diff --git a/lockbox/cipher/des.lua b/lockbox/cipher/des.lua
index 5863f81..7a8f8ea 100644
--- a/lockbox/cipher/des.lua
+++ b/lockbox/cipher/des.lua
@@ -3,7 +3,6 @@ require("lockbox").insecure();
 local Array = require("lockbox.util.array");
 
 local Bit = require("lockbox.util.bit");
-local Math = require("math");
 
 
 local AND = Bit.band;
@@ -146,8 +145,8 @@ local packBytes = function(bits)
     local bytes = {}
 
     for k, _ in pairs(bits) do
-        local index = Math.floor((k - 1) / 8) + 1;
-        local shift = 7 - Math.fmod((k - 1), 8);
+        local index = math.floor((k - 1) / 8) + 1;
+        local shift = 7 - math.fmod((k - 1), 8);
 
         local bit = bits[k];
         local byte = bytes[index];
diff --git a/lockbox/digest/md2.lua b/lockbox/digest/md2.lua
index 71a5ee8..d0f6b61 100644
--- a/lockbox/digest/md2.lua
+++ b/lockbox/digest/md2.lua
@@ -1,7 +1,6 @@
 require("lockbox").insecure();
 
 local Bit = require("lockbox.util.bit");
-local String = require("string");
 local Queue = require("lockbox.util.queue");
 
 local SUBST = {
@@ -123,7 +122,7 @@ local MD2 = function()
     end
 
     public.asHex = function()
-        return String.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
+        return string.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
                 X[ 0], X[ 1], X[ 2], X[ 3], X[ 4], X[ 5], X[ 6], X[ 7],
                 X[ 8], X[ 9], X[10], X[11], X[12], X[13], X[14], X[15]);
     end
diff --git a/lockbox/digest/md4.lua b/lockbox/digest/md4.lua
index 0ab3479..bc32588 100644
--- a/lockbox/digest/md4.lua
+++ b/lockbox/digest/md4.lua
@@ -1,8 +1,6 @@
 require("lockbox").insecure();
 
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local AND = Bit.band;
@@ -32,7 +30,7 @@ local word2bytes = function(word)
 end
 
 local dword2bytes = function(i)
-    local b4, b5, b6, b7 = word2bytes(Math.floor(i / 0x100000000));
+    local b4, b5, b6, b7 = word2bytes(math.floor(i / 0x100000000));
     local b0, b1, b2, b3 = word2bytes(i);
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
@@ -194,7 +192,7 @@ local MD4 = function()
         local  b8, b9, b10, b11 = word2bytes(C);
         local b12, b13, b14, b15 = word2bytes(D);
 
-        return String.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
+        return string.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
                 b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15);
     end
 
diff --git a/lockbox/digest/md5.lua b/lockbox/digest/md5.lua
index 6ce1df2..6264b84 100644
--- a/lockbox/digest/md5.lua
+++ b/lockbox/digest/md5.lua
@@ -1,8 +1,6 @@
 require("lockbox").insecure();
 
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local SHIFT = {
@@ -56,7 +54,7 @@ local word2bytes = function(word)
 end
 
 local dword2bytes = function(i)
-    local b4, b5, b6, b7 = word2bytes(Math.floor(i / 0x100000000));
+    local b4, b5, b6, b7 = word2bytes(math.floor(i / 0x100000000));
     local b0, b1, b2, b3 = word2bytes(i);
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
@@ -178,7 +176,7 @@ local MD5 = function()
         local  b8, b9, b10, b11 = word2bytes(C);
         local b12, b13, b14, b15 = word2bytes(D);
 
-        return String.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
+        return string.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
                 b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15);
     end
 
diff --git a/lockbox/digest/ripemd128.lua b/lockbox/digest/ripemd128.lua
index ebc3e41..38a1fb1 100644
--- a/lockbox/digest/ripemd128.lua
+++ b/lockbox/digest/ripemd128.lua
@@ -1,8 +1,6 @@
 require("lockbox").insecure();
 
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local AND = Bit.band;
@@ -32,7 +30,7 @@ local word2bytes = function(word)
 end
 
 local dword2bytes = function(i)
-    local b4, b5, b6, b7 = word2bytes(Math.floor(i / 0x100000000));
+    local b4, b5, b6, b7 = word2bytes(math.floor(i / 0x100000000));
     local b0, b1, b2, b3 = word2bytes(i);
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
@@ -330,7 +328,7 @@ local RIPEMD128 = function()
 
         local fmt = "%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x";
 
-        return String.format(fmt,
+        return string.format(fmt,
                  b0, b1, b2, b3, b4, b5, b6, b7, b8, b9,
                 b10, b11, b12, b13, b14, b15);
     end
diff --git a/lockbox/digest/ripemd160.lua b/lockbox/digest/ripemd160.lua
index 5b42d73..2ea5dcb 100644
--- a/lockbox/digest/ripemd160.lua
+++ b/lockbox/digest/ripemd160.lua
@@ -1,8 +1,6 @@
 require("lockbox").insecure();
 
