LEGEND
(a) TF[n] - a reference number (I call these the Top FIPS set).
(b) Numbers following (a) are FIPS prime exponents
Hence TF[1] 61, -0
(immediately below) represents (Mersenne prime) 261
- 20 = 261 - 1
(c) The pairs following are {abs(Discriminant),
h(D)} which yield prime order elliptic curves.
All discriminants are negative, the sign being implied.
Discriminants are in C-format hexadecimal.
TF[1]
61, -0.
{0x2B, 1}
{0x3BB, 4} {0x4CB, 4}
{0x2E3, 5}
{0x44B, 6}
{0x1933, 17} {0x14D3, 20}
{0x8893, 21}
{0xA70B, 28}
{0xD0AB, 35} {0xD85B, 36}
{0x64B3, 56}
{0x33223, 56}
{0x43DCB, 66} {0x29C6B, 68}
{0x1F5BB, 72}
{0x94FB, 74}
{0x29D03, 90} {0xCABB, 95}
{0x5AD23, 102}
{0x86CFB, 102} {0x79263,
112} {0xBE24B, 112} {0x90DDB, 124}
{0x9AE5B, 128} {0x1C80BB,
128} {0x395E3, 129} {0x22E3BB, 135}
{0x3C39B, 141} {0x99753,
144} {0x2A7EEB, 144} {0x45623, 164}
{0x132C5B, 164} {0x2AFFB,
165} {0xC64C3, 168} {0xB245B, 170}
{0xC5B13, 195} {0x242C83,
218} {0x5B9D3, 223} {0x1AB5C3, 240}
{0x203CEB, 240} {0x750943,
245} {0x6CEC3B, 247} {0x35D73B, 248}
{0x248BDB, 256}
TF[2]
89, -0.
{0x10B, 2}
{0x1F3, 3} {0x2DBB, 12}
{0x4873, 14}
{0x12F73, 22}
{0x11BB3, 36} {0x8C03, 46}
{0x2D17B, 54}
{0xD9FB, 56}
{0xBC2F3, 96} {0xEFC43, 100}
{0x5D4C3, 104}
{0x89323, 108} {0xF2E33,
163} {0xC9AFB, 164} {0x22B83B, 164}
{0x1E0823, 167} {0x173B93,
171} {0x73283, 181} {0x20180B, 203}
{0x940F3, 222} {0x1C0FDB,
224} {0x27A76B, 226} {0x3F419B, 228}
{0xE4D9B, 240} {0x410D43,
240} {0x2D1683, 248} {0x561523, 252}
{0x2DB42B, 256}
TF[3] 107,
-0.
{0xCAB, 8}
{0x1A6B, 9} {0x41CB, 15}
{0x7893, 22}
{0x1BB3B, 49}
{0x38A1B, 76} {0xB1A33, 94}
{0x50283, 100}
{0xDB53B, 100} {0xC392B,
108} {0x1311D3, 111} {0x119D13, 119}
{0x714AB, 120} {0x4017B,
124} {0xED673, 141} {0x13AEF3, 155}
{0x1AB64B, 168} {0x24E8DB,
175} {0xB6703, 178} {0x32DD83, 190}
{0xD7D9B, 192} {0x42B713,
236} {0x25F123, 247}
TF[4] 127,
-0.
{0x133, 3}
{0xDB3, 8} {0x340B, 16}
{0x39AB, 16}
{0x33BB, 20}
{0xBB1B, 38} {0x1817B, 40}
{0x169C3, 50}
{0x1EFE3, 80}
{0x13BCB, 82} {0x11483, 88}
{0x28FE3, 88}
{0x1E57B, 98}
{0x5519B, 99} {0xC4723, 112}
{0xF0313, 150}
{0x95983, 176} {0x1C9AEB,
192} {0x45F93, 208} {0x39FF33, 216}
{0x378163, 217} {0x17F3E3,
220} {0x246BB3, 220} {0x184F7B, 222}
{0x234DC3, 233}
TF[5] 157,
+32, -0.
