Secret Sharing Using the Chinese Remainder Theorem
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High Quality Content by WIKIPEDIA articles! Secret sharing consists of recovering a secret S from a set of shares, each containing partial information about the secret. Secret sharing can thus use the CRT to produce the shares presented in the congruence equations and the secret could be recovered by solving the system of congruences to get the unique solution, which will be the secret to recover. There are several types of secret sharing schemes. The most basic types are the so-called threshold schemes, where only the cardinality of the set of shares matters. In other words, given a secret S,...
High Quality Content by WIKIPEDIA articles! Secret sharing consists of recovering a secret S from a set of shares, each containing partial information about the secret. Secret sharing can thus use the CRT to produce the shares presented in the congruence equations and the secret could be recovered by solving the system of congruences to get the unique solution, which will be the secret to recover. There are several types of secret sharing schemes. The most basic types are the so-called threshold schemes, where only the cardinality of the set of shares matters. In other words, given a secret S, and n shares, any set of t shares is a set with the smallest cardinality from which the secret can be recovered, in the sense that any set of t-1 shares is not enough to give S. This is known as a threshold access structure. We call such schemes (t,n) threshold secret sharing schemes, or t-out-of-n scheme. Threshold secret sharing schemes differ from one another by the method of generating the shares, starting from a certain secret.
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