174 class Curve(object):  class
196     def __init__(self, curve, x, y):  argument
197         self.curve = curve
199             self.x = (x % curve.p)
203             self.y = (y % curve.p)
206         # Check that the point is indeed on the curve
208             if (pow(y, 2, curve.p) != ((pow(x, 3, curve.p) + (curve.a * x) + curve.b ) % curve.p)):
209                 raise Exception("Error: point is not on curve!")
216         curve = self.curve
217         # Check that we are on the same curve
218         if Q.curve != curve:
219             raise Exception("Point add error: two point don't have the same curve")
222             return Point(self.curve, self.x, self.y)
228             if (((y1 + y2) % curve.p) == 0):
230                 return Point(self.curve, None, None)
233                 L = ((3*pow(x1, 2, curve.p) + curve.a) * modinv(2*y1, curve.p)) % curve.p
236             L = ((y2 - y1) * modinv((x2 - x1) % curve.p, curve.p)) % curve.p
237         resx = (pow(L, 2, curve.p) - x1 - x2) % curve.p
238         resy = ((L * (x1 - resx)) - y1) % curve.p
240         return Point(self.curve, resx, resy)
244             return Point(self.curve, None, None)
246             return Point(self.curve, self.x, -self.y)
254         Q = Point(P.curve, None, None)
275     def __init__(self, curve, x):  argument
276         self.curve = curve
280     def __init__(self, curve, Y):  argument
282         if Y.curve != curve:
283             raise Exception("Error: curve and point curve differ in public key!")
284         self.curve = curve
294     curve = privkey.curve
295     q = curve.q
296     gx = curve.gx
297     gy = curve.gy
298     G = Point(curve, gx, gy)
300         return PubKey(curve, privkey.x * G)
302         return PubKey(curve, modinv(privkey.x, q) * G)
304 def genKeyPair(curve, is_eckcdsa=False):  argument
305     p = curve.p
306     q = curve.q
307     gx = curve.gx
308     gy = curve.gy
309     G = Point(curve, gx, gy)
316     privkey = PrivKey(curve, x)
493     # Get important parameters from the curve
494     p = privkey.curve.p
495     q = privkey.curve.q
496     gx = privkey.curve.gx
497     gy = privkey.curve.gy
498     G = Point(privkey.curve, gx, gy)
539     # Get important parameters from the curve
540     p = pubkey.curve.p
541     q = pubkey.curve.q
542     gx = pubkey.curve.gx
543     gy = pubkey.curve.gy
545     G = Point(pubkey.curve, gx, gy)
570 def eckcdsa_genKeyPair(curve):  argument
571     return genKeyPair(curve, True)
589     # Get important parameters from the curve
590     p = privkey.curve.p
591     q = privkey.curve.q
592     gx = privkey.curve.gx
593     gy = privkey.curve.gy
594     G = Point(privkey.curve, gx, gy)
645     # Get important parameters from the curve
646     p = pubkey.curve.p
647     q = pubkey.curve.q
648     gx = pubkey.curve.gx
649     gy = pubkey.curve.gy
650     G = Point(pubkey.curve, gx, gy)
697     # Get important parameters from the curve
698     p = privkey.curve.p
699     q = privkey.curve.q
700     gx = privkey.curve.gx
701     gy = privkey.curve.gy
702     G = Point(privkey.curve, gx, gy)
724 # *| I   1. Reject the signature if r is not a valid point on the curve.
733     # Get important parameters from the curve
734     p = pubkey.curve.p
735     q = pubkey.curve.q
736     gx = pubkey.curve.gx
737     gy = pubkey.curve.gy
738     G = Point(pubkey.curve, gx, gy)
746     # Check r is on the curve
747     W = Point(pubkey.curve, stringtoint(wx), stringtoint(wy))
791     # Get important parameters from the curve
792     p = privkey.curve.p
793     q = privkey.curve.q
794     gx = privkey.curve.gx
795     gy = privkey.curve.gy
796     G = Point(privkey.curve, gx, gy)
835     # Get important parameters from the curve
836     p = pubkey.curve.p
837     q = pubkey.curve.q
838     gx = pubkey.curve.gx
839     gy = pubkey.curve.gy
840     G = Point(pubkey.curve, gx, gy)
879     # Get important parameters from the curve
880     p = privkey.curve.p
881     q = privkey.curve.q
882     gx = privkey.curve.gx
883     gy = privkey.curve.gy
884     G = Point(privkey.curve, gx, gy)
919     # Get important parameters from the curve
920     p = pubkey.curve.p
921     q = pubkey.curve.q
922     gx = pubkey.curve.gx
923     gy = pubkey.curve.gy
924     G = Point(pubkey.curve, gx, gy)
963     # Get important parameters from the curve
964     p = privkey.curve.p
965     q = privkey.curve.q
966     gx = privkey.curve.gx
967     gy = privkey.curve.gy
968     G = Point(privkey.curve, gx, gy)
1007     # Get important parameters from the curve
1008     p = pubkey.curve.p
1009     q = pubkey.curve.q
1010     gx = pubkey.curve.gx
1011     gy = pubkey.curve.gy
1012     G = Point(pubkey.curve, gx, gy)
1066 def gen_self_test(curve, hashfunc, sig_alg_sign, sig_alg_verify, sig_alg_genkeypair, num, hashfunc_…  argument
