1{-# LANGUAGE DeriveDataTypeable #-}
2{-# LANGUAGE GeneralizedNewtypeDeriving #-}
3-- |
4-- Module      : Crypto.ECC.Simple.Types
5-- License     : BSD-style
6-- Maintainer  : Vincent Hanquez <vincent@snarc.org>
7-- Stability   : Experimental
8-- Portability : Excellent
9--
10-- References:
11--   <https://tools.ietf.org/html/rfc5915>
12--
13{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
14module Crypto.ECC.Simple.Types
15    ( Curve(..)
16    , Point(..)
17    , Scalar(..)
18    , CurveType(..)
19    , CurveBinaryParam(..)
20    , CurvePrimeParam(..)
21    , curveSizeBits
22    , curveSizeBytes
23    , CurveParameters(..)
24    -- * Specific curves definition
25    , SEC_p112r1(..)
26    , SEC_p112r2(..)
27    , SEC_p128r1(..)
28    , SEC_p128r2(..)
29    , SEC_p160k1(..)
30    , SEC_p160r1(..)
31    , SEC_p160r2(..)
32    , SEC_p192k1(..)
33    , SEC_p192r1(..) -- aka prime192v1
34    , SEC_p224k1(..)
35    , SEC_p224r1(..)
36    , SEC_p256k1(..)
37    , SEC_p256r1(..) -- aka prime256v1
38    , SEC_p384r1(..)
39    , SEC_p521r1(..)
40    , SEC_t113r1(..)
41    , SEC_t113r2(..)
42    , SEC_t131r1(..)
43    , SEC_t131r2(..)
44    , SEC_t163k1(..)
45    , SEC_t163r1(..)
46    , SEC_t163r2(..)
47    , SEC_t193r1(..)
48    , SEC_t193r2(..)
49    , SEC_t233k1(..) -- aka NIST K-233
50    , SEC_t233r1(..)
51    , SEC_t239k1(..)
52    , SEC_t283k1(..)
53    , SEC_t283r1(..)
54    , SEC_t409k1(..)
55    , SEC_t409r1(..)
56    , SEC_t571k1(..)
57    , SEC_t571r1(..)
58    ) where
59
60import           Data.Data
61import           Crypto.Internal.Imports
62import           Crypto.Number.Basic (numBits)
63
64class Curve curve where
65    curveParameters :: proxy curve -> CurveParameters curve
66    curveType :: proxy curve -> CurveType
67
68-- | get the size of the curve in bits
69curveSizeBits :: Curve curve => proxy curve -> Int
70curveSizeBits proxy =
71    case curveType proxy of
72        CurvePrime (CurvePrimeParam p)   -> numBits p
73        CurveBinary (CurveBinaryParam c) -> numBits c - 1
74
75-- | get the size of the curve in bytes
76curveSizeBytes :: Curve curve => proxy curve -> Int
77curveSizeBytes proxy = (curveSizeBits proxy + 7) `div` 8
78
79-- | Define common parameters in a curve definition
80-- of the form: y^2 = x^3 + ax + b.
81data CurveParameters curve = CurveParameters
82    { curveEccA :: Integer     -- ^ curve parameter a
83    , curveEccB :: Integer     -- ^ curve parameter b
84    , curveEccG :: Point curve -- ^ base point
85    , curveEccN :: Integer     -- ^ order of G
86    , curveEccH :: Integer     -- ^ cofactor
87    } deriving (Show,Eq,Data)
88
89newtype CurveBinaryParam = CurveBinaryParam Integer
90    deriving (Show,Read,Eq,Data)
91
92newtype CurvePrimeParam = CurvePrimeParam Integer
93    deriving (Show,Read,Eq,Data)
94
95data CurveType =
96      CurveBinary CurveBinaryParam
97    | CurvePrime CurvePrimeParam
98    deriving (Show,Read,Eq,Data)
99
100-- | ECC Private Number
101newtype Scalar curve = Scalar Integer
102    deriving (Show,Read,Eq,Data,NFData)
103
104-- | Define a point on a curve.
