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According to this question and its answer Is it safe to reuse Ether addresses? it is theoretically possible to leak your private key by reusing your ETH address.

Since my ETH address is derived from my mnemonic seed, would this also possibly leak my mnemonic seed and thus potentially give access to my other funds (BTC, Dash etc.)?

If no, is there any threat to other generated ETH addresses from this seed?

  • The only thing required to sign transactions is the private key (the mnemonic seed is not needed). The public key is know once a transaction is signed. Elliptic Curve Cryptography, states that is computationally hard to determine the private key given only the public key. Quantom computer can change that assertion but today they are really far from being close. – Ismael Aug 30 '17 at 17:49
  • Correct. The question is whether you can derive the mnemonic seed once you have the private key. – A1m Sep 2 '17 at 11:24
  • It is kind of useless to calculate the mnemonic seed, because you already have the private key. But it is computationally hard to determine seed from the private key. To derive the private key you use a key derivation function, and then further transform to generate a hd wallet. – Ismael Sep 2 '17 at 16:46
  • If you use a hardware wallet your mnemonic seed might hold various cryptocurrencies. The question is, whether breaking the private key of one of them (e.g. by address reuse) would expose all your other wallets. Apparently not as you say if its cryptographically hard to compute the mnemonic seed from the private key. Is this also safe against quantum computers? – A1m Sep 3 '17 at 11:11
  • If they use BIP44/32 HD wallets then the problem is finding preimages of HMAC-SHA512, so it should be similar to break SHA2-512. There are no public know attacks to the full SHA2-512. IMHO if a private key from a hardware wallet is compromised I'd assume all others keys can also be compromised. It is unlikely they were compromised with today computers, so it must have been some other way a trojan, keylogger, etc. – Ismael Sep 3 '17 at 21:10
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The only thing required to sign transactions is the private key (the mnemonic seed is not needed), you already have the public key once a transaction is signed in the blockchain.

Elliptic Curve Cryptography guarantee that it is computationally hard to determine the private key given only the public key. Quantom computers can change that assertion but today they are really far from being close.

It is kind of useless to calculate the mnemonic seed, because you already have the private key. But it is hard to determine seed from the private key. To derive the private key you use a key derivation to get a binary seed, and then further transform it to generate a hd wallet.

The security of this steps is based on key derivation function used PBKDF2. From the wikipedia page:

One weakness of PBKDF2 is that while its number of iterations can be adjusted to make it take an arbitrarily large amount of computing time, it can be implemented with a small circuit and very little RAM, which makes brute-force attacks using application-specific integrated circuits or graphics processing units relatively cheap.

So it is hard but it might not ressist a determined attack with ASIC chips.

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