12
There is no substitute in terms of security and trust for running a full node.
There are different "lightweight client" concepts. Some of them are...
BIP37 (bloom filter):
[minus] With current used false-positive rates, peers may learn all wallet addresses
[minus] Usually done over an unencrypted channel (p2p 8333), ISPs, etc. learn also all your ...
7
You're right, there is no strict requirement that the private key is strictly less than the group order.
However, it is required that the resulting public key is uniform, which implies that (x % n) must be uniformly distributed between 1 and n-1 inclusive (or at least indistinguishably close to uniform). The easiest way to accomplish this is by saying that ...
3
There are significantly more than 10k full nodes on the network. The 10k figure is simply the number of reachable nodes which listen publicly for new connections. There are many more times that amount which do not have open ports. Luke-jr publishes information about nodes his own knows about[1], suggesting there are in the order of 100k nodes.
It only takes ...
1
Support for SSL protected RPC was removed in Bitcoin Core version 0.12.0 (released in february 2016).
See https://bitcoin.org/en/release/v0.12.0#rpc-low-level-api-changes for the release notes on this, and also a workaround.
1
What you are describing is a textbook example of a 51% attack. Bitcoin protocol is designed to accept the chain that has the most proof of work (most often this is same as the longest chain). If a miner needs to change block 90, he will have to recalculate hashes starting from block 90-100. To make his attack successful, the miner will have to mine blocks ...
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