The state could try to convience you to give out an "official" bitcoin adress
By "convince" you mean threaten with punishment (caging, ruin, death), right?
No, I mean really convice.
No, I really don't think you mean "convince".
You're talking about governments. Governments don't "convince". They threaten with punishment.
Here is an illustrated difference between convincing and what governments do:
- Convincing: Hey mate, can I have your Bitcoin address? No? Well, here's an argument. Still no? OK. No problem, carry on.
- What governments do: Hey mate, can I have your Bitcoin address? No? Well, here's some papers with orders. Still no? OK. Five years in a cage for resisting the orders in the papers.
Do you see what I mean now?
Of course can and will the state force you to reveal at least one adress. But how will they force you to give them all of your adresses you're dealing with?
If theres a way to force you in compliance a state will do so. But I don't see how in this case.
Just for starters how about:
record your internet activity, make the use of strong encryption without key disclosure to the state a crime, secure a warrant for your home/computer/safety-deposit boxes, make the penalty for the refusal to provide passphrase (any passphrase) worse than the underlying crime (i.e. it is 5 years in prison and forfeiture of the value of the bitcoin address for hiding it from the state, but if asked to provide passphrase for an encrypted doc failure to reveal is 30 years in prison and forfeiture of all assets for not providing the passphrase), use
enhanced interrogation techniques (a euphemism for torture make no mistake about it), employ the use of drugs to compel you to testify against yourself, deem your non-compliance an enemy of the state and seize all property and assets even if the underlying crime can't be proven (truthful or not), keep you under surveillance, compel your neighbors, business associates, or family members to testify against you ...
Worst case scenario, just deem you a national security risk and assassinate you without any due process or trial (he was a terrorist we had to act without trial or he could have gotten away). While that might not get them your private keys it may make other subjects less likely to hide things from their masters for fear that future "misunderstandings" might result in their extermination (the occasional mis-assassination if useful to ensure the populace doesn't stray to far from the accepted norm).
Not saying the state will do so however the state makes the rules. The idea that there is a limit to what the state "can" do is just laughable. Governments have murdered more of their own people (people they exist to protect) than any criminal, terrorist or foreign enemy ever has.
Just some examples:
U.S.S.R. (1917-1987) 61,911,000
Communist China (1949-1987) 35,236,000
Nazi Germany (1933-1945) 20,946,000
Nationalist (or Kuomintang) China (1928-1949) 10,076,000
Japan (1936-1945) 5,964,000
Cambodia (1975-1979) 2,035,000
Turkey (1909-1918) 1,883,000
Vietnam (1945-1987) 1,678,000
North Korea (1948-1987) 1,663,000
Poland (1945-1948) 1,585,000
Pakistan (1958-1987) 1,503,000
Mexico (1900-1920) 1,417,000
Yugoslavia (1944-1987) 1,072,000
Czarist Russia (1900-1917) 1,066,000
Note these aren't governments killing "others" (i.e. the United States' extermination of Native Americans, or the number of humans who died under slavery) these are the known accounts of governments killing "self" and just in the last century.
Exact numbers may not ever be known but a pretty conservative number is that ~200 million "citizens" were killed by their own government just in the prior century. So please don't think there is a limit on what the state can do.