ref: b0a059537147237e868b4a8f07922ae8a349e55c
dir: /sys/src/libauthsrv/elligator2.mp/
#elligator2: # curve a*x^2+y^2==1+d*x^2*y^2 # input r0 # n is any non-square # elligator2(p,a,d, n, r0, X,Y,Z,T) mod(p) { r = n*r0*r0; D = (d*r+a-d)*(d*r-a*r-d); N = (r+1)*(a-2*d); ND = N*D; if(ND == 0) { c = 1; e = 0; } else { e = msqrt(ND, p); if(e != 0) { c = 1; e = 1/e; } else { c = -1; e = n*r0*misqrt(n*ND, p); } } s = c*N*e; t = -c*N*(r-1)*((a-2*d)*e)^2-1; X = 2*s*t; Y = (1-a*s*s)*(1+a*s*s); Z = (1+a*s*s)*t; T = (2*s)*(1-a*s*s); }