{0x3B923, 51}
{0x5A20B, 68} {0x2F21B, 91}
{0x16163B, 100}
{0x9143B, 113} {0x15785B,
154} {0x270793, 171} {0x402583, 198}
{0x233383, 222} {0x70EE6B,
224} {0x1E3523, 227} {0x23F803, 248}
TF[6] 191,
-64, +0.
{0x14C0B, 36}
{0x1577B, 55} {0x4562B, 90}
{0x13CA6B, 123}
{0x22430B, 144} {0x7BDC3,
148} {0xB81CB, 161} {0x2BDF0B, 168}
{0x34A6B3, 198} {0x45962B,
213}
TF[7] 191,
+96, +32, +0.
{0x18C5B, 29}
{0xA5D3, 53} {0x3092B, 60}
{0x2378B, 70}
{0x7CF33, 72}
{0x2477B, 123} {0x9029B, 164} {0x2092C3,
214}
TF[8] 192,
-64, -0.
{0xEB, 2}
{0x287B, 14} {0x59383, 58}
{0x2CF6B, 68}
{0x7451B, 74}
{0x8768B, 74} {0x86533, 120}
{0xB210B, 144}
{0x1DC8F3, 150} {0xF8E63,
166} {0x15EBDB, 182} {0x2B3BEB, 200}
{0x1689EB, 212} {0x1D6653,
245}
TF[9] 222,
+96, +64, +0.
{0x1ECB, 17}
{0x5FCB, 18} {0x1B3E3B, 110}
{0x71623, 119}
{0xA8523, 146} {0x5B74B,
169} {0x51E1B, 170} {0x6402B, 184}
{0x31133, 225} {0x49973B,
226} {0x3CE44B, 228} {0x182C13, 244}
TF[10] 224,
-96, +0.
{0x23, 2}
{0x513, 8} {0x17E3, 10}
{0x1E74B, 52}
{0x9E21B, 62}
{0x4FAA3, 72} {0x206D3, 90}
{0x2AD2B, 93}
{0x15F853, 111} {0x9D00B,
112} {0x6F5A3, 160} {0x142E33, 174}
{0x1A1463, 208} {0xBB0EB,
213} {0x3AF76B, 252}
TF[11] 254,
-96, -0.
{0x258BB, 52}
{0x5237B, 54} {0x56E1B, 69}
{0x15C44B, 146}
{0x4145CB, 208} {0x1F04FB,
224}
TF[12] 254,
-64, +0.
{0x4AFB, 16}
{0xF7AB, 28} {0x52B3, 48}
{0x14DC3, 52}
{0x2285B, 53}
{0x21B9B, 55} {0x21C4B, 60}
{0x2924B, 61}
{0x25AFB, 62}
{0x1FA63, 104} {0x6D993, 130} {0x558B3,
134}
{0x23C7B, 156} {0x1FC723,
160} {0xF2BAB, 174} {0x2D66D3, 175}
{0x79100B, 254}
TF[13] 254,
+64, +32, +0.
{0x7BD3, 37}
{0x1ACEB, 44} {0x1448B, 48}
{0x144DB, 56}
{0x796C3, 58}
{0x5C623, 78} {0x6EA43, 100}
{0x197DA3, 125}
{0x4AB43, 144} {0xFF5BB,
144} {0x11389B, 144} {0x21EF9B, 144}
{0x1D78B3, 168} {0x19B9F3,
184} {0x88D63, 232} {0x3429C3, 240}
{0x39A8BB, 240}
TF[14] 255,
+96, -0.
{0x9CE53, 98}
{0x5F0FB, 108} {0xB2BA3, 112} {0x81F13,
128}
{0x111AF3, 183} {0x163453,
192} {0x7AA3A3, 230}
TF[15] 256,
+96, -0.
{0x1283B, 32}
{0x2E3DB, 42} {0x439B3, 84}
{0x84163, 91}
{0x10C94B, 106} {0x10523B,
142} {0xFA2BB, 160} {0x32E4B3, 180}
{0x11CAEB, 196} {0x157FF3,
196} {0x4B1F1B, 230} {0x2F8933, 240}
{0x1ABF93, 245}
TF[16] 288,
+128, -96, +0.
