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

+prec = 191
+
+F = GF(2^191, 'g', modulus = x^191 + x^9 + 1)
+F.inject_variables()
+R.<x,y> = F[]
+
+def str_to_poly(str):
+	I=Integer(str, base=16)
+	v=F(0)
+	for i in range (0,F.degree()):
+		if(I >> i) & 1 > 0:
+			v = v + g^i
+	return v
+
+def poly_to_str(poly):
+	vec=poly._vector_()
+	string = ""
+	for i in range(0,len(vec)):
+		string = string + str(vec[len(vec) - i - 1])
+	return hex(Integer(string, base=2))
+
+n = 0x800000000000000000000000000000000000000000000201
+
+npoly = str_to_poly(n)
+	
+def Binary_MontMult(a,b,n,prec):
+	r=(2^prec).__xor__(n); rpoly = str_to_poly(r)
+	r2poly = rpoly*rpoly; r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1; rinv = poly_to_str(rinvpoly)
+	
+	apoly = str_to_poly(a); bpoly = str_to_poly(b)
+	
+	cpoly = apoly * bpoly * rinvpoly; c = poly_to_str(cpoly)	
+
+	return (c,cpoly)
+
+def Binary_MontR(n,prec):
+	r=(2^prec).__xor__(n); rpoly = str_to_poly(r); r = poly_to_str(rpoly)
+
+	return(r,rpoly)
+
+def Binary_MontR2(n,prec):
+	r=(2^prec).__xor__(n); rpoly = str_to_poly(r);
+	r2poly = rpoly*rpoly; r2 = poly_to_str(r2poly)
+
+	return(r2,r2poly)
+
+def Binary_MontExp(b,e,n,prec):
+	r=(2^prec).__xor__(n); rpoly = str_to_poly(r)
+	r2poly = rpoly*rpoly; r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1; rinv = poly_to_str(rinvpoly)
+
+	bpoly = str_to_poly(b)
+	
+	xpoly = (1 * r2poly * rinvpoly)
+	exp = e
+	for i in reversed(xrange(prec)):
+		xpoly = xpoly * xpoly * rinvpoly
+		if(exp.digits(base=2,padto=prec)[i] == 1):
+			xpoly = bpoly * xpoly * rinvpoly
+	cpoly = xpoly; c = poly_to_str(cpoly)
+
+	return(c,cpoly)
+
+def Binary_ModAdd(a,b,n,prec):
+	apoly = str_to_poly(a); bpoly = str_to_poly(b)
+	
+	cpoly = apoly + bpoly; c = poly_to_str(cpoly)
+
+	return (c,cpoly)
+
+def Binary_ModSub(a,b,n,prec):
+	apoly = str_to_poly(a); bpoly = str_to_poly(b)
+	
+	cpoly = apoly + bpoly; c = poly_to_str(cpoly)
+
+	return (c,cpoly)	
+	
+def Binary_MontMult1(b,n,prec):
+	r=(2^prec).__xor__(n); rpoly = str_to_poly(r)
+	r2poly = rpoly*rpoly; r2 = poly_to_str(r2poly)
+	rinvpoly = rpoly^-1; rinv = poly_to_str(rinvpoly)
+	
+	bpoly = str_to_poly(b)
+	
+	cpoly = 1 * bpoly * rinvpoly; c = poly_to_str(cpoly)	
+
+	return (c,cpoly)
+
+def Binary_ModExp(b,e,n,prec):
+
+	bpoly = str_to_poly(b)
+	
+	xpoly = (1)
+	exp = e
+	for i in reversed(xrange(prec)):
+		xpoly = xpoly * xpoly
+		if(exp.digits(base=2,padto=prec)[i] == 1):
+			xpoly = bpoly * xpoly
+	cpoly = xpoly; c = poly_to_str(cpoly)
+
+	return(c,cpoly)