Crate ark_cp6_782

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This library implements the CP6_782 curve generated in [BCGMMW20, “Zexe”]. The name denotes that it was generated using the Cocks–Pinch method for the embedding degree 6. The main feature of this curve is that the scalar field equals the base field of the BLS12_377 curve.

Curve information:

  • Base field: q = 22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577
  • Scalar field: r = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
  • valuation(q - 1, 2) = 3
  • valuation(r - 1, 2) = 46

G1 curve equation: y^2 = x^3 + ax + b, where

  • a = 5,
  • b = 17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414,

G2 curve equation: y^2 = x^3 + Ax + B

  • A = Fq3(0, 0, 5)
  • B = Fq3(7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612, 0, 0)

Modules

fq
fq3
fq6
fr
g1
g2

Structs

CP6_782
Fq3Config
Fq6Config
FqConfig
FrConfig
G1Prepared
G2Prepared

Constants

ATE_IS_LOOP_COUNT_NEG
ATE_IS_LOOP_COUNT_NEG = false
ATE_LOOP_COUNT
ATE_LOOP_COUNT = 506464946133393486072777102926336625944849939610982267859828541006717966526573193706126370441346337661774335955699621
FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0
FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0 = 7000705447348627246181409558336018323010329260726930841638672011287206690002601216854775649561085256265269640040570922609783227469279331691880282815325569032149343779036142830666859805506518426649197067288711084398033
FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG
FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG = true
FINAL_EXPONENT_LAST_CHUNK_W1
FINAL_EXPONENT_LAST_CHUNK_W1 = 86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951562986
TWIST
TWIST = (0, 1, 0)

Type Definitions

Fq
Fq3
Fq6
Fr
G1Affine
G1Projective
G2Affine
G2Projective
GT