diff --git a/src/zcash/Proof.cpp b/src/zcash/Proof.cpp
index d4fd90b69..ab7c64483 100644
--- a/src/zcash/Proof.cpp
+++ b/src/zcash/Proof.cpp
@@ -20,43 +20,16 @@ BOOST_STATIC_ASSERT(sizeof(mp_limb_t) == 8);
 
 namespace libzcash {
 
+// FE2IP as defined in the protocol spec and IEEE Std 1363a-2004.
 bigint<8> fq2_to_bigint(const curve_Fq2 &e)
 {
     auto modq = curve_Fq::field_char();
     auto c0 = e.c0.as_bigint();
     auto c1 = e.c1.as_bigint();
 
-    // TODO: It should be possible to use libsnark's bigint
-    // to do this stuff.
-
-    bigint<8> res;
-    // Multiply c1 by modq
-    mpn_mul(res.data, c1.data, 4, modq.data, 4);
-    // Add c0
-    mpn_add(res.data, res.data, 8, c0.data, 4);
-
-    return res;
-}
-
-// Compares two bigints, returning 0 if equal, 1 if a > b, and -1 if a < b
-template<mp_size_t LIMBS>
-int cmp_bigint(const bigint<LIMBS> &a, const bigint<LIMBS> &b)
-{
-    for (ssize_t i = LIMBS-1; i >= 0; i--) {
-        if (a.data[i] < b.data[i]) {
-            return -1;
-        } else if (a.data[i] > b.data[i]) {
-            return 1;
-        }
-    }
-
-    return 0;
-}
-
-// Returns whether a > b
-bool cmp_fq2(const curve_Fq2 &a, const curve_Fq2 &b)
-{
-    return cmp_bigint(fq2_to_bigint(a), fq2_to_bigint(b)) > 0;
+    bigint<8> temp = c1 * modq;
+    temp += c0;
+    return temp;
 }
 
 // Writes a bigint in big endian
@@ -87,7 +60,7 @@ bigint<LIMBS> read_bigint(const base_blob<8 * LIMBS * sizeof(mp_limb_t)> &blob)
 template<>
 Fq::Fq(curve_Fq element) : data()
 {
-    write_bigint(data, element.as_bigint());
+    write_bigint<4>(data, element.as_bigint());
 }
 
 template<>
@@ -97,9 +70,7 @@ curve_Fq Fq::to_libsnark_fq() const
 
     // Check that the integer is smaller than the modulus
     auto modq = curve_Fq::field_char();
-    if (cmp_bigint(element_bigint, modq) != -1) {
-        throw std::logic_error("element is not in Fq");
-    }
+    element_bigint.limit(modq, "element is not in Fq");
 
     return curve_Fq(element_bigint);
 }
@@ -107,33 +78,18 @@ curve_Fq Fq::to_libsnark_fq() const
 template<>
 Fq2::Fq2(curve_Fq2 element) : data()
 {
-    write_bigint(data, fq2_to_bigint(element));
+    write_bigint<8>(data, fq2_to_bigint(element));
 }
 
 template<>
 curve_Fq2 Fq2::to_libsnark_fq2() const
 {
-    auto modq = curve_Fq::field_char();
-    auto combined = read_bigint<8>(data);
-
-    // TODO: It should be possible to use libsnark's bigint
-    // to do this stuff.
-
+    bigint<4> modq = curve_Fq::field_char();
+    bigint<8> combined = read_bigint<8>(data);
     bigint<5> res;
     bigint<4> c0;
-
-    mpn_tdiv_qr(res.data, c0.data, 0, combined.data, 8, modq.data, 4);
-
-    if (res.data[4] != 0) {
-        throw std::logic_error("element is not in Fq2");
-    }
-
-    bigint<4> c1;
-    memcpy(c1.data, res.data, 4 * sizeof(mp_limb_t));
-
-    if (cmp_bigint(c1, modq) != -1) {
-        throw std::logic_error("element is not in Fq2");
-    }
+    bigint<8>::div_qr(res, c0, combined, modq);
+    bigint<4> c1 = res.shorten(modq, "element is not in Fq2");
 
     return curve_Fq2(curve_Fq(c0), curve_Fq(c1));
 }
@@ -183,7 +139,7 @@ CompressedG2::CompressedG2(curve_G2 point)
     point.to_affine_coordinates();
 
     x = Fq2(point.X);
-    y_gt = cmp_fq2(point.Y, -(point.Y));
+    y_gt = fq2_to_bigint(point.Y) > fq2_to_bigint(-(point.Y));
 }
 
 template<>
@@ -195,7 +151,7 @@ curve_G2 CompressedG2::to_libsnark_g2() const
     auto y_coordinate = ((x_coordinate.squared() * x_coordinate) + alt_bn128_twist_coeff_b).sqrt();
     auto y_coordinate_neg = -y_coordinate;
 
-    if (cmp_fq2(y_coordinate, y_coordinate_neg) != y_gt) {
+    if ((fq2_to_bigint(y_coordinate) > fq2_to_bigint(y_coordinate_neg)) != y_gt) {
         y_coordinate = y_coordinate_neg;
     }