sage: Overhaul SWU script

sage/shallue_van_de_woestijne.sage

@@ -1,32 +1,28 @@
+### See C function `shallue_van_de_woestijne`
 
-### http://www.di.ens.fr/~fouque/pub/latincrypt12.pdf
+load("secp256k1_params.sage")
 
-# Parameters for secp256k1
-p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
-a = 0
-b = 7
-F = FiniteField (p)
-C = EllipticCurve ([F(a), F(b)])
+b = F(7)
+c = F(-3).nth_root(2)
+d = (c - 1) / 2
 
 def svdw(t):
-    sqrt_neg_3 = F(-3).nth_root(2)
-
     ## Compute candidate x values
-    w  = sqrt_neg_3 * t / (1 + b + t^2)
+    w  = c * t / (1 + b + t^2)
     x = [ F(0), F(0), F(0) ]
-    x[0] = (-1 + sqrt_neg_3) / 2 - t * w
-    x[1] = -1 - x[0]
-    x[2] = 1 + 1 / w^2
+    x[0] = d - t * w
+    x[1] = -(x[0] + 1)
+    x[2] = 1 + (1 / w^2 if w != 0 else 0)
 
-    print
-    print "On %2d" % t
-    print " x1 %064x" % x[0]
-    print " x2 %064x" % x[1]
-    print " x3 %064x" % x[2]
+    # print()
+    # print("On %2d" % t)
+    # print(" x1 %064x" % x[0])
+    # print(" x2 %064x" % x[1])
+    #print(" x3 %064x" % x[2])
 
     ## Select which to use
-    alph = jacobi_symbol(x[0]^3 + b, p)
-    beta = jacobi_symbol(x[1]^3 + b, p)
+    alph = jacobi_symbol(x[0]^3 + b, P)
+    beta = jacobi_symbol(x[1]^3 + b, P)
     if alph == 1 and beta == 1:
         i = 0
     elif alph == 1 and beta == -1:
@@ -36,16 +32,39 @@ def svdw(t):
     elif alph == -1 and beta == -1:
         i = 2
     else:
-        print "Help! I don't understand Python!"
+        assert False
 
     ## Expand to full point
     sign = 1 - 2 * (int(F(t)) % 2)
     ret_x = x[i]
     ret_y = sign * F(x[i]^3 + b).nth_root(2)
     return C.point((ret_x, ret_y))
 
+def print_fe_const(f):
+    print(f"SECP256K1_FE_CONST(", end="")
+    print((7 * "0x%08x, " + "0x%08x") % tuple((int(f) >> (32 * (7 - (i % 8)))) & 0xffffffff for i in range(8)), end="")
+    print(")", end="")
+
+def print_ge_storage_const(g):
+    print(f"SECP256K1_GE_STORAGE_CONST(", end="")
+    print((15 * "0x%08x, " + "0x%08x") % tuple((int(g[int(i // 8)]) >> (32 * (7 - (i % 8)))) & 0xffffffff for i in range(16)), end="")
+    print(")", end="")
 
 ## main
-for i in range(1, 11):
-    res = svdw(i)
-    print "Result: %064x %064x" % res.xy()
+print("secp256k1_fe negc = ", end="")
+print_fe_const(-c)
+print(";")
+
+print("secp256k1_fe d = ", end="")
+print_fe_const(d)
+print(";")
+
+print()
+
+print("secp256k1_ge_storage results[34] = {")
+for i in range(0, 17):
+    for s in [1, -1]:
+        res = svdw(s*i)
+        print_ge_storage_const(res)
+        print(",")
+print("}")