Quote from: doobadoo on May 07, 2014, 03:38:50 AM

[...] does a the strength of a pub/private ecdsa key pair weaken if the privkey is used to sign a significant number of msgs.

In a nutshell: In theory it does weaken. In practice, it doesn't matter... yet.

Just spending from an address already weakens it, because it involves signing the transaction with the private key, which is why re-using addresses is a bad practice also from a security point of view (in addition to the privacy issue).

In practice there is no imminent danger when signing transactions and messages, because the computational effort required to derive the private key from the publicly available information is still prohibitively large, but further down the line there is the small matter of quantum computing, as Vitalik explained.

Having said that, the Merkle-Signature Scheme (MSS) is resistant to quantum computing, so it may well become adopted by cryptocurrencies well in advance of quantum computing availability.

Related References:

Edit: just wanted to add that, as you mentioned, K should never be reused, and a good random number generator should be used if you plan to sign a large number of messages.