Initial commit

test.sage

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+q = 50177
+
+Fq.<yq> = PolynomialRing(ZZ.quotient(q))
+Rq = Fq.quotient(yq**256+1, "xq")
+xq = Rq.gen()
+
+F2q.<y2q> = PolynomialRing(ZZ.quotient(q*2))
+R2q = F2q.quotient(y2q**256+1, "x2q")
+x2q = R2q.gen()
+
+F2.<y2> = PolynomialRing(ZZ.quotient(2))
+R2 = F2.quotient(y2**256+1, "x2")
+x2 = R2.gen()
+
+def center(x, m):
+	x = x % m
+	if x < m/2:
+		return x
+	else:
+		return x - m
+
+def f(x):
+	return (R2([int(i)%2 for i in x.list()]), Rq([int(i)%q for i in x.list()]))
+
+def g(a, b):
+	al = a.list()
+	bl = b.list()
+	return R2q([int(al[i])*q-int(bl[i])*2*(q//2) for i in range(len(al))])
+
+def add(ab, cd):
+	return (ab[0]+cd[0], ab[1]+cd[1])
+
+def mul(ab, cd):
+	return (ab[0]*cd[0], ab[1]*cd[1])
+
+a = -x2q**2 + 3*x2q + 2
+b = 4*x2q + x2q**4
+print(g(*mul(f(a), f(b))))
+print(a*b)