1075         keypair = sig_alg_genkeypair(curve)
1082 …    test_name = sig_alg_name + "_" + hashfunc_name + "_" + curve.name.upper() + "_" + str(test_num)
1092         out_vectors += "#ifdef WITH_CURVE_"+curve.name.upper()+"\n"
1097         out_vectors += "\tconst u8 k_buf[] = "+bigint_to_C_array(k, getbytelen(curve.q))
1103         out_vectors += "\t.ec_str_p = &"+curve.name+"_str_params,\n"
1114         out_vectors += "#endif /* WITH_CURVE_"+curve.name+" */\n"
1122         out_name += "#ifdef WITH_CURVE_"+curve.name.upper()+"/* For "+test_name+" */\n"
1126         out_name += "#endif /* WITH_CURVE_"+curve.name+" for "+test_name+" */\n"
1141             out_vectors += "#ifdef WITH_CURVE_"+curve.name.upper()+"\n"
1146             out_vectors += "\tconst u8 k_buf[] = "+bigint_to_C_array(k, getbytelen(curve.q))
1152             out_vectors += "\t.ec_str_p = &"+curve.name+"_str_params,\n"
1163             out_vectors += "#endif /* WITH_CURVE_"+curve.name+" */\n"
1169             out_name += "#ifdef WITH_CURVE_"+curve.name.upper()+"/* For "+test_name+" */\n"
1173             out_name += "#endif /* WITH_CURVE_"+curve.name+" for "+test_name+" */\n"
1180 def gen_self_tests(curve, num):  argument
1184 …vectors = [[ gen_self_test(curve, hashf, sign, verify, genkp, num, hash_name, sig_alg_name, total_…
1243     # regarding an EC curve, but since the ASN.1 structure is quite
1272     # Get curve (sequence)
1273     (check, size_Curve, Curve) = extract_DER_sequence(ECParameters[size_ECPVer+size_FieldID:])
1276     # Get A in curve
1277     (check, size_A, A) = extract_DER_octetstring(Curve)
1280     # Get B in curve
1281     (check, size_B, B) = extract_DER_octetstring(Curve[size_A:])
1427 ### Curve helpers
1447     Take as input some elliptic curve parameters and generate the
1474     # Compute the number of points on the curve
1627     print("In order to add a curve, there are two ways:")
1628     print("Adding a user defined curve with explicit parameters:")
1631     print("\t> name: name of the curve in the form of a string")
1632     print("\t> prime: prime number representing the curve prime field")
1634     print("\t> cofactor: cofactor of the curve")
1635     print("\t> a: 'a' coefficient of the short Weierstrass equation of the curve")
1636     print("\t> b: 'b' coefficient of the short Weierstrass equation of the curve")
1639     print("\t> oid: optional OID of the curve")
1642     print("\t1) These elements are verified to indeed satisfy the curve equation.")
1644 …print("\t3) The script automatically generates all the necessary files for the curve to be include…
1645 …print("\tYou will find the new curve definition in the usual 'lib_ecc_config.h' file (one can acti…
1647     print("Adding a user defined curve through RFC3279 ASN.1 parameters:")
1650     print("\t> ECfile: the DER or PEM encoded file containing the curve parameters (see RFC3279)")
1655 … called \"prime\" curves are supported. Then, one can extract an explicit curve representation in …
1662 …print("\t*A specific named user define curve can be removed with the --remove toggle: in this case…
1663     print("\tlocate which named curve must be deleted.")
1668 …print("\tIn this case, X test vectors will be generated for *each* (curve, sign algorithm, hash al…
1682     Get elliptic curve parameters from command line
1752             print("--remove option expects a curve name provided with --name")
1756 … everything related to user defined "+name.replace("user_defined_", "")+" curve. Enter y to confir…
1758             print("NOT removing curve "+name.replace("user_defined_", "")+" (cancelled).")
1761         print("Removing user defined curve "+name.replace("user_defined_", "")+" ...")
1763             print("Error: you must provide a curve name with --remove")
1775             print("Error: curve name "+name+" does not seem to be present in the sources!")
1780             print("Warning: curve name "+name+" self tests do not seem to be present ...")
1825             print("Error: option ECfile needs a curve name!")
1849 …print("Error: missing "+err_string+" in explicit curve definition (name, prime, a, b, gx, gy, orde…
1865     # Check that the provided generator is on the curve
1867 …print("Error: the given parameters (prime, a, b, gx, gy) do not verify the elliptic curve equation…
1901     # Add the curve mapping
1906     # Add the new curve type in the enum
1913     # Add the new curve define in the config
1918     # Add the new curve meson option in the meson.options file
1927         # Create curve
1928         c = Curve(a, b, prime, order, cofactor, gx, gy, cofactor * order, name, oid)
1938                     magic = "ADD curve test case here"
1946         magic = "ADD curve test vectors header here"