Hacker News Reader

Comment by loup-vaillant | Hacker News Reader

Okay, I went through my sources, and remembered I got my conversion from Wikipedia¹. Strangely, Wikipedia gives a different map than the RFC. (One DJB paper agrees with the RFC, so either the Wikipedia is wrong, or I'm missing something.) That's why I didn't multiply by any constant.

I have a problem however: how do I find the modular square root of -486664?

[1]: https://en.wikipedia.org/wiki/Montgomery_curve#Equivalence_w...

View on HN

    sage: p=2^255-19
    sage: sqrt(GF(p)(-486664))
    6853475219497561581579357271197624642482790079785650197046958215289687604742

The formula in Wikipedia is not wrong, but note that it maps E_{a,d} to M_{A, B} with B = 4/(a - d) = -486664. curve25519, and pretty much every Montgomery curve, is defined with B = 1, so you need some extra twisting to get there.

Excellent, thank you. I'll get on it right away.

Reply on news.ycombinator.com