{0xDC3, 6}
{0x1FC3, 12} {0x1031B, 44}
{0x25F4B, 48}
{0x4F873, 55}
{0x48D7B, 64} {0x22723, 80}
{0x226F93, 152}
{0x2054E3, 160} {0x45968B,
256}
TF[17] 318,
-160, -0.
{0x8E8BB, 72}
{0x13DAD3, 90} {0x2049BB, 145} {0x553A9B,
240}
{0x2CDB9B, 242} {0x15182B,
252}
TF[18] 319,
+128, -64, -0.
{0x10AB, 8}
{0xA0E3, 52} {0x22A7B, 80}
{0x209BC3, 250}
TF[19] 349,
-160, +128, -0.
{0x30B3B, 41}
{0x1DA33, 84} {0xADA13, 99}
{0x4A5B2B, 180}
{0x190A6B, 194}
TF[20] 349,
-128, -96, -0.
{0x27B23, 64}
{0x1C543, 84} {0x16073B, 136} {0x197E63,
144}
{0xA31FB, 148} {0x2FA343,
162} {0x5696FB, 212} {0x4533BB, 229}
{0x3A3D53, 242}
TF[21] 350,
-64, -32, -0.
{0x1E23, 18}
{0x79F3, 33} {0xC413, 72}
{0x5FE63, 79}
{0x1D23B, 80}
{0x29308B, 192} {0xC73D3, 220} {0x224263,
222}
TF[22] 381,
-192, -32, -0.
{0x30B3B, 41}
{0x7400B, 85} {0x88153, 112}
{0x8B8BB, 119}
{0x10A3B3, 135} {0xBFD73,
145} {0x19E95B, 213}
TF[23] 382,
+64, -0.
{0x6C43, 28}
{0xC86B, 29} {0x127BB, 45}
{0x17953, 48}
{0x6AD5B, 124} {0xD9ED3,
129} {0xD69B3, 132} {0x1ADDC3, 160}
{0x10ACE3, 216} {0x22FB73,
240}
TF[24] 382,
+192, +160, +0.
{0x105B, 14}
{0x41BB, 24} {0x15F43, 27}
{0x27C7DB, 184}
{0x14C4E3, 249}
TF[25] 382,
+160, +96, +0.
{0x118E3, 48}
{0x1F90E3, 192} {0xD679B, 196} {0x14C683,
212}
{0x54F373, 234} {0x2DA723,
245}
TF[26] 383,
+160, +96, +0.
{0x103, 4}
{0x12BB, 12} {0xA2D3, 26}
{0x55AB, 36}
{0x37B5B, 46}
{0xA00F3, 96} {0x17F3FB, 159}
TF[27] 415,
+192, +128, +0.
{0x182B, 12}
{0x2EAB, 20} {0x14CB3, 40}
{0xB143, 48}
{0x110CB3, 112} {0x3BDEFB,
238} {0x3680B3, 250}
TF[28] 445,
-224, -192, +0.
{0xEE3, 10}
{0x1FC3, 12} {0x10A83, 39}
{0x54DF3, 76}
{0x62E63, 81}
{0x13C64B, 125} {0xB62D3, 216}
TF[29] 445,
-224, -96, -0.
{0x31033, 60}
{0xAAF83, 130} {0x13886B, 167} {0x892C3,
170}
{0xE312B, 184} {0x3B831B,
192} {0x323D5B, 195}
TF[30] 448,
-224, -0.
{0x43B73, 53}
{0x4AFFB, 72} {0x8CDBB, 80}
{0x452CB, 96}
{0x5C6E3, 128} {0xF3883,
148} {0x62CFB, 176}
TF[31] 448,
+192, -160, +0.
{0x2FB, 4}
{0x2D9E3B, 168} {0x3B0FCB, 231} {0x4AFCFB, 248}
TF[32] 448,
-160, -32, -0.
