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## Bandersnatch

255-bit prime field TwistedEdwards curve.

Curve from https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957

$ax^2 + y^2 \equiv 1 + dx^2y^2$

### Parameters

NameValue
p0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
a-0x05
d0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7
n0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1
h0x04

### Characteristics

• j-invariant:
0x1f40
• Discriminant:
-0x08

### SAGE

p = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001K = GF(p)a = K(-0x05)d = K(0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7)E = EllipticCurve(K, (K(-1/48) * (a^2 + 14*a*d + d^2),K(1/864) * (a + d) * (-a^2 + 34*a*d - d^2)))def to_weierstrass(a, d, x, y):	return ((5*a + a*y - 5*d*y - d)/(12 - 12*y), (a + a*y - d*y -d)/(4*x - 4*x*y))def to_twistededwards(a, d, u, v):	y = (5*a - 12*u - d)/(-12*u - a + 5*d)	x = (a + a*y - d*y -d)/(4*v - 4*v*y)	return (x, y)# No generator definedE.set_order(0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1 * 0x04)# This curve is a Weierstrass curve (SAGE does not support TwistedEdwards curves) birationally equivalent to the intended curve.# You can use the to_weierstrass and to_twistededwards functions to convert the points.

### JSON

{  "name": "Bandersnatch",  "desc": "Curve from https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957",  "form": "TwistedEdwards",  "field": {    "type": "Prime",    "p": "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001",    "bits": 255  },  "params": {    "a": {      "raw": "-0x05"    },    "d": {      "raw": "0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7"    }  },  "order": "0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1",  "cofactor": "0x04",  "characteristics": {    "j_invariant": "0x1f40",    "discriminant": "-0x08"  }}

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