Yesterday

Since the late 1990s elliptic curves was slowly progressing as a major form of public key cryptography.
Slowly because in 10+ years the adoption has not reached 10% and older more traditionnal RSA and DL-mod P-based crypto remained strong.

For bitcoin and for almost anyone in 2009, to use ECC crypto would be an obvious choice [less bytes to write in the blockchain]. Yet bitcoin has opted for a peculiar unorthodox choice.

Today

In 2014/2015 some incredible events have occurred. The ECC adoption movement is now likely to come to reverse.
Here are some interesting recent events:

1. A very academic long-time suspicion about backdoors inside standard NIST/NSA elliptic curves became mainstream in late 2013 after Schneier has reviewed the Snowden documents.
2. In October 2014 I took part and the first Catacrypt 2014 conference in San Francisco. Since then a number of similar events was organized: e.g. this event in Brussels.
3. In August 2015 NSA have announced that P-256 [the most commonly used elliptic curve] is no longer recommended, now P-384 is the norm.
4. December 2015: A sudden wave of 70 lawsuits about using ECCs with standard HTTPS connections.
5. December 2015: Microsoft releases a new ECC crypto library FourQ.

Tomorrow

The NSA says that Elliptic Curves are no longer a long term solution.