A method and system distributes N shares of a secret among cooperating entities by representing the secret as a secret polynomial, and forming a splitting polynomial with the secret polynomial as one or more of the coefficients. In one embodiment, the method represents the secret as a secret polynomial over GF(q), where q is a prime number or a power of a prime number. A splitting polynomial of degree (K−1) over GF(qm) is constructed, where K is the number of shares to reconstruct the secret and m is a positive integer. The coefficients of the splitting polynomial are formed with the secret polynomial and random information. The method further evaluates the splitting polynomial at N points with arithmetic defined on GF(qm) to generate the N shares of the secret.
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机译：一种方法和系统，通过将秘密表示为秘密多项式，并以秘密多项式作为一个或多个系数来形成分裂多项式，从而在合作实体之间分配N个秘密份额。在一个实施例中，该方法将该秘密表示为GF（q）上的秘密多项式，其中q是质数或质数的幂。构造了一个在GF（q m ）上的度数（K-1）的分裂多项式，其中K是要重构秘密的份额数，m是正整数。分割多项式的系数由秘密多项式和随机信息形成。该方法还使用在GF（q m ）上定义的算法对N个点的分裂多项式进行评估，以生成N个秘密部分。
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