diff --git a/beacon_chain_impl/bls.py b/beacon_chain_impl/bls.py
index b03c1ae..a55fee8 100644
--- a/beacon_chain_impl/bls.py
+++ b/beacon_chain_impl/bls.py
@@ -3,8 +3,8 @@ try:
 except:
     from pyblake2 import blake2s
 blake = lambda x: blake2s(x).digest()
-from py_ecc.optimized_bn128 import G1, G2, add, multiply, FQ, FQ2, pairing, \
-    normalize, field_modulus, b, b2, is_on_curve, curve_order
+from py_ecc.optimized_bn128 import G1, G2, neg, add, multiply, FQ, FQ2, FQ12, pairing, \
+    normalize, field_modulus, b, b2, is_on_curve, curve_order, final_exponentiate
 
 def compress_G1(pt):
     x, y = normalize(pt)
@@ -34,7 +34,11 @@ def sqrt_fq2(x):
         y *= hex_root
     return y
 
+cache = {}
+
 def hash_to_G2(m):
+    if m in cache:
+        return cache[m]
     k2 = m
     while 1:
         k1 = blake(k2)
@@ -46,7 +50,9 @@ def hash_to_G2(m):
         if xcb ** ((field_modulus ** 2 - 1) // 2) == FQ2([1,0]):
             break
     y = sqrt_fq2(xcb)
-    return multiply((x, y, FQ2([1,0])), 2*field_modulus-curve_order)
+    o = multiply((x, y, FQ2([1,0])), 2*field_modulus-curve_order)
+    cache[m] = o
+    return o
 
 def compress_G2(pt):
     assert is_on_curve(pt, b2)
@@ -73,7 +79,8 @@ def privtopub(k):
     return compress_G1(multiply(G1, k))
 
 def verify(m, pub, sig):
-    return pairing(decompress_G2(sig), G1) == pairing(hash_to_G2(m), decompress_G1(pub))
+    return final_exponentiate(pairing(decompress_G2(sig), G1, False) * \
+                              pairing(hash_to_G2(m), neg(decompress_G1(pub)), False)) == FQ12.one()
 
 def aggregate_sigs(sigs):
     o = FQ2([1,0]), FQ2([1,0]), FQ2([0,0])
diff --git a/beacon_chain_impl/test_full_pos.py b/beacon_chain_impl/test_full_pos.py
index e3e889a..9e75a87 100644
--- a/beacon_chain_impl/test_full_pos.py
+++ b/beacon_chain_impl/test_full_pos.py
@@ -4,8 +4,9 @@ from full_pos import blake, mk_genesis_state_and_block, compute_state_transition
 import random
 import bls
 from simpleserialize import serialize, deserialize, eq, deepcopy
+import time
 
-privkeys = [int.from_bytes(blake(str(i).encode('utf-8'))[:4], 'big') for i in range(500)]
+privkeys = [int.from_bytes(blake(str(i).encode('utf-8'))[:4], 'big') for i in range(1000)]
 print('Generated privkeys')
 keymap = {}
 for i,k in enumerate(privkeys):
@@ -80,7 +81,9 @@ print('Crystallized state length:', len(serialize(c)))
 print('Active state length:', len(serialize(a)))
 print('Block size:', len(serialize(block)))
 block2, c2, a2 = mock_make_child((c, a), block, 0, 0.8, [])
+t = time.time()
 assert compute_state_transition((c, a), block, block2)
+print("Normal block (basic attestation only) processed in %.4f sec" % (time.time() - t))
 print('Verified a block!')
 block3, c3, a3 = mock_make_child((c2, a2), block2, 0, 0.8, [(0, 0.75)])
 print('Verified a block with a committee!')
@@ -89,3 +92,6 @@ while a3.height % SHARD_COUNT > 0:
     print('Height: %d' % a3.height)
 print('FFG bitmask:', bin(int.from_bytes(a3.ffg_voter_bitmask, 'big')))
 block4, c4, a4 = mock_make_child((c3, a3), block3, 1, 0.55, [])
+t = time.time()
+assert compute_state_transition((c3, a3), block3, block4)
+print("Epoch transition processed in %.4f sec" % (time.time() - t))