diff --git a/ed25519.lua b/ed25519.lua
index a3907fa..1942aaa 100644
--- a/ed25519.lua
+++ b/ed25519.lua
@@ -1,4 +1,4 @@
---- The Ed25519 signature scheme.
+--- The Ed25519 digital signature scheme.
 --
 -- **Note:** This library is provided for compatibility and provides no side
 -- channel resistance by itself.
@@ -6,228 +6,10 @@
 -- @module ed25519
 --
 
-local expect = require "cc.expect".expect
-local fp     = require "ccryptolib.internal.fp"
-local fq     = require "ccryptolib.internal.fq"
-local sha512 = require "ccryptolib.internal.sha512"
-
-local unpack = unpack or table.unpack
-
-local D = fp.mul(fp.num(-121665), fp.invert(fp.num(121666)))
-local K = fp.kmul(D, 2)
-
-local O = {fp.num(0), fp.num(1), fp.num(1), fp.num(0)}
-local G = nil
-
-local function double(P1)
-    local P1x, P1y, P1z = unpack(P1)
-    local a = fp.square(P1x)
-    local b = fp.square(P1y)
-    local c = fp.square(P1z)
-    local d = fp.kmul(c, 2)
-    local e = fp.add(a, b)
-    local f = fp.add(P1x, P1y)
-    local g = fp.square(f)
-    local h = fp.sub(g, e)
-    local i = fp.sub(b, a)
-    local j = fp.sub(d, i)
-    local P3x = fp.mul(h, j)
-    local P3y = fp.mul(i, e)
-    local P3z = fp.mul(j, i)
-    local P3t = fp.mul(h, e)
-    return {P3x, P3y, P3z, P3t}
-end
-
-local function add(P1, N1)
-    local P1x, P1y, P1z, P1t = unpack(P1)
-    local N1p, N1m, N1z, N1t = unpack(N1)
-    local a = fp.sub(P1y, P1x)
-    local b = fp.mul(a, N1m)
-    local c = fp.add(P1y, P1x)
-    local d = fp.mul(c, N1p)
-    local e = fp.mul(P1t, N1t)
-    local f = fp.mul(P1z, N1z)
-    local g = fp.sub(d, b)
-    local h = fp.sub(f, e)
-    local i = fp.add(f, e)
-    local j = fp.add(d, b)
-    local P3x = fp.mul(g, h)
-    local P3y = fp.mul(i, j)
-    local P3z = fp.mul(h, i)
-    local P3t = fp.mul(g, j)
-    return {P3x, P3y, P3z, P3t}
-end
-
-local function sub(P1, N1)
-    local P1x, P1y, P1z, P1t = unpack(P1)
-    local N1p, N1m, N1z, N1t = unpack(N1)
-    local a = fp.sub(P1y, P1x)
-    local b = fp.mul(a, N1p)
-    local c = fp.add(P1y, P1x)
-    local d = fp.mul(c, N1m)
-    local e = fp.mul(P1t, N1t)
-    local f = fp.mul(P1z, N1z)
-    local g = fp.sub(d, b)
-    local h = fp.add(f, e)
-    local i = fp.sub(f, e)
-    local j = fp.add(d, b)
-    local P3x = fp.mul(g, h)
-    local P3y = fp.mul(i, j)
-    local P3z = fp.mul(h, i)
-    local P3t = fp.mul(g, j)
-    return {P3x, P3y, P3z, P3t}
-end
-
-local function niels(P1)
-    local P1x, P1y, P1z, P1t = unpack(P1)
-    local N3p = fp.add(P1y, P1x)
-    local N3m = fp.sub(P1y, P1x)
-    local N3z = fp.add(P1z, P1z)
-    local N3t = fp.mul(P1t, K)
-    return {N3p, N3m, N3z, N3t}
-end
-
-local function scale(P1)
-    local P1x, P1y, P1z = unpack(P1)
-    local zInv = fp.invert(P1z)
-    local P3x = fp.mul(P1x, zInv)
-    local P3y = fp.mul(P1y, zInv)
-    local P3z = fp.num(1)
-    local P3t = fp.mul(P3x, P3y)
-    return {P3x, P3y, P3z, P3t}
-end
-
-local function encode(P1)
-    local P1x, P1y = unpack(P1)
-    local y = fp.encode(P1y)
-    local xBit = fp.canonicalize(P1x)[1] % 2
-    return y:sub(1, -2) .. string.char(y:byte(-1) + xBit * 128)
-end
-
-local function decode(str)
-    local P3y = fp.decode(str)
-    local a = fp.square(P3y)
