# Differential representation of binary curve as a public key

Given elliptic curve $$E$$ over binary field $$k$$, a public key is the pair $$(x,y)$$ in $$E$$ and $$x$$ and $$y$$ in $$k$$. The differential representation of $$(x,y)$$ is $$w = x + y$$.

What security implications are there from using $$w$$ as the public key, rather than $$(x,y)$$?

Assume the curve is BBE251 (http://binary.cr.yp.to/bbe-20090604.pdf).

• Did you see the bottom of page 4 of the linked article? – kelalaka Jan 23 '19 at 10:00
• The bottom of page 4 is the beginning of the section "How these speeds were achieved: high level". – Thomas Ryan Stovall Jan 23 '19 at 14:13