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local AND = Bit.band;
@@ -32,7 +30,7 @@ local word2bytes = function(word)
 end
 
 local dword2bytes = function(i)
-    local b4, b5, b6, b7 = word2bytes(Math.floor(i / 0x100000000));
+    local b4, b5, b6, b7 = word2bytes(math.floor(i / 0x100000000));
     local b0, b1, b2, b3 = word2bytes(i);
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
@@ -381,7 +379,7 @@ local RIPEMD160 = function()
 
         local fmt = "%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x";
 
-        return String.format(fmt,
+        return string.format(fmt,
                  b0, b1, b2, b3, b4, b5, b6, b7, b8, b9,
                 b10, b11, b12, b13, b14, b15, b16, b17, b18, b19);
     end
diff --git a/lockbox/digest/sha1.lua b/lockbox/digest/sha1.lua
index 3e429e8..5a6e2e8 100644
--- a/lockbox/digest/sha1.lua
+++ b/lockbox/digest/sha1.lua
@@ -1,8 +1,6 @@
 require("lockbox").insecure();
 
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local AND = Bit.band;
@@ -32,7 +30,7 @@ end
 
 local dword2bytes = function(i)
     local b4, b5, b6, b7 = word2bytes(i);
-    local b0, b1, b2, b3 = word2bytes(Math.floor(i / 0x100000000));
+    local b0, b1, b2, b3 = word2bytes(math.floor(i / 0x100000000));
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
 
@@ -163,7 +161,7 @@ local SHA1 = function()
         local b12, b13, b14, b15 = word2bytes(h3);
         local b16, b17, b18, b19 = word2bytes(h4);
 
-        return String.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
+        return string.format("%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x",
                 b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19);
     end
 
diff --git a/lockbox/digest/sha2_224.lua b/lockbox/digest/sha2_224.lua
index 3897c26..6ee7245 100644
--- a/lockbox/digest/sha2_224.lua
+++ b/lockbox/digest/sha2_224.lua
@@ -1,6 +1,4 @@
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local CONSTANTS = {
@@ -44,7 +42,7 @@ end
 
 local dword2bytes = function(i)
     local b4, b5, b6, b7 = word2bytes(i);
-    local b0, b1, b2, b3 = word2bytes(Math.floor(i / 0x100000000));
+    local b0, b1, b2, b3 = word2bytes(math.floor(i / 0x100000000));
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
 
@@ -188,7 +186,7 @@ local SHA2_224 = function()
         local b20, b21, b22, b23 = word2bytes(h5);
         local b24, b25, b26, b27 = word2bytes(h6);
 
-        return String.format(fmt, b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15
+        return string.format(fmt, b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15
                 , b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27);
     end
 
diff --git a/lockbox/digest/sha2_256.lua b/lockbox/digest/sha2_256.lua
index 4cd2f35..74136d7 100644
--- a/lockbox/digest/sha2_256.lua
+++ b/lockbox/digest/sha2_256.lua
@@ -1,6 +1,4 @@
 local Bit = require("lockbox.util.bit");
-local String = require("string");
-local Math = require("math");
 local Queue = require("lockbox.util.queue");
 
 local CONSTANTS = {
@@ -44,7 +42,7 @@ end
 
 local dword2bytes = function(i)
     local b4, b5, b6, b7 = word2bytes(i);
-    local b0, b1, b2, b3 = word2bytes(Math.floor(i / 0x100000000));
+    local b0, b1, b2, b3 = word2bytes(math.floor(i / 0x100000000));
     return b0, b1, b2, b3, b4, b5, b6, b7;
 end
 
@@ -191,7 +189,7 @@ local SHA2_256 = function()
         local b24, b25, b26, b27 = word2bytes(h6);
         local b28, b29, b30, b31 = word2bytes(h7);
 
-        return String.format(fmt, b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15
+        return string.format(fmt, b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15
                 , b16, b17, b18, b19, b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31);
     end
 
diff --git a/lockbox/kdf/pbkdf2.lua b/lockbox/kdf/pbkdf2.lua
index e13e57d..c9e4388 100644
--- a/lockbox/kdf/pbkdf2.lua
+++ b/lockbox/kdf/pbkdf2.lua
@@ -1,7 +1,6 @@
 local Bit = require("lockbox.util.bit");
 local Array = require("lockbox.util.array");
 local Stream = require("lockbox.util.stream");
-local Math = require("math");
 
 local AND = Bit.band;
 local RSHIFT = Bit.rshift;
@@ -86,7 +85,7 @@ local PBKDF2 = function()
     end
 
     public.finish = function()
-        local blocks = Math.ceil(dKeyLen / blockLen);
+        local blocks = math.ceil(dKeyLen / blockLen);
 
         dKey = {};
 
diff --git a/lockbox/util/array.lua b/lockbox/util/array.lua
index 899419d..61ed06e 100644
--- a/lockbox/util/array.lua
+++ b/lockbox/util/array.lua
@@ -1,5 +1,4 @@
 