-    local b = fp.sub(a, fp.num(1))
-    local c = fp.mul(a, D)
-    local d = fp.add(c, fp.num(1))
-    local P3x = fp.sqrtDiv(b, d)
-    if not P3x then return nil end
-    local xBit = fp.canonicalize(P3x)[1] % 2
-    if xBit ~= bit32.extract(str:byte(-1), 7) then
-        P3x = fp.neg(P3x)
-        P3x = fp.carry(P3x)
-    end
-    local P3z = fp.num(1)
-    local P3t = fp.mul(P3x, P3y)
-    return {P3x, P3y, P3z, P3t}
-end
-
-G = decode("Xfffffffffffffffffffffffffffffff")
-
-local function signedRadixW(bits, w)
-    -- TODO Find a more elegant way of doing this.
-    local wPow = 2 ^ w
-    local wPowh = wPow / 2
-    local out = {}
-    local acc = 0
-    local mul = 1
-    for i = 1, #bits do
-        acc = acc + bits[i] * mul
-        mul = mul * 2
-        while i == #bits and acc > 0 or mul > wPow do
-            local rem = acc % wPow
-            if rem >= wPowh then rem = rem - wPow end
-            acc = (acc - rem) / wPow
-            mul = mul / wPow
-            out[#out + 1] = rem
-        end
-    end
-    return out
-end
-
-local function radixWTable(P, w)
-    local out = {}
-    for i = 1, 255 / w do
-        local row = {niels(P)}
-        for j = 2, 2 ^ w / 2 do
-            P = add(P, row[1])
-            row[j] = niels(P)
-        end
-        out[i] = row
-        P = double(P)
-    end
-    return out
-end
-
-local G_W = 5
-local G_TABLE = radixWTable(G, G_W)
-
-local function WNAF(bits, w)
-    -- TODO Find a more elegant way of doing this.
-    local wPow = 2 ^ w
-    local wPowh = wPow / 2
-    local out = {}
-    local acc = 0
-    local mul = 1
-    for i = 1, #bits do
-        acc = acc + bits[i] * mul
-        mul = mul * 2
-        while i == #bits and acc > 0 or mul > wPow do
-            if acc % 2 == 0 then
-                acc = acc / 2
-                mul = mul / 2
-                out[#out + 1] = 0
-            else
-                local rem = acc % wPow
-                if rem >= wPowh then rem = rem - wPow end
-                acc = acc - rem
-                out[#out + 1] = rem
-            end
-        end
-    end
-    while out[#out] == 0 do out[#out] = nil end
-    return out
-end
-
-local function WNAFTable(P, w)
-    local dP = double(P)
-    local out = {niels(P)}
-    for i = 3, 2 ^ w, 2 do
-        out[i] = niels(add(dP, out[i - 2]))
-    end
-    return out
-end
-
-local function mulG(bits)
-    local sw = signedRadixW(bits, G_W)
-    local R = O
-    for i = 1, #sw do
-        local b = sw[i]
-        if b > 0 then
-            R = add(R, G_TABLE[i][b])
-        elseif b < 0 then
-            R = sub(R, G_TABLE[i][-b])
-        end
-    end
-    return R
-end
-
-local function mul(P, bits)
-    local naf = WNAF(bits, 5)
-    local tbl = WNAFTable(P, 5)
-    local R = O
-    for i = #naf, 1, -1 do
-        local b = naf[i]
-        if b == 0 then
-            R = double(R)
-        elseif b > 0 then
-            R = add(R, tbl[b])
-        else
-            R = sub(R, tbl[-b])
-        end
-    end
-    return R
-end
+local expect  = require "cc.expect".expect
+local fq      = require "ccryptolib.internal.fq"
+local ed25519 = require "ccryptolib.internal.ed25519"
+local sha512  = require "ccryptolib.internal.sha512"
 
 local mod = {}
 
@@ -243,7 +25,7 @@ function mod.publicKey(sk)
     local h = sha512.digest(sk)
     local x = fq.decodeClamped(h:sub(1, 32))
 
-    return encode(scale(mulG(fq.bits(x))))
+    return ed25519.encode(ed25519.scale(ed25519.mulG(fq.bits(x))))
 end
 
 --- Signs a message.
@@ -266,8 +48,8 @@ function mod.sign(sk, pk, msg)
 
     -- Commitment.
     local k = fq.decodeWide(sha512.digest(h:sub(33) .. msg))
-    local r = mulG(fq.bits(k))
-    local rStr = encode(scale(r))
+    local r = ed25519.mulG(fq.bits(k))
+    local rStr = ed25519.encode(ed25519.scale(r))
 
     -- Challenge.
     local e = fq.decodeWide(sha512.digest(rStr .. pk .. msg))
@@ -293,7 +75,7 @@ function mod.verify(pk, msg, sig)
     expect(3, sig, "string")
     assert(#sig == 64, "signature length must be 64")
 
-    local y = decode(pk)
+    local y = ed25519.decode(pk)
     if not y then return nil end
 
     local rStr = sig:sub(1, 32)
@@ -301,11 +83,11 @@ function mod.verify(pk, msg, sig)
 
     local e = fq.decodeWide(sha512.digest(rStr .. pk .. msg))
 
-    local gs = mulG(fq.bits(fq.decode(sStr)))
-    local ye = mul(y, fq.bits(e))
-    local rv = add(gs, niels(ye))
+    local gs = ed25519.mulG(fq.bits(fq.decode(sStr)))
+    local ye = ed25519.mul(y, fq.bits(e))
+    local rv = ed25519.add(gs, ed25519.niels(ye))
 
-    return encode(scale(rv)) == rStr
+    return ed25519.encode(ed25519.scale(rv)) == rStr
 end
 
