implement GLWE key switching

arith/sage/ring.sage

@@ -0,0 +1,77 @@
+def run_test(a, b):
+	print("\nnew test:")
+	print(a)
+	print(b)
+	c = a*b
+	print(c)
+	print(c.list())
+
+
+
+n_iters = 100
+Q= 65537
+print(Q)
+N=4
+F = GF(Q)
+R = QuotientRing(F[x], x^N + 1, names="X")
+print(R)
+
+a = R([4,2,1,0])
+b = R([1,2,3,4])
+run_test(a,b)
+
+
+#  print("Elements of the polynomial ring:")
+#  for e in R:
+#      print(e)
+
+
+# Other:
+# ======
+#
+#  t = R.gen()
+#  a =  0 + t   + 2*t^2 + 3*t^3 + 4*t^4 + 5*t^5
+#  b =  5 + 4*t + 3*t^2 + 2*t^3 + 1*t^4 + 0*t^5
+#  print("add", a+b)
+#  print("sub", a-b)
+#  print("mul", a*b)
+#  a =  0 + t   + 2*t^2 + 3*t^3 + 4*t^4 + 5*t^5
+
+# print("ring elem mul testvectors")
+#
+#
+# def randvec(size=N):return [int(random()*(Q-1)) for t in range(size)]
+#
+# a_vecs = [None]*n_iters
+# b_vecs = [None]*n_iters
+# c_vecs = [None]*n_iters
+#
+# for i in range(n_iters):
+#     a_vec = randvec()
+#     b_vec = randvec()
+#     a_pol = R(a_vec)
+#     b_pol = R(b_vec)
+#
+#     c_pol = a_pol*b_pol
+#
+#     a_vecs[i] = a_pol.list()
+#     b_vecs[i] = b_pol.list()
+#     c_vecs[i] = c_pol.list()
+#
+# print("let a_vecs = vec!{};\n".format(a_vecs))
+# print("let b_vecs = vec!{};\n".format(b_vecs))
+# print("let c_vecs = vec!{};".format(c_vecs))
+
+
+# # cyclotomic
+# 
+# Q= 65537
+# print(Q)
+# N=4
+# F = GF(Q)
+# R = QuotientRing(F[x], x^N - 1, names="X")
+# print(R)
+# 
+# a = R([1,0,0,2])
+# b = R([0,0,0,2])
+# run_test(a, b)