Brief History of Elliptic Curve Cryptography
Introduced by V. Miller and N. Koblitz circa 1985.
Bit-for-bit gives very strong cryptography, compared to
RSA, EC, etc: backbone of $2 billion/year industry.
Elliptic curves are not well understood by mathematicians or
Perhaps danger of hidden attacks possibly outweighs
benefits of use (?).
Therefore it is crucial to understand various risks.
Many mathematically interesting challenges remain.