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Let us first consider the problem without involving Shamir secret-sharing at all. Suppose that $n = 140$ and that the secret $\sigma$ is a 140-byte Twitter message. The space is thus restricted considerably, from all possible $256$ byte values to the printable characters permitted to be used in Twitter messages, and the distribution in this restricted space ...


I'm not sure I understand your question entirely. If there is only one possible message, then the ciphertext can be trivially decrypted simply by choosing this message. I'll assume instead that the ciphertext contains the shuffled bit pattern of a name chosen from a set of more than one name. The problem with bit shuffling is that the number of set bits ...


Security is clearly broken if there is a polynomial-length period with non-negligible probability (where by this I mean if a random point falls in a cycle with a poly-length period with non-negligible probability). In order to find a preimage, just go forward until you get back to the starting point, keeping the previous value each time.

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