Downloading the pruned blockchain file directly from external source
It introduces too much trust into the download source. It's the same thing as just uploading a datadir. You aren't verifying any of the blockchain history; what you download could be a fork of the blockchain. Having such...
Does a clearnet connection to my lightning node not require a TLS certificate?
Lightning network connections do not use TLS or certificates at all, as far as I know (note that this may be different for other types of connections, like RPC). To explain why, let us look at how they are used in the HT...
Brassard-Høyer-Tapp (BHT) Algorithm and Bitcoin (BIP360)
Grover's is related and some considerations were discussed here on Stackexchange, too. We could design a black box function to break both P2PKH and P2SH (and P2WSH, etc.) addresses in 2^80 single-threaded quantum comput...
How do you derive the private key from two signatures that share the same k value?
ECDSA signatures are pairs (r,s) where r=(k*G).x mod n, and s = (m + r*x)/k mod n, where x is the secret key, k is the random nonce, and m is the message. If you have two s values s1 and s2 for the same secret key and wi...