105data Point curve =
106      Point Integer Integer
107    | PointO -- ^ Point at Infinity
108    deriving (Show,Read,Eq,Data)
109
110instance NFData (Point curve) where
111    rnf (Point x y) = x `seq` y `seq` ()
112    rnf PointO = ()
113
114data SEC_p112r1 = SEC_p112r1 deriving (Show,Read,Eq)
115data SEC_p112r2 = SEC_p112r2 deriving (Show,Read,Eq)
116data SEC_p128r1 = SEC_p128r1 deriving (Show,Read,Eq)
117data SEC_p128r2 = SEC_p128r2 deriving (Show,Read,Eq)
118data SEC_p160k1 = SEC_p160k1 deriving (Show,Read,Eq)
119data SEC_p160r1 = SEC_p160r1 deriving (Show,Read,Eq)
120data SEC_p160r2 = SEC_p160r2 deriving (Show,Read,Eq)
121data SEC_p192k1 = SEC_p192k1 deriving (Show,Read,Eq)
122data SEC_p192r1 = SEC_p192r1 deriving (Show,Read,Eq)
123data SEC_p224k1 = SEC_p224k1 deriving (Show,Read,Eq)
124data SEC_p224r1 = SEC_p224r1 deriving (Show,Read,Eq)
125data SEC_p256k1 = SEC_p256k1 deriving (Show,Read,Eq)
126data SEC_p256r1 = SEC_p256r1 deriving (Show,Read,Eq)
127data SEC_p384r1 = SEC_p384r1 deriving (Show,Read,Eq)
128data SEC_p521r1 = SEC_p521r1 deriving (Show,Read,Eq)
129data SEC_t113r1 = SEC_t113r1 deriving (Show,Read,Eq)
130data SEC_t113r2 = SEC_t113r2 deriving (Show,Read,Eq)
131data SEC_t131r1 = SEC_t131r1 deriving (Show,Read,Eq)
132data SEC_t131r2 = SEC_t131r2 deriving (Show,Read,Eq)
133data SEC_t163k1 = SEC_t163k1 deriving (Show,Read,Eq)
134data SEC_t163r1 = SEC_t163r1 deriving (Show,Read,Eq)
135data SEC_t163r2 = SEC_t163r2 deriving (Show,Read,Eq)
136data SEC_t193r1 = SEC_t193r1 deriving (Show,Read,Eq)
137data SEC_t193r2 = SEC_t193r2 deriving (Show,Read,Eq)
138data SEC_t233k1 = SEC_t233k1 deriving (Show,Read,Eq)
139data SEC_t233r1 = SEC_t233r1 deriving (Show,Read,Eq)
140data SEC_t239k1 = SEC_t239k1 deriving (Show,Read,Eq)
141data SEC_t283k1 = SEC_t283k1 deriving (Show,Read,Eq)
142data SEC_t283r1 = SEC_t283r1 deriving (Show,Read,Eq)
143data SEC_t409k1 = SEC_t409k1 deriving (Show,Read,Eq)
144data SEC_t409r1 = SEC_t409r1 deriving (Show,Read,Eq)
145data SEC_t571k1 = SEC_t571k1 deriving (Show,Read,Eq)
146data SEC_t571r1 = SEC_t571r1 deriving (Show,Read,Eq)
147
148-- | Define names for known recommended curves.
