These search terms could be subjects or groups and could take in lot of people, some of whom would be New Zealanders.
Although the GCSB is supposed to be targeting "foreign intelligence" it is not illegal for it to retain Waihopai's intercept intelligence on New Zealanders if it was "incidentally obtained intelligence", that is, if the New Zealanders weren't a specific target, and the intelligence was relevant to the GCSB's security objectives.
In addition, many New Zealanders can legally be targeted by the GCSB as "foreign persons" if they are active in "foreign organisations", the definition of which is broad enough to include Greenpeace or the New Zealand subsidiary of a multi-national corporation.
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Former Prime Minister Jenny Shipley qualifies as a "foreign person" because she is on the board of the China Construction Bank.
The Cullen/Reddy report removes the problem of "mass surveillance" by saying it "suggests a kind of active monitoring of the general population that does not occur". However, I don't think any critic of government surveillance has ever envisaged the surveillance going that far.
An over-the-top definition of mass surveillance avoids the reality of a mass collection of communications data at Waihopai and the possibility that the international phone calls or emails of any New Zealander could be caught in the net, accidentally or not. In theory, their communications could be subsequently analysed by a GCSB operative.
The next question is what happens to the "haystack" of communications collected at the Waihopai spy station. The report says that most of these communications "will be of no relevance and will be discarded without ever being examined by an analyst".
They may be discarded by the analyst, but to what extent are they stored, either here or overseas, for later mining by the GCSB or its Five Eyes partners?
We know that the US National Security Agency has access to raw communications from its Five Eyes partners, and that it stores billions of communications for later analysis.
This is relevant to the concern, correctly raised by Cullen and Reddy, that close co-operation with Five Eyes partners "creates a risk of some loss of independence, both operationally and potentially also in relation to our intelligence, defence and foreign policy settings". Our national interests "do not and cannot exactly coincide with those of any other country".
The reality is that when New Zealand is sharing raw communications data with other Fives Eyes partners some of the intelligence they glean from it will be used for foreign policy objectives which are not the same as New Zealand's.
But this seems to be a secondary consideration to the net benefit Cullen and Reddy say New Zealand receives from Five Eyes intelligence sharing. It is hard to judge this as any benefits are largely invisible to the public.
Have any terrorist plots been found? Not as far as we know. Have our trade interests been advanced? No one has pointed out how. Has our diplomacy been assisted? I can't see any evidence.
Yet the downside of New Zealand's participation in Five Eyes surveillance is substantial. There was a cool reception in Beijing when the Snowden papers revealed the GCSB's spying on China. Joining intelligence forces with America against China is hardly the way to optimise our trade with that important country.
New Zealand's ambassador was called in to the Brazilian foreign ministry when it was revealed the GCSB had been gathering Five Eyes intercept data on Brazilian Roberto Azevedo in an unsuccessful attempt to stop him heading off our Trade Minister Tim Groser to become Director-General of the WTO.
Yes, we need to be concerned about possible terrorist activity. But do we need to be in the Five Eyes to detect any plots? The reality is that the police and intelligence forces of friendly nations share information on terrorism (and other international crime) regardless of who is in or out of the Five Eyes.
I don't think Cullen and Reddy make much of a case for us to stay in this five-nation spy network.
Keith Locke is a former Green MP.