class BinaryTab(Tab):
def __init__(self, master, name):
Tab.__init__(self, master, name)
self.a = Polynomial("z^8 + z") # initially E : y^2 + xy = x^3 + (z^8 + z)x^2 + (z + 1)
self.b = Polynomial("z + 1")
self.r = 9 # field is initially GF(2^9)
self.modulus = Polynomial("z^9 + z^8 + 1") # initial irred poly
self.Gx = Polynomial("z^8 + z^6 + z^2 + 1") # initially G = (z^8 + z^6 + z^2 + 1, z^7 + z^5 + z^4 + z + 1)
self.Gy = Polynomial("z^7 + z^5 + z^4 + z + 1")
self.Px = Polynomial("z^8 + z^5 + z^3 + z") # initially P = (z^8 + z^5 + z^3 + z, z^8 + z^4 + z + 1)
self.Py = Polynomial("z^8 + z^4 + z + 1")
self.Qx = Polynomial("z^6 + z^4 + z^3 + z") # initially Q = (z^6 + z^4 + z^3 + z, z^5 + 1)
self.Qy = Polynomial("z^5 + 1")
self.k = 179
self.n = 5 # initially n = 5 random curves
self.m = 10 # initially m = 10 random points
outputFrame = Frame(self)
Button(outputFrame, text="Clear Output", bg="blue", fg="white", command=(lambda: self.clear()), borderwidth=1).pack(side=BOTTOM, pady=3)
self._output = Text(outputFrame, height=15, width=70)
self._output.insert(END, "You are responsible for making sure the irreducible polynomial you use is actually irreducible. "
"The default, z^9 + z^8 + 1, is irreducible.\n\n")
self._output.pack(side=LEFT)
scrollbar = Scrollbar(outputFrame)
scrollbar.pack(side=RIGHT, fill=Y)
scrollbar.config(command=self._output.yview)
ecInfo = Frame(self)
polyFrame = Frame(self)
ptsInfo1 = Frame(self)
ptsInfo2 = Frame(self)
arithmeticFrame = Frame(self)
orderFrame = Frame(self)
listFrame = Frame(self)
ptsFrame = Frame(self)
self.curveString = StringVar()
self.curveString.set("E : F_(2^" + str(self.r) + ") : y^2 + xy = x^3 + ")
curveLabel = Label(ecInfo, textvariable=self.curveString, bg="orange", fg="black", borderwidth=1).grid(row=1, column=1)
self._a = Entry(ecInfo, width=25)
self._a.insert(0, self.a)
self._a.bind("<Return>", (lambda event: self.changeA()))
self._a.grid(row=1, column=2)
Label(ecInfo, text="x^2 + ", bg="orange", fg="black", borderwidth=1).grid(row=1, column=3)
self._b = Entry(ecInfo, width=25)
self._b.insert(0, self.b)
self._b.bind("<Return>", (lambda event: self.changeB()))
self._b.grid(row=1, column=4)
Label(polyFrame, text="Irreducible Polynomial: ", bg="orange", fg="black", borderwidth=1).grid(row=1, column=1, pady=3)
self._irred = Entry(polyFrame, width=51)
self._irred.insert(0, self.modulus)
self._irred.bind("<Return>", (lambda event: self.changeModulus()))
self._irred.grid(row=1, column=2, pady=3)
Label(ptsInfo1, text="Generator G = (", bg="orange", fg="black", borderwidth=1).grid(row=1, column=1, pady=3)
self._Gx = Entry(ptsInfo1, width=15)
self._Gx.insert(0, self.Gx)
self._Gx.bind("<Return>", (lambda event: self.changeG()))
self._Gx.grid(row=1, column=2, pady=3)
Label(ptsInfo1, text=", ", bg="orange", fg="black", borderwidth=1).grid(row=1, column=3, pady=3)
self._Gy = Entry(ptsInfo1, width=15)
self._Gy.insert(0, self.Gy)
self._Gy.bind("<Return>", (lambda event: self.changeG()))
self._Gy.grid(row=1, column=4, pady=3)
Label(ptsInfo1, text="), k = ", bg="orange", fg="black", borderwidth=1).grid(row=1, column=5, pady=3)
self._k = Entry(ptsInfo1, width=5)
self._k.insert(0, self.k)
self._k.bind("<Return>", (lambda event: self.changeK()))
self._k.grid(row=1, column=6, pady=3)
Label(ptsInfo2, text="P = ", bg="blue", fg="white", borderwidth=1).grid(row=1, column=1, pady=3)
self._Px = Entry(ptsInfo2, width=15)
self._Px.insert(0, self.Px)
self._Px.bind("<Return>", (lambda event: self.changeP()))
self._Px.grid(row=1, column=2, pady=3)