{0x4463B, 54}
{0x285BB, 62} {0x86EC3, 84}
{0x28C93, 92}
{0x1B63B, 106} {0x1B1AB,
112} {0xA62DB, 120} {0x1D4ADB, 220}
{0x833DB, 242} {0x405C33,
256}
TF[33] 448,
+64, +32, +0.
{0xCF93, 40}
{0xA113, 48} {0x289B3, 72}
{0x44E83, 96}
{0x24ABD3, 136} {0x6D5AB,
184} {0x1510FB, 192} {0x874BB, 201}
{0x102963, 206} {0x6B4C3,
224} {0x2F2033, 244}
TF[34] 477,
-160, -32, -0.
{0x1EEB, 14}
{0xC5263, 111} {0x159B3B, 168}
TF[35] 480,
+256, -160, +0.
{0x944B, 25}
{0x14CB3, 40} {0x48B3B, 88}
{0x317CB, 104}
{0x74233, 116} {0x1E50CB,
148} {0x1DDAAB, 198} {0x3B9EAB, 212}
TF[36] 480,
+96, +32, -0.
{0x2443, 11}
{0xEEC3, 56} {0x1D3FB, 74}
{0x15463, 78}
{0x11A3BB, 154} {0xE86F3,
162}
TF[37] 509,
-160, +0.
{0x11E3, 10}
{0x10B13, 45} {0x16DFE3, 108} {0x1051DB,
150}
{0x4964B3, 200} {0x4E878B,
200}
TF[38] 511,
-224, +0.
No solutions with h(D)<=256.
TF[39] 511,
-224, -128, +0.
{0x363EB, 54}
{0xB6023, 94} {0xEFD73, 140}
{0x14C9BB, 156}
{0x1E6273, 212} {0x2EC3AB,
224}
TF[40] 512,
+96, -0.
{0x33A3, 31}
{0x3D55B, 54} {0x147F3, 64}
{0x1949B, 66}
{0x161293, 82} {0x48CDB,
106} {0x56F63, 164} {0x189F1B, 240}
TF[41] 512,
-32, +0.
{0x53CE3, 57}
{0x4F303, 76} {0x7700B, 84}
{0x4355B, 92}
{0x1AD493, 168} {0x13B5EB,
252}
TF[42] 512,
-32, -0.
{0x1723, 7}
{0xC61AB, 130} {0xF59B3, 141} {0x64790B,
243}
TF[43] 512,
+224, +64, +0.
{0x23, 2}
{0xBCB, 7} {0x2B93, 12}
{0x25EB, 26}
{0x45693, 92}
{0x4B343, 96} {0x5173B, 100}
{0x4E29B, 104}
{0xF4A0B, 116} {0x243CAB,
200} {0x34E6A3, 256}
TF[44] 521,
-0.
{0x6E53, 24}
{0x24B2DB, 216} {0x3C818B, 232}
TF[45] 541,
+224, -64, -0.
{0x267B, 45}
{0x36913, 57} {0xB081B, 147}
{0x31283, 152}
{0x1875BB, 204} {0x2066FB,
236}
TF[46] 541,
-160, -96, -0.
{0x1BFA3, 56}
{0x1FA83, 62} {0xEF75B, 111}
{0x10DAD3, 128}
{0x20ABE3, 140}
TF[47] 542,
+256, +32, +0.
{0x7C233, 72}
{0x14FB3, 74} {0x5B6DB, 168}
{0x1C1F3B, 195}
{0x26A1F3, 210} {0x3AB98B,
232} {0x2423CB, 244}
TF[48] 543,
+224, +32, +0.
{0xA3, 1}
{0x297A3, 79} {0x9EEF3, 80}
{0x13E6A3, 115}
{0x10AEC3, 140}
TF[49] 544,
-96, +0.
{0x3903, 24}
{0x30716B, 200} {0x2C654B, 208} {0x10C503, 216}
{0x5C74B, 230} {0x48884B,
252}
TF[50] 544,
-32, +0.
{0x171DB, 48}
{0x3173B, 68} {0x49A3B, 79}
{0x28C9C3, 254}
TF[51] 574,
-256, -128, -0.
