This is a technical but quite informative article, nominally about which elliptic curves have good security properties, but also discusses the intentions behind using EC instead of older systems like RSA (basically, EC is safer against some known classes of attacks).
Posting partly because EC vs RSA came up here a few days ago.
See also Section 7.3 and Appendix C (and the BADA55 Crypto paper that the email in Appendix C refers to).