We study security of some homomorphic cryptosystems with similar algebraic structure. It is found out that those cryptosystems have special common properties. Based on these properties, we pose two cycling attacks and point out some parameters under which the attacks are efficient. It is verified that randomly selected parameters almost impossibly submit to such attacks. Anyhow, two effective methods are given to construct weak parameters for certain homomorphic cryptosystems, and two moduli over 1 024 bits computed by them are shown to be vulnerable to our cycling attacks. It is concluded that strong primes should be used to avert weak parameters.
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