149instance Curve SEC_p112r1 where
150    curveType _ = typeSEC_p112r1
151    curveParameters _ = paramSEC_p112r1
152
153instance Curve SEC_p112r2 where
154    curveType _ = typeSEC_p112r2
155    curveParameters _ = paramSEC_p112r2
156
157instance Curve SEC_p128r1 where
158    curveType _ = typeSEC_p128r1
159    curveParameters _ = paramSEC_p128r1
160
161instance Curve SEC_p128r2 where
162    curveType _ = typeSEC_p128r2
163    curveParameters _ = paramSEC_p128r2
164
165instance Curve SEC_p160k1 where
166    curveType _ = typeSEC_p160k1
167    curveParameters _ = paramSEC_p160k1
168
169instance Curve SEC_p160r1 where
170    curveType _ = typeSEC_p160r1
171    curveParameters _ = paramSEC_p160r1
172
173instance Curve SEC_p160r2 where
174    curveType _ = typeSEC_p160r2
175    curveParameters _ = paramSEC_p160r2
176
177instance Curve SEC_p192k1 where
178    curveType _ = typeSEC_p192k1
179    curveParameters _ = paramSEC_p192k1
180
181instance Curve SEC_p192r1 where
182    curveType _ = typeSEC_p192r1
183    curveParameters _ = paramSEC_p192r1
184
185instance Curve SEC_p224k1 where
186    curveType _ = typeSEC_p224k1
187    curveParameters _ = paramSEC_p224k1
188
189instance Curve SEC_p224r1 where
190    curveType _ = typeSEC_p224r1
191    curveParameters _ = paramSEC_p224r1
192
193instance Curve SEC_p256k1 where
194    curveType _ = typeSEC_p256k1
195    curveParameters _ = paramSEC_p256k1
196
197instance Curve SEC_p256r1 where
198    curveType _ = typeSEC_p256r1
199    curveParameters _ = paramSEC_p256r1
200
201instance Curve SEC_p384r1 where
202    curveType _ = typeSEC_p384r1
203    curveParameters _ = paramSEC_p384r1
204
205instance Curve SEC_p521r1 where
206    curveType _ = typeSEC_p521r1
207    curveParameters _ = paramSEC_p521r1
208
209instance Curve SEC_t113r1 where
210    curveType _ = typeSEC_t113r1
211    curveParameters _ = paramSEC_t113r1
212
213instance Curve SEC_t113r2 where
214    curveType _ = typeSEC_t113r2
215    curveParameters _ = paramSEC_t113r2
216
217instance Curve SEC_t131r1 where
218    curveType _ = typeSEC_t131r1
219    curveParameters _ = paramSEC_t131r1
220
221instance Curve SEC_t131r2 where
222    curveType _ = typeSEC_t131r2
223    curveParameters _ = paramSEC_t131r2
224
225instance Curve SEC_t163k1 where
226    curveType _ = typeSEC_t163k1
227    curveParameters _ = paramSEC_t163k1
228
229instance Curve SEC_t163r1 where
230    curveType _ = typeSEC_t163r1
231    curveParameters _ = paramSEC_t163r1
232
233instance Curve SEC_t163r2 where
234    curveType _ = typeSEC_t163r2
235    curveParameters _ = paramSEC_t163r2
236
237instance Curve SEC_t193r1 where
238    curveType _ = typeSEC_t193r1
239    curveParameters _ = paramSEC_t193r1
240
241instance Curve SEC_t193r2 where
242    curveType _ = typeSEC_t193r2
243    curveParameters _ = paramSEC_t193r2
244
245instance Curve SEC_t233k1 where
246    curveType _ = typeSEC_t233k1
247    curveParameters _ = paramSEC_t233k1
248
249instance Curve SEC_t233r1 where
250    curveType _ = typeSEC_t233r1
251    curveParameters _ = paramSEC_t233r1
252
253instance Curve SEC_t239k1 where
254    curveType _ = typeSEC_t239k1
255    curveParameters _ = paramSEC_t239k1
256
257instance Curve SEC_t283k1 where
258    curveType _ = typeSEC_t283k1
259    curveParameters _ = paramSEC_t283k1
260
261instance Curve SEC_t283r1 where
262    curveType _ = typeSEC_t283r1
263    curveParameters _ = paramSEC_t283r1
264
265instance Curve SEC_t409k1 where
266    curveType _ = typeSEC_t409k1
267    curveParameters _ = paramSEC_t409k1
268
269instance Curve SEC_t409r1 where
270    curveType _ = typeSEC_t409r1
271    curveParameters _ = paramSEC_t409r1
272
273instance Curve SEC_t571k1 where
274    curveType _ = typeSEC_t571k1
275    curveParameters _ = paramSEC_t571k1
276
277instance Curve SEC_t571r1 where
278    curveType _ = typeSEC_t571r1
279    curveParameters _ = paramSEC_t571r1
280
281{-
282curvesOIDs :: [ (CurveName, [Integer]) ]
283curvesOIDs =
284    [ (SEC_p112r1, [1,3,132,0,6])
285    , (SEC_p112r2, [1,3,132,0,7])
286    , (SEC_p128r1, [1,3,132,0,28])
287    , (SEC_p128r2, [1,3,132,0,29])
288    , (SEC_p160k1, [1,3,132,0,9])
289    , (SEC_p160r1, [1,3,132,0,8])
290    , (SEC_p160r2, [1,3,132,0,30])
291    , (SEC_p192k1, [1,3,132,0,31])
292    , (SEC_p192r1, [1,2,840,10045,3,1,1])
293    , (SEC_p224k1, [1,3,132,0,32])
294    , (SEC_p224r1, [1,3,132,0,33])
295    , (SEC_p256k1, [1,3,132,0,10])
