Security Analysis of Poker-Resembled Protocol Based on Hidden Number Problem

In order to remedy the flaw of SRA mental poker protocol, we propose poker-resembled protocols over Zopf*_p and Zopf*_N, where p is a strong prime and N is the product of two strong primes. Using the results of hidden number problem, we analyze the security of these protocols and prove that when the first card drawing player is malicious, the security of the random permutation and the secret key selected by the card shuffling player can be reduced to the difficulty in predicting the ?(log log p)/2 + 1? most significant bits of cards(plaintext) and the ?2 log log p? most significant bits of her secret key. And in the case card shuffling player is malicious, the security of the secret key of the first card drawing player can be reduced to the difficulty in predicting the ?2 log log p? most significant bits of the secret key.