Label(ptsInfo2, text=", ", bg="blue", fg="white", borderwidth=1).grid(row=1, column=3, pady=3)
self._Py = Entry(ptsInfo2, width=15)
self._Py.insert(0, self.Py)
self._Py.bind("<Return>", (lambda event: self.changeP()))
self._Py.grid(row=1, column=4, pady=3)
Label(ptsInfo2, text="), Q = ", bg="blue", fg="white", borderwidth=1).grid(row=1, column=5, pady=3)
self._Qx = Entry(ptsInfo2, width=15)
self._Qx.insert(0, self.Qx)
self._Qx.bind("<Return>", (lambda event: self.changeQ()))
self._Qx.grid(row=1, column=6, pady=3)
Label(ptsInfo2, text=", ", bg="blue", fg="white", borderwidth=1).grid(row=1, column=7, pady=3)
self._Qy = Entry(ptsInfo2, width=15)
self._Qy.insert(0, self.Qy)
self._Qy.bind("<Return>", (lambda event: self.changeQ()))
self._Qy.grid(row=1, column=8)
Label(ptsInfo2, text=")", bg="blue", fg="white", borderwidth=1).grid(row=1, column=9, pady=3)
Button(arithmeticFrame, text="P + Q", bg="blue", fg="white", command=(lambda: self.add())).grid(row=1, column=1, padx=5, pady=3)
Button(arithmeticFrame, text="kP", bg="blue", fg="white", command=(lambda: self.mult())).grid(row=1, column=2, padx=5, pady=3)
Button(arithmeticFrame, text="log_G(P)", bg="blue", fg="white", command=(lambda: self.log())).grid(row=1, column=3, padx=5, pady=3)
Button(orderFrame, text="Order(E)", bg="blue", fg="white", command=(lambda: self.order())).grid(row=1, column=1, padx=5, pady=3)
Button(orderFrame, text="Order(G)", bg="blue", fg="white", command=(lambda: self.pointOrder())).grid(row=1, column=2, padx=5, pady=3)
Label(listFrame, text="Generate ", bg="orange", fg="black", borderwidth=1).grid(row=1, column=1, pady=3)
self._n = Entry(listFrame, width=3)
self._n.insert(0, self.n)
self._n.bind("<Return>", (lambda event: self.changeN()))
self._n.grid(row=1, column=2, pady=3)
Button(listFrame, text="Random ECs", bg="orange", fg="black", command=(lambda: self.randomECs())).grid(row=1, column=3, padx=5, pady=3)
Label(ptsFrame, text="List ", bg="orange", fg="black", borderwidth=1).grid(row=1, column=1, pady=3)
self._m = Entry(ptsFrame, width=3)
self._m.insert(0, self.m)
self._m.bind("<Return>", (lambda event: self.changeM()))
self._m.grid(row=1, column=2, pady=3)
Button(ptsFrame, text="Random points on E", bg="orange", fg="black", command=(lambda: self.randomPoints())).grid(row=1, column=3, padx=5, pady=3)
ecInfo.pack(side=TOP)
polyFrame.pack(side=TOP)
ptsInfo1.pack(side=TOP)
ptsInfo2.pack(side=TOP)
arithmeticFrame.pack(side=TOP)
orderFrame.pack(side=TOP)
listFrame.pack(side=TOP)
ptsFrame.pack(side=TOP)
outputFrame.pack(side=BOTTOM)
def changeA(self):
temp = self._a.get()
if Polynomial.isValid(temp):
self.a = Polynomial(temp) % self.modulus
self._a.delete(0, END)
self._a.insert(0, self.a)
E = BinaryEllipticCurve(self.a, self.b, self.modulus)
self._output.insert(END, str(E) + "\n")
else:
self._a.delete(0, END)
self._a.insert(0, self.a)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeB(self):
temp = self._b.get()
if Polynomial.isValid(temp):
self.b = Polynomial(temp) % self.modulus
self._b.delete(0, END)
self._b.insert(0, self.b)
E = BinaryEllipticCurve(self.a, self.b, self.modulus)
self._output.insert(END, str(E) + "\n")
else:
self._b.delete(0, END)
self._b.insert(0, self.b)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeModulus(self):
temp = self._irred.get()
if Polynomial.isValid(temp):
self.modulus = Polynomial(temp)
self.r = self.modulus.degree()
self.curveString.set("E : F_(2^" + str(self.r) + ") : y^2 + xy = x^3 + ")
self._irred.delete(0, END)
self._irred.insert(0, self.modulus)
