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I am thinking about following this plan:

  1. Regularly buy bitcoins in an online exchange, 100€/month at market prices.
  2. Once the balance in the exchange exceeds a certain limit (500€), move those bitcoins to cold storage, as long-term savings.

(the reason why I want to do 2 is that I do not feel I really own bitcoins until they are in a wallet under my control)

With this scheme I would be transferring to my cold wallet a couple of times per year. I have read that reusing a bitcoin address is not recommended. I am worried about these two facts:

  1. Will reusing my cold-storage address decrease the security of my cold-storage wallet?
  2. The balance of the offline wallet will be visible on the blockchain. I have read about privacy implications of having several parties transfer to a single bitcoin address (employer being able to see my rent, for example), but since the only one transferring to this account will be myself, from the account in the online exchange, there is no danger of private information becoming public, correct? That is, from these regular transfers no spending habits can be inferred. Furthermore, the receiving address will not be linked to any real persona. The only one knowing the identity of the sender is the exchange, and the identity of the receiver (the cold wallet) is completely hidden since he is not engaging in other transactions with any other party. Is this correct?

Note: I am not planning to spend from the offline wallet at the moment, and I know that spending changes the security and privacy implications. I am planning to only save into the offline wallet.

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Q1: Depens on how you use it. Transactions to an address does not decrease it's security. Using a cold-storage wallet and taking it online exposes your wallet and it's security.

Q2: It's correct. Most exchanges require KYC(know your customer), they store information about you and your withdrawal addresses. It's possible to create a new address for each withdrawal. It's hard to prove that you are in possession of the withdrawal address.

(the reason why I want to do 2 is that I do not feel I really own bitcoins until they are in a wallet under my control)

Can't stress this part enough, you only own bitcoin if only you own the private keys.

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    "you only own bitcoin if only you own the private keys" At least from a technical point of view. Not sure about the legal status of your bitcoins deposited on on exchange (who is the "real owner"?), but what is sure is that anything can happen to them (as MtGox showed). But once you transfer the bitcoins to your private wallet, the only one able to damage your property is yourself alone, by negligence, carelessness or simply lack of technical skills (as longs as the bitcoin protocol holds, of course).
    – blueFast
    Commented Nov 20, 2017 at 7:30
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  1. No it will not decrease the security of this wallet. Security concerns happen when you have to use your private key (i.e when you spend money).

  2. Reusing an address will indeed allow other people to have more information about the amount of bitcoin under the control of the same person.

Furthermore, someone having access to a large set of payment data (i.e bank or payment processor such as paypal) will have an easier time to match your bitcoin address to your identity.

Outside people having a privileged access to payment data (i.e most people), it will only have a very limited impact on your privacy.

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