source 2007 Hisil--Carter--Dawson
parameter b
assume b = a^2-1
compute UU  = XX1^2
compute WW  = ZZ1^2
compute RR  = ((X1+Z1)^2-XX1-ZZ1)^2
compute A   = 4(UU - WW)
compute AA  = A^2
compute B   = 2(UU + WW)+ a RR
compute BB  = B^2
compute AB  = (A+B)^2-AA-BB
compute C   = b RR^2
compute Q   = 2(BB-C)
compute X3  = X1(AB - Q)
compute Z3  = Z1(AB + Q)
compute Y3  = Y1(Q^2 - 4 AA C)
compute XX3 = X3^2
compute ZZ3 = Z3^2