ref: 5fc5c18208546c77f2c279f7f6acf6b01a2d2645
dir: /sys/src/libauthsrv/decaf.mp/
# negate r when n > (p-1)/2 decaf_neg(p, n, r) { mod(p) m = -r; r = n > (p-1)>>1 ? m : r; } # field F_p # curve a*x**2+y**2==1+d*x**2*y**2 # input X,Y,Z,T (extended coordinates) decaf_encode(p,a,d, X,Y,Z,T, s) mod(p) { r = misqrt((a-d)*(Z+Y)*(Z-Y), p); u = (a-d)*r; decaf_neg(p, -2*u*Z, r); s = u*(r*(a*Z*X-d*Y*T)+Y)/a; decaf_neg(p, s, s); } # field F_p # curve a*x**2+y**2==1+d*x**2*y**2 # input s # output in extended coordinates decaf_decode(p,a,d, s, ok,X,Y,Z,T) { if(s > (p-1)>>1){ ok = 0; } else mod(p) { ss = s^2; Z = 1+a*ss; u = Z^2 - 4*d*ss; v = u*ss; if(v == 0) ok = 1; else { ok = msqrt(v, p); if(ok != 0){ v = 1/ok; ok = 1; } } if(ok != 0) { decaf_neg(p, u*v, v); w = v * s * (2-Z); if(s == 0) w = w + 1; X = 2*s; Y = w * Z; T = w * X; } } }