def unpack(T, Qx, Qy):
aa, bb = T.get()
aa = aa.muls(Qy)
a = Fp4(aa, bb)
t = Fp2(Qx)
if curve.SexticTwist == D_TYPE:
b = Fp4(t)
c = Fp4()
else:
b = Fp4()
c = Fp4(t).times_i()
return Fp12(a, b, c)
def __init__(self, a=None, b=None, c=None):
if b is None:
if a is None:
self.a = Fp4()
self.b = Fp4()
self.c = Fp4()
else:
self.a = a.copy()
self.b = Fp4()
self.c = Fp4()
else:
self.a = a.copy()
self.b = b.copy()
self.c = c.copy()
def fromBytes(self, E):
FS = curve.EFS
a = Fp4(Fp2(Fp(big.from_bytes(E[0:FS])),
Fp(big.from_bytes(E[FS:2 * FS]))),
Fp2(Fp(big.from_bytes(E[2 * FS:3 * FS])),
Fp(big.from_bytes(E[3 * FS:4 * FS]))))
b = Fp4(Fp2(Fp(big.from_bytes(E[4 * FS:5 * FS])),
Fp(big.from_bytes(E[5 * FS:6 * FS]))),
Fp2(Fp(big.from_bytes(E[6 * FS:7 * FS])),
Fp(big.from_bytes(E[7 * FS:8 * FS]))))
c = Fp4(Fp2(Fp(big.from_bytes(E[8 * FS:9 * FS])),
Fp(big.from_bytes(E[9 * FS:10 * FS]))),
Fp2(Fp(big.from_bytes(E[10 * FS:11 * FS])),
Fp(big.from_bytes(E[11 * FS:12 * FS]))))
self.set(a, b, c)
def rand(self): # mutable
r = Fp4()
r.rand()
self.a = r.copy()
r.rand()
self.b = r.copy()
r.rand()
self.c = r.copy()
return self
def g(A, B, Qx, Qy):
if A == B:
AA, BB, CC = dbl(A)
else:
AA, BB, CC = add(A, B)
CC = CC.muls(Qx)
AA = AA.muls(Qy)
a = Fp4(AA, BB)
if curve.SexticTwist == D_TYPE:
b = Fp4(CC)
c = Fp4()
else:
b = Fp4()
c = Fp4(CC).times_i()
return Fp12(a, b, c)
def smul(self,other) :
if curve.SexticTwist == D_TYPE :
w1=self.a.a*other.a.a
w2=self.a.b*other.a.b
w3=self.b.a*other.b.a
ta=self.a.a+self.a.b
tb=other.a.a+other.a.b
tc=ta*tb
tc-=(w1+w2)
ta=self.a.a+self.b.a
tb=other.a.a+other.b.a
td=ta*tb
td-=(w1+w3)
ta=self.a.b+self.b.a
tb=other.a.b+other.b.a
te=ta*tb
te-=(w2+w3)
w1+=w2.mulQNR()
self.a=Fp4(w1,tc)
self.b=Fp4(td,te)
self.c=Fp4(w3)
else :
w1=self.a.a*other.a.a
w2=self.a.b*other.a.b
w3=self.c.b*other.c.b
ta=self.a.a+self.a.b
tb=other.a.a+other.a.b
tc=ta*tb
tc-=(w1+w2)
ta=self.a.a+self.c.b
tb=other.a.a+other.c.b
td=ta*tb
td-=(w1+w3)
ta=self.a.b+self.c.b
tb=other.a.b+other.c.b
te=ta*tb
te-=(w2+w3)
w1+=w2.mulQNR()
self.a=Fp4(w1,tc)
self.b=Fp4(w3.mulQNR())
self.b.times_i()
self.c=Fp4(te.mulQNR(),td)
return self
def zero():
return Fp12(Fp4(Fp2(Fp(0))))
def one():
return Fp12(Fp4(Fp2(Fp(1))))
def pack(AA, BB, CC):
i = CC.inverse()
return Fp4(AA * i, BB * i)