Merge branch 'aaisha' into 'master'

POINT Multiplication

See merge request !27

ECC Over GF(2m)/sage/point_doubling_affine_mont-master/README.md

+# point_doubling_affine_Mont
+def Pointdoubling_affine_Mont(x1,y1,a,PRECISION):
+
+    r=(2^PRECISION).__xor__(n); rpoly = str_to_poly(r)
+	r2poly = rpoly * rpoly; r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1; rinv = poly_to_str(rinvpoly)
+
+    x1_poly= str_to_poly(x1)
+    y1_poly=str_to_poly(y1)
+
+    x1_poly_MD = x1_poly * r2poly * rinvpoly
+    y1_poly_MD = y1_poly * r2poly * rinvpoly
+
+#print 'x1_poly=',x1_poly
+#print 'y1_poly=',y1_poly
+
+    xpoly_MD = (1 * r2poly * rinvpoly)
+	exp = 2^PRECISION-2
+	for i in reversed(xrange(PRECISION)):
+		xpoly_MD = xpoly_MD * xpoly_MD * rinvpoly
+		if(exp.digits(base=2,padto=PRECISION)[i] == 1):
+			xpoly_MD = y1_poly_MD * xpoly_MD * rinvpoly
+	inv_y1_poly_MD = xpoly_MD
+	
+	c_MD = (3 * r2poly * rinvpoly)
+	c1_MD = c_MD * x1_poly_MD * rinvpoly
+	c2_MD = c1_MD * x1_poly_MD * rinvpoly
+	a_MD = (a * r2poly * rinvpoly)
+	c3_MD = (c2_MD + a_MD)
+	c4_MD = (2 * r2poly * rinvpoly)
+	c5_MD = c3_MD * c4_MD * rinvpoly
+	
+	s_poly_MD = c5_MD * inv_y1_poly_MD * rinvpoly
+	
+	
+	c6_MD = s_poly_MD * s_poly_MD * rinvpoly
+	c7_MD = c4_MD * x1_poly_MD * rinvpoly
+	
+	x2_poly_MD = c6_MD - c7_MD
+
+    c8_MD = (x1_poly_MD - x2_poly_MD)
+	c9_MD = s_poly_MD * c8_MD * rinvpoly
+	
+	y2_poly_MD = c9_MD - y1_poly_MD
+	
+
+
+
+    print 'x2_MD=',poly_to_str(x2_poly_MD)
+    print 'y2_MD=',poly_to_str(y2_poly_MD)
+

ECC Over GF(2m)/sage/pointdoubling-master/README.md

+# PointDoubling
+

ECC Over GF(2m)/sage/pointdoubling_affine-master/README.md

+# PointDoubling_Affine
+def Pointdoubling_affine(x1,y1,a,n,PRECISION):
+
+
+     x1_poly = str_to_poly(x1)
+     y1_poly = str_to_poly(y1)
+ 
+     #print 'x1_poly =', x1_poly
+     #print 'y1_poly =', y1_poly
+
+     xpoly = (1)
+     expp = 2^PRECISION-2
+     for i in reversed(xrange(PRECISION)):
+	                  xpoly = xpoly * xpoly
+	                  if(expp.digits(base = 2,padto=PRECISION)[i] == 1):
+					   xpoly = y1_poly* xpoly
+     inv_y1_poly = xpoly
+
+     s_poly = (3*x1_poly*x1_poly+a)*2*inv_y1_poly
+
+     x2_poly = s_poly*s_poly-2*x1_poly
+
+     y2_poly = s_poly*(x1_poly-x2_poly)-y1_poly
+
+     print 'x2 =',poly_to_str(x2_poly)
+     print 'y2 =',poly_to_str(y2_poly)
+
+
+

ECC Over GF(2m)/sage/subfile_point_mult.sage

+def Montgomerize(xg,yg,p,PRECISION): 
+
+    r=(2^PRECISION)#.__xor__(n)
+    rpoly = str_to_poly(r)
+	r2poly = rpoly * rpoly
+	r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1 
+	rinv = poly_to_str(rinvpoly)
+
+    x1_poly = str_to_poly(x1)
+    y1_poly = str_to_poly(y1)
+
+
+    x1_poly_MD = x1_poly * r2poly * rinvpoly
+    y1_poly_MD = y1_poly * r2poly * rinvpoly
+
+    return (x1_poly_MD,y1_poly_MD)
+
+
+def MontgomerizePrep(a,b,p,PRECISION):
+    r=(2^PRECISION).__xor__(n)
+    rpoly = str_to_poly(r)
+	r2poly = rpoly * rpoly
+	r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1 
+	rinv = poly_to_str(rinvpoly)
+
+
+	a_poly = str_to_poly(a)
+    b_poly = str_to_poly(b)
+	a_poly_MD = a_poly * r2poly * rinvpoly
+	b_poly_MD = b_poly * r2poly * rinvpoly
+
+	num2_MD = (2 * r2poly * rinvpoly )
+	num3_MD = (3 * r2poly * rinvpoly )
+	num8_MD = (8 * r2poly * rinvpoly )
+
+def AffineToJacobiTransformation(x1_MD,y1_MD,PRECISION):
+    r=(2^PRECISION).__xor__(n)
+    rpoly = str_to_poly(r)
+	r2poly = rpoly * rpoly
+	r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1 
+	rinv = poly_to_str(rinvpoly)
+
+	x1_MD_Poly = x1_MD
+	y1_MD_Poly = y1_MD
+	z1_MD_Poly = r
+	return(x1_MD_Poly,y1_MD_Poly,z1_MD_Poly)
+
+def JacobiToAffineTransformation(xr1_Mont,yr1_Mont,zr1_Mont,p,PRECISION): 
+
+    r=(2^PRECISION).__xor__(n)
+    rpoly = str_to_poly(r)
+	r2poly = rpoly * rpoly
+	r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1 
+	rinv = poly_to_str(rinvpoly)
+
+
+	xpoly_MD = (1 * r2poly * rinvpoly)
+	exp = 2^PRECISION-2
+	for i in reversed(xrange(PRECISION)):
+		xpoly_MD = xpoly_MD * xpoly_MD * rinvpoly
+		if(exp.digits(base=2,padto=PRECISION)[i] == 1):
+			xpoly_MD = zr1_Mont * xpoly_MD * rinvpoly
+	inv_z1_poly_MD = xpoly_MD
+
+	inv_z2_poly_MD = inv_z1_poly_MD * inv_z1_poly_MD * rinvpoly
+	inv_z1_poly_MD = inv_z2_poly_MD * inv_z2_poly_MD * rinvpoly
+
+	return(xf_mont,yf_mont)
+
+