diff --git a/x25519.lua b/x25519.lua
index fca2ae3..dc4d74d 100644
--- a/x25519.lua
+++ b/x25519.lua
@@ -1,29 +1,20 @@
 local expect = require "cc.expect".expect
 local fp =     require "ccryptolib.fp"
 
-local add = fp.add
-local sub = fp.sub
-local kmul = fp.kmul
-local mul = fp.mul
-local square = fp.square
-local invert = fp.invert
-local encode = fp.encode
-local decode = fp.decode
-
 local function step(dx, x1, z1, x2, z2)
-    local a = add(x1, z1)
-    local aa = square(a)
-    local b = sub(x1, z1)
-    local bb = square(b)
-    local e = sub(aa, bb)
-    local c = add(x2, z2)
-    local d = sub(x2, z2)
-    local da = mul(d, a)
-    local cb = mul(c, b)
-    local x4 = square(add(da, cb))
-    local z4 = mul(dx, square(sub(da, cb)))
-    local x3 = mul(aa, bb)
-    local z3 = mul(e, add(bb, kmul(e, 121666)))
+    local a = fp.add(x1, z1)
+    local aa = fp.square(a)
+    local b = fp.sub(x1, z1)
+    local bb = fp.square(b)
+    local e = fp.sub(aa, bb)
+    local c = fp.add(x2, z2)
+    local d = fp.sub(x2, z2)
+    local da = fp.mul(d, a)
+    local cb = fp.mul(c, b)
+    local x4 = fp.square(fp.add(da, cb))
+    local z4 = fp.mul(dx, fp.square(fp.sub(da, cb)))
+    local x3 = fp.mul(aa, bb)
+    local z3 = fp.mul(e, fp.add(bb, fp.kmul(e, 121666)))
     return x3, z3, x4, z4
 end
 
@@ -40,7 +31,7 @@ local function x25519(dx, bits)
         end
     end
 
-    return mul(x1, invert(z1))
+    return fp.mul(x1, fp.invert(z1))
 end
 
 local function bits(str)
@@ -72,7 +63,7 @@ function mod.publicKey(sk)
     expect(1, sk, "string")
     assert(#sk == 32, "secret key length must be 32")
 
-    return encode(x25519({9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, bits(sk)))
+    return fp.encode(x25519({9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, bits(sk)))
 end
 
 function mod.exchange(sk, pk)
@@ -81,7 +72,7 @@ function mod.exchange(sk, pk)
     expect(2, pk, "string")
     assert(#pk == 32, "public key length must be 32")
 
-    return encode(x25519(decode(pk), bits(sk)))
+    return fp.encode(x25519(fp.decode(pk), bits(sk)))
 end
 
 return mod