{0x6DF3, 18}
{0xA93B, 32} {0x2126B, 39}
{0x10A23, 42}
{0x5A633, 96}
{0x5FD2B, 108} {0xB5D83, 128} {0x433A3,
142}
{0xF422B, 155} {0x171E0B,
216} {0x2BF4B3, 232} {0x239E63, 243}
{0x3B1DC3, 247} {0x29D0BB,
252}
TF[52] 575,
-256, +160, -0.
{0x28F3, 10}
{0x4EFEB, 60} {0x875CB, 74}
{0x3904B, 114}
{0x140C6B, 205} {0x295C23,
220} {0x50CD2B, 236}
TF[53] 575,
+224, -160, -0.
{0x201CB, 164} {0x4CCCCB,
240}
TF[54] 575,
+192, +128, +0.
{0x4F8433, 208}
TF[55] 575,
+192, -96, -0.
{0x38FBB, 74}
{0xA6ABB, 138} {0x6B06B3, 248}
TF[56] 575,
+128, -32, -0.
{0x7DCB, 25}
{0x117BB, 36} {0x5B3B3, 84}
{0x68CE3, 97}
{0x168E13, 168}
TF[57] 607,
-0.
{0x16D53, 47}
{0x6380B, 88} {0xF10D3, 222}
TF[58] 607,
+288, +64, +0.
{0x5F00B, 100} {0x4D323,
112} {0x9A79B, 144} {0x27EE33, 207}
{0x3C092B, 225}
TF[59] 608,
-320, +96, +0.
{0x5E93, 32}
{0x7FC3, 33} {0x768D3, 75}
{0xCE533, 100}
TF[60] 608,
+256, +96, -0.
{0xA3, 1}
{0x8135B, 88} {0x229A9B, 188}
TF[61] 608,
+96, -64, +0.
{0x1C9C3, 36}
TF[62] 637,
+320, -64, -0.
{0x94CB, 40}
{0x8E8BB, 72} {0x2A5B33, 199}
TF[63] 637,
-288, -192, -0.
{0x16B73, 44}
{0x640AB, 144} {0x16E41B, 174}
TF[64] 637,
+224, -32, -0.
{0x223, 3}
{0xB31F3, 136} {0x532A6B, 240} {0x5E0C1B,
249}
TF[65] 637,
-128, -64, -0.
{0xEE3, 10}
{0x9E6B, 20} {0x41FB, 28}
{0x184AB, 52}
{0x26B6F3, 140} {0x160A0B,
162} {0x16A8DB, 251}
TF[66] 638,
+320, +96, +0.
{0xB52DB, 84}
{0x4A503, 98} {0x1AC03B, 104} {0x6D3483,
220}
{0x3989B3, 238} {0x2FF09B,
256}
TF[67] 638,
-64, -32, -0.
{0x4153, 16}
{0x13FCB, 36} {0x7451B, 74}
{0x123583, 130}
{0x20BC7B, 168} {0x2F6833,
183} {0x364B13, 204} {0x185863, 212}
{0x3543A3, 220} {0x1B371B,
228} {0x131A03, 232} {0x183E3B, 252}
TF[68] 639,
+288, -0.
No solutions with h(D)<=256.
TF[69] 640,
+320, -32, +0.
{0x144ECB, 192}
TF[70] 670,
-224, -64, -0.
{0xD453, 36}
{0xE09B, 44} {0xD75CB, 120}
{0x23DCEB, 192}
TF[71] 671,
-288, +64, -0.
{0x15C63, 48}
{0x2B803, 98} {0x114273, 176}
TF[72] 671,
+256, -96, -0.
{0x38763, 72}
{0x8B1FB, 135}
TF[73] 671,
-192, +160, -0.
{0x6A22B, 108} {0x3969B,
138} {0xEC7DB, 192} {0x493A6B, 210}
TF[74] 672,
-192, +0.
{0x101B, 8}
{0x6C13, 42} {0x2A85B, 104}
{0x208E8B, 176}
{0x4B35B3, 256}
TF[75] 672,
+320, +128, +0.
{0xC4DB, 24}
{0x20C9B, 60}
TF[76] 672,
+160, +96, -0.
