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B-409

409-bit binary field Weierstrass curve.
Also known as: sect409r1ansit409r1
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m409
f(x) x^409 + x^87 + 1
a0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
b0x021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
G(0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7, 0x061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706)
n0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173
h0x2

Characteristics

  • OID:
    1.3.132.0.37
  • Seed:
    4099B5A457F9D69F79213D094C4BCD4D4262210B
  • j-invariant:
    754296572979130966367055702570030140076184810784727299570664029563208238737796673624760610953546729716274009429339787708937
  • Trace of Frobenius:
    -6059503967182126918765909026644927652236777310526686418445029
  • Discriminant:
    86886261634090707672817770640384425264505829479043641824438658614111870471004564988634410809058207142318571212147935892575
  • Anomalous:
    false
  • Supersingular:
    false

SAGE

F.<x> = GF(2)[]
K = GF(2^409, name="x", modulus= x^409 + x^87 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f)))
E.set_order(0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 * 0x2)
G = E(K.fetch_int(0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7), K.fetch_int(0x061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706))


JSON

{
"name": "B-409",
"desc": "",
"oid": "1.3.132.0.37",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 409,
"degree": 409,
"poly": [
{
"coeff": "0x01",
"power": 409
},
{
"coeff": "0x01",
"power": 87
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
},
"b": {
"raw": "0x021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f"
}
},
"generator": {
"x": {
"raw": "0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7"
},
"y": {
"raw": "0x061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706"
}
},
"order": "0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173",
"cofactor": "0x2",
"aliases": [
"secg/sect409r1",
"x963/ansit409r1"
],
"characteristics": {
"seed": "4099B5A457F9D69F79213D094C4BCD4D4262210B",
"j_invariant": "754296572979130966367055702570030140076184810784727299570664029563208238737796673624760610953546729716274009429339787708937",
"anomalous": false,
"discriminant": "86886261634090707672817770640384425264505829479043641824438658614111870471004564988634410809058207142318571212147935892575",
"supersingular": false,
"trace_of_frobenius": "-6059503967182126918765909026644927652236777310526686418445029"
}
}

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