Curve448
p, order, cofactor が各曲線で共通
Curve448
P $ 2^{448} - 2^{224} - 1
A 156326
order 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d
cofactor 4
U(P) 5
V(P) 355293926785568175264127502063783334808976399387714271831880898435169088786967410002932673765864550910142774147268105838985595290606362
$ x^2 + y^2 = 1 + dx^2y^2
p $ 2^{448} - 2^{224} - 1
d
611975850744529176160423220965553317543219696871016626328968936415087860042636474891785599283666020414768678979989378147065462815545017
order 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d
cofactor 4
X(P) 345397493039729516374008604150537410266655260075183290216406970281645695073672344430481787759340633221708391583424041788924124567700732
Y(P) 363419362147803445274661903944002267176820680343659030140745099590306164083365386343198191849338272965044442230921818680526749009182718
(u, v) = ((y-1)/(y+1), sqrt(156324)*u/x)
(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))
もうひとつedwards448 と同じ 、ゴルディロックス Goldilocks
p $ 2^{448} - 2^{224} - 1
d
-39081
cofactor 4
order 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d
X(P) 224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635 247710
Y(P) 298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062 832660
(u, v) = (y^2/x^2, (2 - x^2 - y^2)*y/x^3)
(x, y) = (4*v*(u^2 - 1)/(u^4 - 2*u^2 + 4*v^2 + 1), -(u^5 - 2*u^3 - 4*u*v^2 + u)/(u^5 - 2*u^2*v^2 - 2*u^3 - 2*v^2 + u))
RFC 8031 Curve25519 and Curve448 for the Internet Key Exchange Protocol Version 2 (IKEv2) Key Agreement
RFC 8731 Secure Shell (SSH) Key Exchange Method Using Curve25519 and Curve448