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ECC is rapidly becoming the public-key technology of choice for Internet protocols. ECC was introduced in 1985 and has a much stronger security record than RSA. ECC research has found new ways of attacking implementations but has also found nicer curves that avoid such attacks.
As a followup to the Snowden revelations, the TLS working group of the IETF has recently asked the crypto research group (CFRG) to suggest new curves for use in TLS, and NIST has publicly announced that they are considering new curves.
This talk gives a hands-on description of how to compute with elliptic curves. It shows different ways to write elliptic curves and the consequences of this representation for secure and efficient implementation. Algorithms will be presented as Python code snippets and will already be online before the talk at http://ecchacks.cr.yp.to.
The talk will be given as a joint presentation by Daniel J. Bernstein and Tanja Lange.