math/ectab.in: Add the BADA55 curves by Bernstein et al.

diff --git a/math/ectab.in b/math/ectab.in
index afcd472..9665050 100644 (file)
--- a/math/ectab.in
+++ b/math/ectab.in
@@ -768,4 +768,64 @@ curve brainpool-p512t1 prime
   gx 0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da
   gy 0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332
 
+#----- BADA55 curves --------------------------------------------------------
+#
+# These are from http://safecurves.cr.yp.to/bada55.html.  The twist security
+# properties actually seem useful, so I'm including them here, despite the
+# fact that they were obviously made primarily to make a point about
+# `verifiably random' curves.
+#
+# I've had to choose generators myself; in each case, I chose the smallest
+# possible x-coordinate, and the smaller possible y-coordinate for that x.
+
+curve bada55-vr-224 niceprime
+  p 0xffffffffffffffffffffffffffffffff000000000000000000000001
+  a 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
+  b 0xfd9ca54c0738b8a6fb8cf4cdb328e75983d6da1b78b6223463375562
+  r 0xffffffffffffffffffffffffffff0d44ef1096b2b67b7a3dcee7b079
+  h 1
+  gx 3
+  gy 0x32e826f050bdf4c3f4292fa4efa50146b0fd3f342da5e081badbc36c
+
+curve bada55-vpr-224 niceprime
+  p 0xffffffffffffffffffffffffffffffff000000000000000000000001
+  a 0x8110b017fda88a224f3f64f3964926308dec9784b13c08f09f4ffc4a
+  b 0x5587342f92ba3091a9ba09ad867f4cef85778edb831054f9cb5b3ed5
+  r 0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add
+  h 1
+  gx 0
+  gy 0x5bf50773d4af0f3caba87919b7504fcbd4549f9f845d19aa369dbabe
+
+curve bada55-vpt-224 niceprime
+  # The page doesn't provide an isomorphic curve with a = -3, which is
+  # unsurprising because (unlike the real Brainpool curves) there isn't one.
+  # So this is the quadratic twist of BADA55-VPR-224, which (by construction)
+  # also has prime order.
+  #Z sqrt(39bef747a58ef82f6d337dd7dfd37641688b10cacfbd45448673c6dd)
+  p 0xffffffffffffffffffffffffffffffff000000000000000000000001
+  a 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
+  b 0x3c1f1d26b674d3a1a0a34a808decd83dea4fd207b9896a88031ef63a
+  r 0x10000000000000000000000000000b8be5a2c1640bf56a572c0feb527
+  h 1
+  gx 3
+  gy 0x2df5bbdfd22559ee826d7d3ce60914e4f8609579eddd3c0a07dff90c
+
+curve bada55-vr-256 niceprime
+  p 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
+  a 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
+  b 0xbada55ecd8bbead3add6c534f92197deb47fceb9be7e0e702a8d1dd56b5d0b0c
+  r 0xffffffff00000000fffffffffffffffebedc2797003336661a49d76a903bdb91
+  h 1
+  gx 0
+  gy 0x5310d24619c2e5b721e14dcedc3332d0be3ce9347161ebbc14a43fc7fad546d2
+
+curve bada55-vr-384 niceprime
+  p 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
+  a 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc
+  b 0xbada55ec3be2ad1f9eeea5881ecf95bbf3ac392526f01d4cd13e684c63a17cc4d5f271642ad83899113817a61006413d
+  r 0xfffffffffffffffffffffffffffffffffffffffffffffffeefe1169b82ff7e5032c683f766fae57359cfc5fc25ffce37
+  h 1
+  gx 2
+  gy 0x37d4cb922a8a155845ae2b2884c788a01a22fbf621a7918dc1f18a89fad6df0ab3169acfa538eb7c6c1c9cda7cfb5023
+
 #----- That's all, folks-----------------------------------------------------