296    , (SEC_p256r1, [1,2,840,10045,3,1,7])
297    , (SEC_p384r1, [1,3,132,0,34])
298    , (SEC_p521r1, [1,3,132,0,35])
299    , (SEC_t113r1, [1,3,132,0,4])
300    , (SEC_t113r2, [1,3,132,0,5])
301    , (SEC_t131r1, [1,3,132,0,22])
302    , (SEC_t131r2, [1,3,132,0,23])
303    , (SEC_t163k1, [1,3,132,0,1])
304    , (SEC_t163r1, [1,3,132,0,2])
305    , (SEC_t163r2, [1,3,132,0,15])
306    , (SEC_t193r1, [1,3,132,0,24])
307    , (SEC_t193r2, [1,3,132,0,25])
308    , (SEC_t233k1, [1,3,132,0,26])
309    , (SEC_t233r1, [1,3,132,0,27])
310    , (SEC_t239k1, [1,3,132,0,3])
311    , (SEC_t283k1, [1,3,132,0,16])
312    , (SEC_t283r1, [1,3,132,0,17])
313    , (SEC_t409k1, [1,3,132,0,36])
314    , (SEC_t409r1, [1,3,132,0,37])
315    , (SEC_t571k1, [1,3,132,0,38])
316    , (SEC_t571r1, [1,3,132,0,39])
317    ]
318-}
319
320typeSEC_p112r1 = CurvePrime $ CurvePrimeParam 0xdb7c2abf62e35e668076bead208b
321paramSEC_p112r1 = CurveParameters
322    { curveEccA = 0xdb7c2abf62e35e668076bead2088
323    , curveEccB = 0x659ef8ba043916eede8911702b22
324    , curveEccG = Point 0x09487239995a5ee76b55f9c2f098
325                    0xa89ce5af8724c0a23e0e0ff77500
326    , curveEccN = 0xdb7c2abf62e35e7628dfac6561c5
327    , curveEccH = 1
328    }
329typeSEC_p112r2 = CurvePrime $ CurvePrimeParam 0xdb7c2abf62e35e668076bead208b
330paramSEC_p112r2 = CurveParameters
331    { curveEccA = 0x6127c24c05f38a0aaaf65c0ef02c
332    , curveEccB = 0x51def1815db5ed74fcc34c85d709
333    , curveEccG = Point 0x4ba30ab5e892b4e1649dd0928643
334                    0xadcd46f5882e3747def36e956e97
335    , curveEccN = 0x36df0aafd8b8d7597ca10520d04b
336    , curveEccH = 4
337    }
338typeSEC_p128r1 = CurvePrime $ CurvePrimeParam 0xfffffffdffffffffffffffffffffffff
339paramSEC_p128r1 = CurveParameters
340    { curveEccA = 0xfffffffdfffffffffffffffffffffffc
341    , curveEccB = 0xe87579c11079f43dd824993c2cee5ed3
342    , curveEccG = Point 0x161ff7528b899b2d0c28607ca52c5b86
343                    0xcf5ac8395bafeb13c02da292dded7a83
344    , curveEccN = 0xfffffffe0000000075a30d1b9038a115
345    , curveEccH = 1
346    }
347typeSEC_p128r2 = CurvePrime $ CurvePrimeParam 0xfffffffdffffffffffffffffffffffff
348paramSEC_p128r2 = CurveParameters
349    { curveEccA = 0xd6031998d1b3bbfebf59cc9bbff9aee1
350    , curveEccB = 0x5eeefca380d02919dc2c6558bb6d8a5d
351    , curveEccG = Point 0x7b6aa5d85e572983e6fb32a7cdebc140
352                    0x27b6916a894d3aee7106fe805fc34b44
353    , curveEccN = 0x3fffffff7fffffffbe0024720613b5a3
354    , curveEccH = 4
355    }
356typeSEC_p160k1 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffeffffac73
357paramSEC_p160k1 = CurveParameters
358    { curveEccA = 0x000000000000000000000000000000000000000000
359    , curveEccB = 0x000000000000000000000000000000000000000007
360    , curveEccG = Point 0x003b4c382ce37aa192a4019e763036f4f5dd4d7ebb
361                    0x00938cf935318fdced6bc28286531733c3f03c4fee
362    , curveEccN = 0x0100000000000000000001b8fa16dfab9aca16b6b3
363    , curveEccH = 1
364    }
365typeSEC_p160r1 = CurvePrime $ CurvePrimeParam 0x00ffffffffffffffffffffffffffffffff7fffffff
366paramSEC_p160r1 = CurveParameters
367    { curveEccA = 0x00ffffffffffffffffffffffffffffffff7ffffffc
368    , curveEccB = 0x001c97befc54bd7a8b65acf89f81d4d4adc565fa45
369    , curveEccG = Point 0x004a96b5688ef573284664698968c38bb913cbfc82
370                    0x0023a628553168947d59dcc912042351377ac5fb32
371    , curveEccN = 0x0100000000000000000001f4c8f927aed3ca752257
372    , curveEccH = 1
373    }
374typeSEC_p160r2 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffeffffac73
375paramSEC_p160r2 = CurveParameters
376    { curveEccA = 0x00fffffffffffffffffffffffffffffffeffffac70
377    , curveEccB = 0x00b4e134d3fb59eb8bab57274904664d5af50388ba
378    , curveEccG = Point 0x0052dcb034293a117e1f4ff11b30f7199d3144ce6d
379                    0x00feaffef2e331f296e071fa0df9982cfea7d43f2e
380    , curveEccN = 0x0100000000000000000000351ee786a818f3a1a16b
381    , curveEccH = 1
382    }
383typeSEC_p192k1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffeffffee37
384paramSEC_p192k1 = CurveParameters
385    { curveEccA = 0x000000000000000000000000000000000000000000000000
386    , curveEccB = 0x000000000000000000000000000000000000000000000003
387    , curveEccG = Point 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d