{0x10453, 35}
{0x18E27B, 125} {0x6B537B, 255}
TF[77] 701,
-352, +96, -0.
{0x39B, 10}
{0x2F0B, 13} {0xB9F6B, 90}
{0x888A3, 94}
{0x132663, 242}
TF[78] 701,
-320, +128, -0.
{0x5403, 36}
{0x36673, 64} {0x54493, 76}
{0x5852B, 76}
{0x308F3, 187} {0x173083,
200} {0x243BA3, 208} {0xE99F3, 224}
TF[79] 701,
-288, +256, -0.
{0x86E3, 50}
{0x5E443, 96} {0x51763, 99}
{0x139483, 156}
{0x20333B, 213}
TF[80] 701,
-288, -192, -0.
{0x4E13, 16}
{0x19B5B, 40} {0xE780B, 160}
{0x40724B, 201}
{0x34325B, 251}
TF[81] 702,
-352, -128, -0.
{0x392B03, 243} {0xD49A3,
252}
TF[82] 703,
+288, -0.
No solutions with h(D)<=256.
TF[83] 703,
+352, +224, +0.
{0x16153, 52}
{0x398B3, 97}
TF[84] 703,
+320, -256, -0.
{0x127FAB, 195} {0x6DE0B,
200}
TF[85] 703,
+256, +96, +0.
{0x46663, 56}
{0x885D3, 96} {0x594D3, 107}
{0x3D2E0B, 251}
TF[86] 703,
-224, +32, -0.
{0x10B, 2}
{0x241AB, 42} {0x2D3EB, 59}
{0xF23CB, 100}
{0x2C81B, 116} {0x3FD23,
156}
TF[87] 703,
-128, -32, +0.
{0x10D2B, 40}
{0xA01FB, 78} {0x1833A3, 124} {0x449983,
215}
TF[88] 704,
+256, -224, +0.
{0x65B, 7}
{0x3C62B, 79} {0x3D3423, 235}
TF[89] 704,
-224, -96, -0.
{0x7163, 53}
{0x16243B, 236}
TF[90] 733,
-256, -64, -0.
{0xEBC3, 28}
{0x20983, 64} {0x313F3, 94}
{0x113C53, 112}
{0xC539B, 144} {0x173F3B,
176} {0x1D0CCB, 196}
TF[91] 734,
+352, -0.
{0x1E73, 16}
{0x61693, 80} {0xF7DCB, 132}
{0xC4233, 196}
{0x12E343, 236} {0x19E943,
248}
TF[92] 736,
-256, +224, +0.
{0x435D3, 65}
{0xEDD33, 110}
TF[93] 765,
-384, -160, +0.
{0x57FA3, 84}
{0xD44F3, 212} {0x52AC3B, 216} {0x255763,
224}
TF[94] 765,
-224, -96, -0.
{0xFFD4B, 101}
TF[95] 766,
-320, -256, -0.
{0x301B, 20}
{0x277F3, 63} {0x3C4E3, 132}
{0x199B73, 204}
TF[96] 766,
+256, +192, +0.
{0x29773, 43}
{0x7F28B, 72} {0x1FA33, 123}
TF[97] 767,
-192, +0.
{0x11983, 30}
{0x233CB, 72} {0x3DF3DB, 235}
TF[98] 767,
+128, -64, -0.
{0x1A0E3, 28}
{0x12CF3, 40} {0x29FFB, 43}
{0xB9BAB, 96}
{0x8AE83, 105}
TF[99] 768,
-96, -0.
{0x92B, 5}
{0xF193, 31} {0x9703, 54}
{0x9B953, 76}
{0x31E2B, 87}
{0x648BB, 100} {0x148A23, 101} {0xD3B2B,
132}
{0x146E4B, 196}
TF[100] 768,
-352, +32, +0.
{0xCEFB, 30}
{0x36593B, 246}
TF[101] 768,
+256, +64, +0.
{0x9CD3, 24}
{0x1E8BB, 64} {0x337CB, 100}
{0x102013, 128}
{0xFFF73, 138} {0x518DEB,
228}