E = BinaryEllipticCurve(self.a, self.b, self.modulus)
self._output.insert(END, "The irreducible polynomial is now set to " + str(self.modulus) + ".\n")
else:
self._irred.delete(0, END)
self._irred.insert(0, self.modulus)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeG(self):
tempx = self._Gx.get()
tempy = self._Gy.get()
if Polynomial.isValid(tempx) and Polynomial.isValid(tempy):
self.Gx = Polynomial(tempx) % self.modulus
self.Gy = Polynomial(tempy) % self.modulus
self._Gx.delete(0, END)
self._Gy.delete(0, END)
self._Gx.insert(0, self.Gx)
self._Gy.insert(0, self.Gy)
self._output.insert(END, "G = " + str(PolynomialPoint(self.Gx, self.Gy, 1)) + "\n")
else:
self._Gx.delete(0, END)
self._Gy.delete(0, END)
self._Gx.insert(0, self.Gx)
self._Gy.insert(0, self.Gy)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeP(self):
tempx = self._Px.get()
tempy = self._Py.get()
if Polynomial.isValid(tempx) and Polynomial.isValid(tempy):
self.Px = Polynomial(tempx) % self.modulus
self.Py = Polynomial(tempy) % self.modulus
self._Px.delete(0, END)
self._Py.delete(0, END)
self._Px.insert(0, self.Px)
self._Py.insert(0, self.Py)
self._output.insert(END, "P = " + str(PolynomialPoint(self.Px, self.Py, 1)) + "\n")
else:
self._Px.delete(0, END)
self._Py.delete(0, END)
self._Px.insert(0, self.Px)
self._Py.insert(0, self.Py)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeQ(self):
tempx = self._Qx.get()
tempy = self._Qy.get()
if Polynomial.isValid(tempx) and Polynomial.isValid(tempy):
self.Qx = Polynomial(tempx) % self.modulus
self.Qy = Polynomial(tempy) % self.modulus
self._Qx.delete(0, END)
self._Qy.delete(0, END)
self._Qx.insert(0, self.Qx)
self._Qy.insert(0, self.Qy)
self._output.insert(END, "Q = " + str(PolynomialPoint(self.Qx, self.Qy, 1)) + "\n")
else:
self._Qx.delete(0, END)
self._Qy.delete(0, END)
self._Qx.insert(0, self.Qx)
self._Qy.insert(0, self.Qy)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeK(self):
try:
self.k = int(self._k.get())
self._k.delete(0, END)
self._k.insert(0, self.k)
self._output.insert(END, "k = " + str(self.k) + "\n")
except ValueError:
self._k.delete(0, END)
self._k.insert(0, self.k)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeN(self):
try:
self.n = int(self._n.get())
self._n.delete(0, END)
self._n.insert(0, self.n)
self._output.insert(END, "Random curve selection will now generate " + str(self.n) + " curve")
if self.n != 1:
self._output.insert(END, "s")
self._output.insert(END, ".\n")
except ValueError:
self._n.delete(0, END)
self._n.insert(0, self.n)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def changeM(self):
try:
self.m = int(self._m.get())
self._m.delete(0, END)
self._m.insert(0, self.m)
self._output.insert(END, "Random point selection will now generate " + str(self.m) + " point")
if self.m != 1:
self._output.insert(END, "s")
self._output.insert(END, ".\n")
except ValueError:
self._m.delete(0, END)
self._m.insert(0, self.m)
self._output.insert(END, "There was an error with your input. Please try again.\n")
def add(self):
P = PolynomialPoint(self.Px, self.Py, Polynomial("1"))
Q = PolynomialPoint(self.Qx, self.Qy, Polynomial("1"))
R = P.add(Q, self.a, self.b, self.modulus)
self._output.insert(END, str(P) + " + " + str(Q) + " = " + str(R) + "\n")
def mult(self):
P = PolynomialPoint(self.Px, self.Py, Polynomial("1"))
R = P.mult(self.k, self.a, self.b, self.modulus)
self._output.insert(END, str(self.k) + str(P) + " = " + str(R) + "\n")
def log(self):
E = BinaryEllipticCurve(self.a, self.b, self.modulus)
