New Zealand is publicly a party to a few SOIs - searching New Zealand Treaties Online turns up agreements with Australia, France, Korea, Spain, and NATO. We also have one with the USA. It's mentioned in a few public treaties - the 1994 NAVSTAR treaty (article 4.1), 2010 Science and Technology Cooperation Agreement (definitions) and the 2016 Space Technology Safeguards Agreement (Article V.4). The Treaties all use different names, but the best one seems to be in the science and technology agreement, which calls it the:
Security of Information Agreement between the New Zealand Minister of Defence and the United States Secretary of Defense of September 2 1952, as amended by the Exchange of Notes between the Government of New Zealand and the Government of the United States of America concerning the safe-guarding of classified information of 1961 and the Exchange of Notes constituting an Understanding adding to the Annex of General Security Procedures contained in the Exchange of Notes November 17, 1961; of 1982.I was interested in the terms of this agreement and in whether it might impact the OIA, so in November 2018 I asked MFAT for a copy. They refused. I complained to the Ombudsman, on the grounds that if they were going to say "the Americans won't let us", they had an obligation to at least ask them. MFAT dragged things out for a year, then made the complaint go away by promising to do actually consult, then didn't do it and refused again. I went back to the Ombudsman, who was Not Impressed with MFAT's deceit, and extracted a commitment from them to make their own assessment under the OIA, then advise the US of it and ask for comments. That was in June 2021. In December MFAT was still dragging its feet. This week, they finally replied, blaming the delay on the pandemic and saying that the US had agreed to release an unclassified summary. Which looks fairly comprehensive for the original 1952 agreement, but is entirely uninformative for the 1961 and 1982 amendments which expanded and replaced it.
Naturally this will be going back to the Ombudsman, as I have some strong arguments for release. And one of these is that despite all the secrecy, we can pretty much guess the exact wording of the 1961 agreement, because the US's equivalent agreements with Canada and the UK from that era have been made public and are essentially identical. I would expect the New Zealand-USA agreement covering the same subject from the same period and approved at the same level and in the same format to be the same, barring the names and diplomatic flourishes. As for the 1982 amendments requiring "investigative and monitoring steps" to provide confidence, the US signed an SOI with Israel in 1982 which included a clause (clause 6) requiring periodic visits to assess security. The 2002 Australia-USA SOI - released as part of its government's treaty series - also includes a "security visits" clause (12) as well as one requiring each party to provide information about security procedures on request (13). Given the closer relationship between NZ and the USA, I'd expect the NZ agreement to include both clauses from the Australian one, but the exact language is likely to be similar to that of the 1982 US-Israel SOI.
(The biggest reason for release is of course that democracies shouldn't make secret treaties, as they have no democratic legitimacy. But that's an argument for the politicians, not the Ombudsman).
Does the agreement actually undermine the OIA? The summary, publicly available equivalent agreements, and MFAT's behaviour all suggest this. But we're not actually allowed to know. Because it is a secret.