Is libsecp256k1 faster than OpenSSL? Bitcoin Core is eventually going to replace OpenSSL with libsecp256k1 for all ECDSA operations. As I understand it, this is motivated by wanting consensus-critical rules to not depend on OpenSSL.

Is libsecp256k1 signature verification also faster than OpenSSL? I've heard conflicting information about that.
Yes it's a lot faster. For example from one of the core developers:

reddit - Pieter Wuille / 2015-02-19 18:13


  Just did a benchmark on libsecp256k1's current master, without GMP,
  without hand-written assembly, and it's around 3.6x faster than
  OpenSSL on my machine (64-bit code, i7 cpu). When the assembly is
  compiled in (which does not require any extra dependencies anymore),
  it's 4.9 times faster.


http://www.reddit.com/r/Bitcoin/comments/2weymr/experiment_bitcoin_core_0100_initial_sync_time/coqghm2

This talks about signature verification, which is currently the bottleneck when catching up to the blockchain.