388                    0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d
389    , curveEccN = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d
390    , curveEccH = 1
391    }
392typeSEC_p192r1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffeffffffffffffffff
393paramSEC_p192r1 = CurveParameters
394    { curveEccA = 0xfffffffffffffffffffffffffffffffefffffffffffffffc
395    , curveEccB = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
396    , curveEccG = Point 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
397                    0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
398    , curveEccN = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831
399    , curveEccH = 1
400    }
401typeSEC_p224k1 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffffffffffffffffffeffffe56d
402paramSEC_p224k1 = CurveParameters
403    { curveEccA = 0x0000000000000000000000000000000000000000000000000000000000
404    , curveEccB = 0x0000000000000000000000000000000000000000000000000000000005
405    , curveEccG = Point 0x00a1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c
406                    0x007e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5
407    , curveEccN = 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7
408    , curveEccH = 1
409    }
410typeSEC_p224r1 = CurvePrime $ CurvePrimeParam 0xffffffffffffffffffffffffffffffff000000000000000000000001
411paramSEC_p224r1 = CurveParameters
412    { curveEccA = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
413    , curveEccB = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
414    , curveEccG = Point 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
415                    0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
416    , curveEccN = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
417    , curveEccH = 1
418    }
419typeSEC_p256k1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
420paramSEC_p256k1 = CurveParameters
421    { curveEccA = 0x0000000000000000000000000000000000000000000000000000000000000000
422    , curveEccB = 0x0000000000000000000000000000000000000000000000000000000000000007
423    , curveEccG = Point 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
424                    0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
425    , curveEccN = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
426    , curveEccH = 1
427    }
428typeSEC_p256r1 = CurvePrime $ CurvePrimeParam 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
429paramSEC_p256r1 = CurveParameters
430    { curveEccA = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
431    , curveEccB = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
432    , curveEccG = Point 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
433                    0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
434    , curveEccN = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
435    , curveEccH = 1
436    }
437typeSEC_p384r1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
438paramSEC_p384r1 = CurveParameters
439    { curveEccA = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc
440    , curveEccB = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
441    , curveEccG = Point 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7
442                    0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f
443    , curveEccN = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
444    , curveEccH = 1
445    }
446typeSEC_p521r1 = CurvePrime $ CurvePrimeParam 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
447paramSEC_p521r1 = CurveParameters
448    { curveEccA = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
449    , curveEccB = 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
450    , curveEccG = Point 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
451                    0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650
452    , curveEccN = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409
453    , curveEccH = 1
454    }
455typeSEC_t113r1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000201
456paramSEC_t113r1 = CurveParameters
457    { curveEccA = 0x003088250ca6e7c7fe649ce85820f7
458    , curveEccB = 0x00e8bee4d3e2260744188be0e9c723
459    , curveEccG = Point 0x009d73616f35f4ab1407d73562c10f
460                    0x00a52830277958ee84d1315ed31886
461    , curveEccN = 0x0100000000000000d9ccec8a39e56f