-local String = require("string");
 local Bit = require("lockbox.util.bit");
 local Queue = require("lockbox.util.queue");
 
@@ -15,11 +14,11 @@ Array.fromString = function(string)
     local bytes = {};
 
     local i = 1;
-    local byte = String.byte(string, i);
+    local byte = string.byte(string, i);
     while byte ~= nil do
         bytes[i] = byte;
         i = i + 1;
-        byte = String.byte(string, i);
+        byte = string.byte(string, i);
     end
 
     return bytes;
@@ -32,7 +31,7 @@ Array.toString = function(bytes)
 
     local byte = bytes[i];
     while byte ~= nil do
-        chars[i] = String.char(byte);
+        chars[i] = string.char(byte);
         i = i + 1;
         byte = bytes[i];
     end
@@ -89,15 +88,15 @@ end
 
 local fromHexTable = {};
 for i = 0, 255 do
-    fromHexTable[String.format("%02X", i)] = i;
-    fromHexTable[String.format("%02x", i)] = i;
+    fromHexTable[string.format("%02X", i)] = i;
+    fromHexTable[string.format("%02x", i)] = i;
 end
 
 Array.fromHex = function(hex)
     local array = {};
 
-    for i = 1, String.len(hex) / 2 do
-        local h = String.sub(hex, i * 2 - 1, i * 2);
+    for i = 1, string.len(hex) / 2 do
+        local h = string.sub(hex, i * 2 - 1, i * 2);
         array[i] = fromHexTable[h];
     end
 
@@ -107,7 +106,7 @@ end
 
 local toHexTable = {};
 for i = 0, 255 do
-    toHexTable[i] = String.format("%02X", i);
+    toHexTable[i] = string.format("%02X", i);
 end
 
 Array.toHex = function(array)
diff --git a/lockbox/util/base64.lua b/lockbox/util/base64.lua
index 6f1743d..f1e4724 100644
--- a/lockbox/util/base64.lua
+++ b/lockbox/util/base64.lua
@@ -1,4 +1,3 @@
-local String = require("string");
 local Bit = require("lockbox.util.bit");
 
 local Stream = require("lockbox.util.stream");
@@ -81,7 +80,7 @@ Base64.toStream = function(base64)
 
       local yield = coroutine.yield;
 
-      for c in String.gmatch(base64, ".") do
+      for c in string.gmatch(base64, ".") do
           if (c == "=") then
               bits = RSHIFT(bits, 2); bitCount = bitCount - 2;
           else
diff --git a/lockbox/util/stream.lua b/lockbox/util/stream.lua
index f81a18c..a198d87 100644
--- a/lockbox/util/stream.lua
+++ b/lockbox/util/stream.lua
@@ -1,5 +1,4 @@
 local Queue = require("lockbox.util.queue");
-local String = require("string");
 
 local Stream = {};
 
@@ -8,7 +7,7 @@ Stream.fromString = function(string)
     local i = 0;
     return function()
         i = i + 1;
-        return String.byte(string, i);
+        return string.byte(string, i);
     end
 end
 
@@ -19,7 +18,7 @@ Stream.toString = function(stream)
 
     local byte = stream();
     while byte ~= nil do
-        array[i] = String.char(byte);
+        array[i] = string.char(byte);
         i = i + 1;
         byte = stream();
     end
@@ -60,15 +59,15 @@ end
 
 local fromHexTable = {};
 for i = 0, 255 do
-    fromHexTable[String.format("%02X", i)] = i;
-    fromHexTable[String.format("%02x", i)] = i;
+    fromHexTable[string.format("%02X", i)] = i;
+    fromHexTable[string.format("%02x", i)] = i;
 end
 
 Stream.fromHex = function(hex)
     local queue = Queue();
 
-    for i = 1, String.len(hex) / 2 do
-        local h = String.sub(hex, i * 2 - 1, i * 2);
+    for i = 1, string.len(hex) / 2 do
+        local h = string.sub(hex, i * 2 - 1, i * 2);
         queue.push(fromHexTable[h]);
     end
 
@@ -79,7 +78,7 @@ end
 
 local toHexTable = {};
 for i = 0, 255 do
-    toHexTable[i] = String.format("%02X", i);
+    toHexTable[i] = string.format("%02X", i);
 end
 
 Stream.toHex = function(stream)