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@@ -30,6 +30,7 @@ Tool for generating Elliptic curve domain parameters. - `--points=TYPE` Generate points of given `TYPE` (random/prime/all/nonprime/none). - `-r / --random` Generate a random curve (using Random approach). - `-u / --unique` Generate a curve with only one generator. + - `--metadata` Compute the curve metadata (j-invariant, discriminant, trace of Frobenius, CM discriminant, embedding degree) #### IO options @@ -91,6 +92,60 @@ Generate a prime field, uniquely generated, prime order curve, don't ask for inp ] } +Generate a prime field, uniquely generated random curve, of size 192 bits, also display its metadata: + + > ecgen --fp -r -u --metadata 192 + [{ + "field": { + "p": "0xc61cc69c570f03c690df1177fa1ac8c5b295587f876df1bf" + }, + "a": "0xaa67a35fbec93655b4a9dc2fa84e2deff18077a4fa12d2ef", + "b": "0x4477eabe9abbcfccaa3f996ed03d58f32b149c42cb22d1b9", + "order": "0xc61cc69c570f03c690df1178443ec606114599ad0f6d8790", + "subgroups": [ + { + "x": "0x909b1f3b6378fb77a2c1d2117fe7229c329a4fa400605a62", + "y": "0x2da7e3fafdd4c3b4b149cf6693151dd559eebf8b081435fd", + "order": "0xc61cc69c570f03c690df1178443ec606114599ad0f6d8790", + "cofactor": "0x1", + "points": [ + { + "x": "0x6831806c80fbd016fb59c2eb20700716eeb392c601deda25", + "y": "0x000000000000000000000000000000000000000000000000", + "order": "0x2" + }, + { + "x": "0x6206b8e9d56a22485c1b2baa6c61292ff51aa0848097e823", + "y": "0xbd0a1bda7ba13c81bb3ecaf4abfd34c054d9e4a41aa00733", + "order": "0xa3" + }, + { + "x": "0x9e196e607959b78f821600fdf263834d4ad2b10046b5921c", + "y": "0x26f2c864a472bacd4bbb3e513b0a1c1f59a919a187fa4b47", + "order": "0xbe3b5" + }, + { + "x": "0x0220c948fbb6403608563efc5cf16a630953281155e62d47", + "y": "0x3a630cd359f8028da08b27df562ab8749e3c2430b8a9f3a9", + "order": "0x202205798a8a981b" + }, + { + "x": "0x76f971b3722e4b8bfc284c7c39adb395ade0baa61b1e6820", + "y": "0xb7304431b86e6a06576005a6da2afcd96b43e1ce62056724", + "order": "0xd07e2df2cc0790a9a06ccfa45" + } + ] + } + ], + "meta": { + "j": "2147872786867739581244581376066320780390424557746041800843", + "discriminant": "1437087699540380117015716490177070508119149165688061690066", + "embedding_degree": "4857702049745916698354329148965234205490318980592629024655", + "frobenius": "-22945399076600858943676192208", + "cm_discriminant": "4726079215049797810784721872708419089129671954601412853631" + } + }] + ### Docs See [docs](docs/readme.md). Also: |