P = PolynomialPoint(self.Px, self.Py, Polynomial("1"))
G = PolynomialPoint(self.Gx, self.Gy, Polynomial("1"))
R = E.log(P, G)
self._output.insert(END, "log_G" + str(P) + " = " + str(R) + "\n")
def order(self):
ord = BinaryEllipticCurve(self.a, self.b, self.modulus).order()
self._output.insert(END, "|E| = " + str(ord) + "\n")
def pointOrder(self):
ord = BinaryEllipticCurve(self.a, self.b, self.modulus).pointOrder(PolynomialPoint(self.Gx, self.Gy, Polynomial("1")))
self._output.insert(END, "|G| = " + str(ord) + "\n")
def randomECs(self):
s = BinaryEllipticCurve.listRandomECs((1<<self.modulus.degree()), self.modulus, self.n)
self._output.insert(END, s + "\n")
def randomPoints(self):
s = BinaryEllipticCurve.listRandomPoints(BinaryEllipticCurve(self.a, self.b, self.modulus), self.m)
self._output.insert(END, s + "\n")
def clear(self):
self._output.delete(1.0, END)
self._output.insert(END, "You are responsible for making sure the irreducible polynomial you use is actually irreducible. "
"The default, z^9 + z^8 + 1, is irreducible.\n\n")
def polynomialFunctions(PolExpr):
newpoli = 0
for c in PolExpr:
if c == '[':
newpoli = 1
elif c == ']':
newpoli = 0
if c == '+' and newpoli == 0:
operation = PolExpr.split('+', 1)
pol1 = strtoPolynomialArray(operation[0])
pol2 = strtoPolynomialArray(operation[1])
polynomial1 = Polynomial(pol1)
polynomial2 = Polynomial(pol2)
print (polynomial1.tostr())
print (polynomial2.tostr())
print ("+__________________")
return (polynomial1.addition(polynomial2).tostr() + "\n")
elif c == '-' and newpoli == 0:
operation = PolExpr.split('-', 1)
pol1 = strtoPolynomialArray(operation[0])
pol2 = strtoPolynomialArray(operation[1])
polynomial1 = Polynomial(pol1)
polynomial2 = Polynomial(pol2)
print (polynomial1.tostr())
print (polynomial2.tostr())
print ("-__________________")
return (polynomial1.substraction(polynomial2).tostr() + "\n")
elif c == '*' and newpoli == 0:
operation = PolExpr.split('*', 1)
pol1 = strtoPolynomialArray(operation[0])
pol2 = strtoPolynomialArray(operation[1])
polynomial1 = Polynomial(pol1)
polynomial2 = Polynomial(pol2)
print (polynomial1.tostr())
print (polynomial2.tostr())
print ("*__________________")
return (polynomial1.multiplication(polynomial2).tostr() + "\n")
elif c == '/' and newpoli == 0:
operation = PolExpr.split('/', 1)
pol1 = strtoPolynomialArray(operation[0])
pol2 = strtoPolynomialArray(operation[1])
polynomial1 = Polynomial(pol1)
polynomial2 = Polynomial(pol2)
print (polynomial1.tostr())
print (polynomial2.tostr())
print ("/__________________")
if polynomial1.degree() < polynomial2.degree():
return "Numerator must have a higher or equal degree compare with the denominator to be able divide both"
if polynomial2.degree() == 0:
return "Division by 0 error"
result = []
result = polynomial1.division(polynomial2)
if len(result) == 3:
return result[0].tostr() + " + " + result[2].tostr() + "/" + "(" + result[1].tostr() + ")" + "\n"
return (result[0].tostr() + "\n")
elif c == '#' and newpoli == 0:
operation = PolExpr.split('#', 1)
pol1 = strtoPolynomialArray(operation[0])
polynomial1 = Polynomial(pol1)
print (polynomial1.tostr())
print ("#__________________")
return (polynomial1.differentiate().tostr() + "\n")
elif c == '@' and newpoli == 0:
operation = PolExpr.split('@', 1)
pol1 = strtoPolynomialArray(operation[0])
evalnum = (operation[1].replace("(", "")).replace(")", "")
polynomial1 = Polynomial(pol1)
print (polynomial1.tostr())
print ("@__________________")
return (str(polynomial1.eval(int(evalnum)))+ "\n")