462    , curveEccH = 2
463    }
464typeSEC_t113r2 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000201
465paramSEC_t113r2 = CurveParameters
466    { curveEccA = 0x00689918dbec7e5a0dd6dfc0aa55c7
467    , curveEccB = 0x0095e9a9ec9b297bd4bf36e059184f
468    , curveEccG = Point 0x01a57a6a7b26ca5ef52fcdb8164797
469                    0x00b3adc94ed1fe674c06e695baba1d
470    , curveEccN = 0x010000000000000108789b2496af93
471    , curveEccH = 2
472    }
473typeSEC_t131r1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000010d
474paramSEC_t131r1 = CurveParameters
475    { curveEccA = 0x07a11b09a76b562144418ff3ff8c2570b8
476    , curveEccB = 0x0217c05610884b63b9c6c7291678f9d341
477    , curveEccG = Point 0x0081baf91fdf9833c40f9c181343638399
478                    0x078c6e7ea38c001f73c8134b1b4ef9e150
479    , curveEccN = 0x0400000000000000023123953a9464b54d
480    , curveEccH = 2
481    }
482typeSEC_t131r2 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000010d
483paramSEC_t131r2 = CurveParameters
484    { curveEccA = 0x03e5a88919d7cafcbf415f07c2176573b2
485    , curveEccB = 0x04b8266a46c55657ac734ce38f018f2192
486    , curveEccG = Point 0x0356dcd8f2f95031ad652d23951bb366a8
487                    0x0648f06d867940a5366d9e265de9eb240f
488    , curveEccN = 0x0400000000000000016954a233049ba98f
489    , curveEccH = 2
490    }
491typeSEC_t163k1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9
492paramSEC_t163k1 = CurveParameters
493    { curveEccA = 0x000000000000000000000000000000000000000001
494    , curveEccB = 0x000000000000000000000000000000000000000001
495    , curveEccG = Point 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8
496                    0x0289070fb05d38ff58321f2e800536d538ccdaa3d9
497    , curveEccN = 0x04000000000000000000020108a2e0cc0d99f8a5ef
498    , curveEccH = 2
499    }
500typeSEC_t163r1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9
501paramSEC_t163r1 = CurveParameters
502    { curveEccA = 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2
503    , curveEccB = 0x0713612dcddcb40aab946bda29ca91f73af958afd9
504    , curveEccG = Point 0x0369979697ab43897789566789567f787a7876a654
505                    0x00435edb42efafb2989d51fefce3c80988f41ff883
506    , curveEccN = 0x03ffffffffffffffffffff48aab689c29ca710279b
507    , curveEccH = 2
508    }
509typeSEC_t163r2 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9
510paramSEC_t163r2 = CurveParameters
511    { curveEccA = 0x000000000000000000000000000000000000000001
512    , curveEccB = 0x020a601907b8c953ca1481eb10512f78744a3205fd
513    , curveEccG = Point 0x03f0eba16286a2d57ea0991168d4994637e8343e36
514                    0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1
515    , curveEccN = 0x040000000000000000000292fe77e70c12a4234c33
516    , curveEccH = 2
517    }
518typeSEC_t193r1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000008001
519paramSEC_t193r1 = CurveParameters
520    { curveEccA = 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01
521    , curveEccB = 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814
522    , curveEccG = Point 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1
523                    0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05
524    , curveEccN = 0x01000000000000000000000000c7f34a778f443acc920eba49
525    , curveEccH = 2
526    }
527typeSEC_t193r2 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000008001
528paramSEC_t193r2 = CurveParameters
529    { curveEccA = 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b
530    , curveEccB = 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae
531    , curveEccG = Point 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f
532                    0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c
533    , curveEccN = 0x010000000000000000000000015aab561b005413ccd4ee99d5
534    , curveEccH = 2
535    }
536typeSEC_t233k1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000000000000000004000000000000000001
537paramSEC_t233k1 = CurveParameters
538    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000
539    , curveEccB = 0x000000000000000000000000000000000000000000000000000000000001
540    , curveEccG = Point 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126
541                    0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3
542    , curveEccN = 0x008000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf
543    , curveEccH = 4
544    }
545typeSEC_t233r1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000000000000000004000000000000000001
546paramSEC_t233r1 = CurveParameters
547    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000001
548    , curveEccB = 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
549    , curveEccG = Point 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
550                    0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
551    , curveEccN = 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
552    , curveEccH = 2
553    }
554typeSEC_t239k1 = CurveBinary $ CurveBinaryParam 0x800000000000000000004000000000000000000000000000000000000001
555paramSEC_t239k1 = CurveParameters
556    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000
557    , curveEccB = 0x000000000000000000000000000000000000000000000000000000000001
558    , curveEccG = Point 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc
559                    0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca
560    , curveEccN = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5
561    , curveEccH = 4
562    }
563typeSEC_t283k1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000000000000000000000000000000010a1
564paramSEC_t283k1 = CurveParameters
565    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000
566    , curveEccB = 0x000000000000000000000000000000000000000000000000000000000000000000000001
567    , curveEccG = Point 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836
568                    0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259
569    , curveEccN = 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61
570    , curveEccH = 4
571    }
572typeSEC_t283r1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000000000000000000000000000000010a1
573paramSEC_t283r1 = CurveParameters
574    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000001
575    , curveEccB = 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
576    , curveEccG = Point 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053
577                    0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4
578    , curveEccN = 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307
579    , curveEccH = 2
580    }
581typeSEC_t409k1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
582paramSEC_t409k1 = CurveParameters
583    { curveEccA = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
584    , curveEccB = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
585    , curveEccG = Point 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746
586                    0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b
587    , curveEccN = 0x007ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf
588    , curveEccH = 4
589    }
590typeSEC_t409r1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
591paramSEC_t409r1 = CurveParameters
592    { curveEccA = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
593    , curveEccB = 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
594    , curveEccG = Point 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7
595                    0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706
596    , curveEccN = 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173
597    , curveEccH = 2
598    }
599typeSEC_t571k1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
600paramSEC_t571k1 = CurveParameters
601    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
602    , curveEccB = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
603    , curveEccG = Point 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972
604                    0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3
605    , curveEccN = 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001
606    , curveEccH = 4
607    }
608typeSEC_t571r1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
609paramSEC_t571r1 = CurveParameters
610    { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
611    , curveEccB = 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a
612    , curveEccG = Point 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19
613                    0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b
614    , curveEccN = 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47
615    , curveEccH = 2
616    }
617