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A threshold secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret. Threshold secret sharing is useful in management of cryptographic keys. Based on Birkhoff interpolation, Tassa has proposed an ideal hierarchical threshold secret sharing scheme. Then based on Sure interpolation and participants' identity,...
Kocarev gave the first cryptosystems based on the semi-group property of Chebyshev polynomials, which seemed excellent but actually insecure. Due to the inherent periodicity of trigonometric function, an attack can easily get plaintext given ciphertext. In this paper, we extend Chebyshev polynomials from real number to finite fields to avoid the attack and present the corresponding key exchange scheme,...
The subset sum problem is to decide whether or not the 0-1 integer programming problem Σi=1n aixi = M; all xi = 0 or 1; has a solution, where the ai and M are given positive integers. This problem is NP-complete, and the difficulty of solving it is the basis of public key cryptosystems of knapsack type. We propose an algorithm which when given an instance of the subset sum problem searches for a solution...
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