Fotiadis Martindale curve which is FST 6.7 k=12 D=2, for Jolijn Cottaar

sage/tnfs/curve/fotiadis_martindale.py

@@ -26,12 +26,18 @@ from tnfs.curve.pairing_friendly_curve import get_curve_parameter_a_j1728, get_c
 from tnfs.curve.pairing_friendly_curve import compute_beta_lambda
 from tnfs.curve.pairing_friendly_curve import BrezingWeng
 
-allowed_code = [1, 10, 17, 19, 20, 23, 24, 25, 26, 27, 28, 29]
+"""
+Curves from ePrint 2019/555
+Also from 2018/969
+"""
+
+allowed_code = [1, 10, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29]
 
 def polynomial_params_from_code(code):
     
     QQx = QQ['x']; (x,) = QQx._first_ngens(1)
     if code == 1:
+        # this is also Family 1 in ePrint 2018/969
         k=8
         D=1
         m=2
@@ -84,6 +90,24 @@ def polynomial_params_from_code(code):
         betax = 4320*x**5 + 3672*x**4 + 2430*x**3 + 954*x**2 + 237*x + 46
         lambx = 36*x**3 + 18*x**2 + 6*x + 1
 
+    elif code == 18:
+        # this is also Family 8 in ePrint 2018/969
+        # and this is FST 6.7 with k=12
+        k=12
+        D=2
+        m=2
+        u_mod_m = [1]
+        zeta_k_mod_rx = x**2
+        exp_tr = 1
+        rx = x**8 - x**4 + 1 # Phi_24(x)
+        tx = x**2 + 1
+        yx = (x**7 - 2*x**3 + x)/2
+        px = (x**14 - 4*x**10 + 2*x**8 + 4*x**6 - 2*x**4 + 5*x**2 + 2)/8
+        cx = (x**6 - 3*x**2 + 2)/8
+        cx == (x**2 - 1)**2 * (x**2 + 2)
+        betax = (x**13 - x**11 - 3*x**9 + 5*x**7 + x**5 - 3*x**3 + 4*x)/2
+        lambx = x**5 + x**3 - x
+
     elif code == 19:
         k=12
         D=3
@@ -274,6 +298,9 @@ def polynomial_params_from_code(code):
     elif D==1:
         assert ((betax**2 + 1) % px) == 0
         assert ((lambx**2 + 1) % rx) == 0
+    elif D==2:
+        assert ((betax**2 + 2) % px) == 0
+        assert ((lambx**2 + 2) % rx) == 0
         
     return px, rx, tx, cx, yx, betax, lambx, D, k, m, u_mod_m
 

sage/tnfs/gen/generate_sparse_curve.py

@@ -65,6 +65,7 @@ from tnfs.curve.pairing_friendly_curve import compute_a_b
 # sage -python -m tnfs.gen.generate_sparse_curve --auri -k 20 -D 1 -a 2 -e0 9 -r 380 384 -w 4 --find_all_w_up_to --2NAF
 #
 # sage -python -m tnfs.gen.generate_sparse_curve --fm -code 17 -p 384 384 -w 5 --find_all_w_up_to --2NAF
+# sage -python -m tnfs.gen.generate_sparse_curve --fm -code 18 -r 249 256 -w 5 --find_all_w_up_to --2NAF
 # sage -python -m tnfs.gen.generate_sparse_curve --fm -code 23 -r 384 384 -w 5 --find_all_w_up_to --2NAF
 # sage -python -m tnfs.gen.generate_sparse_curve --fm -code 25 -r 384 384 -w 5 --find_all_w_up_to --2NAF
 # sage -python -m tnfs.gen.generate_sparse_curve --fm -code 27 -r 384 384 -w 5 --find_all_w_up_to --2NAF
@@ -651,6 +652,8 @@ for u_nbits in range(u_nbits_min, u_nbits_max+1):
                         E = curve(k=k, u=u, D=D, e0=e0, aa=a_auri, a=a, b=b)
                     elif curve == Cyclotomic:
                         E = curve(k=k, u=u, D=D, l=l, e0=e0, a=a, b=b)
+                    elif curve == FotiadisMartindale:
+                        E = curve(code=code, u=u, a=a, b=b)
                     else:
                         E = curve(k=k, u=u, a=a, b=b)
                 else: