typo + curve k=8 new

cost_pairing.py

@@ -183,7 +183,8 @@ proof.arithmetic(False)
 C5=CocksPinchVariantResult(5,10000000147,0xe000000000008000,1,ht=3,hy=-0x11e36418c7c8b454,max_B1=600)
 C6=CocksPinchVariantResult(6,3,0xefffffffffffffe00000000000000000,1,ht=-1,hy=0xffbbffffffffffffc020,allowed_cofactor=420,allowed_size_cofactor=10,max_B1=600)
 C7=CocksPinchVariantResult(7,20,0x5fffb820248,6,ht=-2,allowed_cofactor=1232,allowed_size_cofactor=10,max_B1=600)
-C8=CocksPinchVariantResult(8,4,0xffffffffeff7c200,5,ht=5,hy=-0xd700,allowed_cofactor=420,allowed_size_cofactor=10,max_B1=600)
+#C8=CocksPinchVariantResult(8,4,0xffffffffeff7c200,5,ht=5,hy=-0xd700,allowed_cofactor=420,allowed_size_cofactor=10,max_B1=600)
+C8=CocksPinchVariantResult(8,4,0xffc00020fffffffc,1,ht=1,hy=-0xdc04,allowed_cofactor=420,allowed_size_cofactor=10,max_B1=600)
 
 C8old=CocksPinchVariantResult(8,4,0xe000000000001010,5,ht=1,hy=0x177dc)
 C6old=CocksPinchVariantResult(6,3,0xc0000000000000000040000000000000,5,hy=0x20000000000000000000f)
@@ -606,7 +607,10 @@ def finalExpoCost(C):
         else:
             c_exp_T = (logT-1)*cyclo_s8 + (HwT-1)*cost_m(k)
 
-            # first, this: (because phi_8(p)/r = 1 + c(T^2+p^2)(p-T))
+            # first, this: (because phi_8(p)/r = 1 + c(T^2+p^2)(p+T))
+			# recall that a p^2-power cost is the same as a p-power
+			# for the reason explained in remark \ref{frob}.
+			# What happen if i != 1 when the expo is to the power T^i ?
             c2 = 3*c_exp_T + 2*cost_f(8) + 3*cost_m(k)
 
             # Then, see code/formules-familles-CocksPinch.sage
@@ -622,6 +626,7 @@ def finalExpoCost(C):
             c_exp_hu = (loghu-1)*cyclo_s8 + (Hwhu-1)*cost_m(k)
 
             c2 += 4 * c_exp_T + 2 * c_exp_hu + 2 * c_exp_hy + 10 * cost_m(k)
+			# Do we miss some inversions ?
             if (T%4 == 2 or i == 1 or i == 5):
                 c2 += cost_m(k)