 return mod
diff --git a/internal/ed25519.lua b/internal/ed25519.lua
new file mode 100644
index 0000000..6ac4e5d
--- /dev/null
+++ b/internal/ed25519.lua
@@ -0,0 +1,229 @@
+local fp     = require "ccryptolib.internal.fp"
+
+local unpack = unpack or table.unpack
+
+local D = fp.mul(fp.num(-121665), fp.invert(fp.num(121666)))
+local K = fp.kmul(D, 2)
+
+local O = {fp.num(0), fp.num(1), fp.num(1), fp.num(0)}
+local G = nil
+
+local function double(P1)
+    local P1x, P1y, P1z = unpack(P1)
+    local a = fp.square(P1x)
+    local b = fp.square(P1y)
+    local c = fp.square(P1z)
+    local d = fp.kmul(c, 2)
+    local e = fp.add(a, b)
+    local f = fp.add(P1x, P1y)
+    local g = fp.square(f)
+    local h = fp.sub(g, e)
+    local i = fp.sub(b, a)
+    local j = fp.sub(d, i)
+    local P3x = fp.mul(h, j)
+    local P3y = fp.mul(i, e)
+    local P3z = fp.mul(j, i)
+    local P3t = fp.mul(h, e)
+    return {P3x, P3y, P3z, P3t}
+end
+
+local function add(P1, N1)
+    local P1x, P1y, P1z, P1t = unpack(P1)
+    local N1p, N1m, N1z, N1t = unpack(N1)
+    local a = fp.sub(P1y, P1x)
+    local b = fp.mul(a, N1m)
+    local c = fp.add(P1y, P1x)
+    local d = fp.mul(c, N1p)
+    local e = fp.mul(P1t, N1t)
+    local f = fp.mul(P1z, N1z)
+    local g = fp.sub(d, b)
+    local h = fp.sub(f, e)
+    local i = fp.add(f, e)
+    local j = fp.add(d, b)
+    local P3x = fp.mul(g, h)
+    local P3y = fp.mul(i, j)
+    local P3z = fp.mul(h, i)
+    local P3t = fp.mul(g, j)
+    return {P3x, P3y, P3z, P3t}
+end
+
+local function sub(P1, N1)
+    local P1x, P1y, P1z, P1t = unpack(P1)
+    local N1p, N1m, N1z, N1t = unpack(N1)
+    local a = fp.sub(P1y, P1x)
+    local b = fp.mul(a, N1p)
+    local c = fp.add(P1y, P1x)
+    local d = fp.mul(c, N1m)
+    local e = fp.mul(P1t, N1t)
+    local f = fp.mul(P1z, N1z)
+    local g = fp.sub(d, b)
+    local h = fp.add(f, e)
+    local i = fp.sub(f, e)
+    local j = fp.add(d, b)
+    local P3x = fp.mul(g, h)
+    local P3y = fp.mul(i, j)
+    local P3z = fp.mul(h, i)
+    local P3t = fp.mul(g, j)
+    return {P3x, P3y, P3z, P3t}
+end
+
+local function niels(P1)
+    local P1x, P1y, P1z, P1t = unpack(P1)
+    local N3p = fp.add(P1y, P1x)
+    local N3m = fp.sub(P1y, P1x)
+    local N3z = fp.add(P1z, P1z)
+    local N3t = fp.mul(P1t, K)
+    return {N3p, N3m, N3z, N3t}
+end
+
+local function scale(P1)
+    local P1x, P1y, P1z = unpack(P1)
+    local zInv = fp.invert(P1z)
+    local P3x = fp.mul(P1x, zInv)
+    local P3y = fp.mul(P1y, zInv)
+    local P3z = fp.num(1)
+    local P3t = fp.mul(P3x, P3y)
+    return {P3x, P3y, P3z, P3t}
+end
+
+local function encode(P1)
+    local P1x, P1y = unpack(P1)
+    local y = fp.encode(P1y)
+    local xBit = fp.canonicalize(P1x)[1] % 2
+    return y:sub(1, -2) .. string.char(y:byte(-1) + xBit * 128)
+end
+
+local function decode(str)
+    local P3y = fp.decode(str)
+    local a = fp.square(P3y)
+    local b = fp.sub(a, fp.num(1))
+    local c = fp.mul(a, D)
+    local d = fp.add(c, fp.num(1))
+    local P3x = fp.sqrtDiv(b, d)
+    if not P3x then return nil end
+    local xBit = fp.canonicalize(P3x)[1] % 2
+    if xBit ~= bit32.extract(str:byte(-1), 7) then
+        P3x = fp.neg(P3x)
+        P3x = fp.carry(P3x)
+    end
+    local P3z = fp.num(1)
+    local P3t = fp.mul(P3x, P3y)
+    return {P3x, P3y, P3z, P3t}
+end
+
+G = decode("Xfffffffffffffffffffffffffffffff")
+
+local function signedRadixW(bits, w)
+    -- TODO Find a more elegant way of doing this.
+    local wPow = 2 ^ w
+    local wPowh = wPow / 2
+    local out = {}
+    local acc = 0
+    local mul = 1
+    for i = 1, #bits do
+        acc = acc + bits[i] * mul
+        mul = mul * 2
+        while i == #bits and acc > 0 or mul > wPow do
+            local rem = acc % wPow
+            if rem >= wPowh then rem = rem - wPow end
+            acc = (acc - rem) / wPow
+            mul = mul / wPow
+            out[#out + 1] = rem
+        end
+    end
+    return out
+end
+
+local function radixWTable(P, w)
+    local out = {}
+    for i = 1, 255 / w do
+        local row = {niels(P)}
+        for j = 2, 2 ^ w / 2 do
+            P = add(P, row[1])
+            row[j] = niels(P)
+        end
+        out[i] = row
+        P = double(P)
+    end
+    return out
+end
+
+local G_W = 5
+local G_TABLE = radixWTable(G, G_W)
+
+local function WNAF(bits, w)
+    -- TODO Find a more elegant way of doing this.
+    local wPow = 2 ^ w
+    local wPowh = wPow / 2
+    local out = {}
+    local acc = 0
+    local mul = 1
+    for i = 1, #bits do
+        acc = acc + bits[i] * mul
+        mul = mul * 2
+        while i == #bits and acc > 0 or mul > wPow do
+            if acc % 2 == 0 then
+                acc = acc / 2
+                mul = mul / 2
+                out[#out + 1] = 0
+            else
+                local rem = acc % wPow
+                if rem >= wPowh then rem = rem - wPow end
+                acc = acc - rem
+                out[#out + 1] = rem
+            end
+        end
+    end
+    while out[#out] == 0 do out[#out] = nil end
+    return out
+end
+
+local function WNAFTable(P, w)
+    local dP = double(P)
+    local out = {niels(P)}
+    for i = 3, 2 ^ w, 2 do
+        out[i] = niels(add(dP, out[i - 2]))
+    end
+    return out
+end
+
+local function mulG(bits)
+    local sw = signedRadixW(bits, G_W)
+    local R = O
+    for i = 1, #sw do
+        local b = sw[i]
+        if b > 0 then
+            R = add(R, G_TABLE[i][b])
+        elseif b < 0 then
+            R = sub(R, G_TABLE[i][-b])
+        end
+    end
+    return R
+end
+
+local function mul(P, bits)
+    local naf = WNAF(bits, 5)
+    local tbl = WNAFTable(P, 5)
+    local R = O
+    for i = #naf, 1, -1 do
+        local b = naf[i]
+        if b == 0 then
+            R = double(R)
+        elseif b > 0 then
+            R = add(R, tbl[b])
+        else
+            R = sub(R, tbl[-b])
+        end
+    end
+    return R
+end
+
+return {
+    add = add,
+    niels = niels,
+    scale = scale,
+    encode = encode,
+    decode = decode,
+    mulG = mulG,
+    mul = mul,
+}