sharing schemes form the basis for threshold cryptography. The idea is to split a secret into several shares, such that the secret can be reconstructed whenever a sufficient number of shares are available; if an insufficient number of shares is available, it should not be possible to reconstruct the secret, nor any part of it. In constructing secret sharing schemes one should be aware of several pitfalls, as demonstrated in the following example.
the private key is shared among ten parties, such that each subset of seven parties (or more) is able to issue
signatures, while subsets of six parties (or less) cannot produce valid
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Example
Sending messages to an organization
More than one authenticated individual required to read messages
Signing of messages by a group
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Secret sharing schemes
(t,l) secret sharing schemes break up a secret (usually a
private key) into l pieces These pieces are distributed amongst l individuals In order to recover the original secret, at least t individuals
must cooperate
Thus t is the “breaking point” for the secret
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Secret sharing schemes
Easy to see relationship between secret sharing and solving linear algebra equations (matrices)