An Introduction to the Theory of Elliptic Curves [pdf]

[sr2]

https://www.math.brown.edu/~jhs/Presentations/WyomingEllipticCurve.pdf

[dsacco]

If this interested you, you might want to check out SafeCurves[1]. I didn't see it mentioned in these slides (likely because it approaches the material at a higher/theoretical level), but ECDLP is not the only determining factor in elliptic curve safety; there are also implementation difficulties that can make ECC unsafe even though attackers cannot solve the ECDLP.

DJ Bernstein maintains the SafeCurves website and explains the foregoing in greater detail; the site also tracks security assessments on specific curves. Some are actively used and others are either not well-studied or are just toy examples.

_________

1. http://safecurves.cr.yp.to

[AnkhMorporkian]

For someone with no real interest in cryptography, do elliptic curves have any other interesting applications in computer science?

[bradleyjg → AnkhMorporkian]

Primality Proving: https://ocw.mit.edu/courses/mathematics/18-783-elliptic-curv... (starting on page 5)

[heinrichf → bradleyjg]

Well, I was gonna say factorization (https://en.wikipedia.org/wiki/Lenstra_elliptic_curve_factori...), but I didn't see applications outside cryptography.

[wolfgke → heinrichf]

> but I didn't see applications outside cryptography.

Theoretical computer science (e.g. complexity theory). :-) Always add this application to a research proposal.

[esseti]

tell me that there's a video of the presentation..