The attack is a change of tack for Anonymous which has previously attacked companies such as Mastercard, Visa, and Paypal in response to the card companies' refusal to process donations to Wikileaks.
Its latest operation began on October 14 and targeted child porn on the ‘darknet’ - anonymised sites designed to protect users' identities, which are invisible to normal web users.
Anonymous hackers detected the links to the pornography and removed them but they were up again within five minutes.
In an online statement Anonymous said that it was appalled by any the company for ‘openly supporting child pornography and enabling pedophiles to view innocent children, fueling their issues and putting children at risk of abduction, molestation, rape, and death’.
It read: ‘For this, Freedom Hosting has been declared #OpDarknet Enemy Number One...
‘...we will continue to not only crash Freedom Hosting's server, but any other server we find to contain, promote, or support child pornography.’