Pure Lua SHA-1 and HMAC-SHA1

-- SHA-1 secure hash computation, and HMAC-SHA1 signature computation,
-- in pure Lua (tested on Lua 5.1)
-- License: MIT
--
-- Usage:
--   local hash_as_hex   = sha1(message)            -- returns a hex string
--   local hash_as_data  = sha1_binary(message)     -- returns raw bytes
--
--   local hmac_as_hex   = hmac_sha1(key, message)        -- hex string
--   local hmac_as_data  = hmac_sha1_binary(key, message) -- raw bytes
--
--
-- Pass sha1() a string, and it returns a hash as a 40-character hex string.
-- For example, the call
--
--   local hash = sha1 "http://regex.info/blog/"
--
-- puts the 40-character string
--
--   "7f103bf600de51dfe91062300c14738b32725db5"
--
-- into the variable 'hash'
--
-- Pass sha1_hmac() a key and a message, and it returns the signature as a
-- 40-byte hex string.
--
--
-- The two "_binary" versions do the same, but return the 20-byte string of raw
-- data that the 40-byte hex strings represent.
--
------------------------------------------------------
-- set this to false if you don't want to build several 64k sized tables when
-- loading this file (takes a while but grants a boost of factor 13)
local cfg_caching = true

-- local storing of global functions (minor speedup)
local floor,modf = math.floor,math.modf
local char,format,rep = string.char,string.format,string.rep

-- merge 4 bytes to an 32 bit word
local function bytes_to_w32 (a,b,c,d) return a*0x1000000+b*0x10000+c*0x100+d end
-- split a 32 bit word into four 8 bit numbers
local function w32_to_bytes (i)
    return floor(i/0x1000000)%0x100,floor(i/0x10000)%0x100,floor(i/0x100)%0x100,i%0x100
end

-- shift the bits of a 32 bit word. Don't use negative values for "bits"
local function w32_rot (bits,a)
    local b2 = 2^(32-bits)
    local a,b = modf(a/b2)
    return a+b*b2*(2^(bits))
end

-- caching function for functions that accept 2 arguments, both of values between
-- 0 and 255. The function to be cached is passed, all values are calculated
-- during loading and a function is returned that returns the cached values (only)
local function cache2arg (fn)
    if not cfg_caching then return fn end
    local lut = {}
    for i=0,0xffff do
        local a,b = floor(i/0x100),i%0x100
        lut[i] = fn(a,b)
    end
    return function (a,b)
        return lut[a*0x100+b]
    end
end

-- splits an 8-bit number into 8 bits, returning all 8 bits as booleans
local function byte_to_bits (b)
    local b = function (n)
        local b = floor(b/n)
        return b%2==1
    end
    return b(1),b(2),b(4),b(8),b(16),b(32),b(64),b(128)
end

-- builds an 8bit number from 8 booleans
local function bits_to_byte (a,b,c,d,e,f,g,h)
    local function n(b,x) return b and x or 0 end
    return n(a,1)+n(b,2)+n(c,4)+n(d,8)+n(e,16)+n(f,32)+n(g,64)+n(h,128)
end

-- debug function for visualizing bits in a string
local function bits_to_string (a,b,c,d,e,f,g,h)
    local function x(b) return b and "1" or "0" end
    return ("%s%s%s%s %s%s%s%s"):format(x(a),x(b),x(c),x(d),x(e),x(f),x(g),x(h))
end

-- debug function for converting a 8-bit number as bit string
local function byte_to_bit_string (b)
    return bits_to_string(byte_to_bits(b))
end

-- debug function for converting a 32 bit number as bit string
local function w32_to_bit_string(a)
    if type(a) == "string" then return a end
    local aa,ab,ac,ad = w32_to_bytes(a)
    local s = byte_to_bit_string
    return ("%s %s %s %s"):format(s(aa):reverse(),s(ab):reverse(),s(ac):reverse(),s(ad):reverse()):reverse()
end

-- bitwise "and" function for 2 8bit number
local band = cache2arg (function(a,b)
    local A,B,C,D,E,F,G,H = byte_to_bits(b)
    local a,b,c,d,e,f,g,h = byte_to_bits(a)
    return bits_to_byte(
        A and a, B and b, C and c, D and d,
        E and e, F and f, G and g, H and h)
end)

-- bitwise "or" function for 2 8bit numbers
local bor = cache2arg(function(a,b)
    local A,B,C,D,E,F,G,H = byte_to_bits(b)
    local a,b,c,d,e,f,g,h = byte_to_bits(a)
    return bits_to_byte(
        A or a, B or b, C or c, D or d,
        E or e, F or f, G or g, H or h)
end)

-- bitwise "xor" function for 2 8bit numbers
local bxor = cache2arg(function(a,b)
    local A,B,C,D,E,F,G,H = byte_to_bits(b)
    local a,b,c,d,e,f,g,h = byte_to_bits(a)
    return bits_to_byte(
        A ~= a, B ~= b, C ~= c, D ~= d,
        E ~= e, F ~= f, G ~= g, H ~= h)
end)

-- bitwise complement for one 8bit number
local function bnot (x)
    return 255-(x % 256)
end

-- creates a function to combine to 32bit numbers using an 8bit combination function
local function w32_comb(fn)
    return function (a,b)
        local aa,ab,ac,ad = w32_to_bytes(a)
        local ba,bb,bc,bd = w32_to_bytes(b)
        return bytes_to_w32(fn(aa,ba),fn(ab,bb),fn(ac,bc),fn(ad,bd))
    end
end

-- create functions for and, xor and or, all for 2 32bit numbers
local w32_and = w32_comb(band)
local w32_xor = w32_comb(bxor)
local w32_or = w32_comb(bor)

-- xor function that may receive a variable number of arguments
local function w32_xor_n (a,...)
    local aa,ab,ac,ad = w32_to_bytes(a)
    for i=1,select('#',...) do
        local ba,bb,bc,bd = w32_to_bytes(select(i,...))
        aa,ab,ac,ad = bxor(aa,ba),bxor(ab,bb),bxor(ac,bc),bxor(ad,bd)
    end
    return bytes_to_w32(aa,ab,ac,ad)
end

-- combining 3 32bit numbers through binary "or" operation
local function w32_or3 (a,b,c)
    local aa,ab,ac,ad = w32_to_bytes(a)
    local ba,bb,bc,bd = w32_to_bytes(b)
    local ca,cb,cc,cd = w32_to_bytes(c)
    return bytes_to_w32(
        bor(aa,bor(ba,ca)), bor(ab,bor(bb,cb)), bor(ac,bor(bc,cc)), bor(ad,bor(bd,cd))
    )
end

-- binary complement for 32bit numbers
local function w32_not (a)
    return 4294967295-(a % 4294967296)
end

-- adding 2 32bit numbers, cutting off the remainder on 33th bit
local function w32_add (a,b) return (a+b) % 4294967296 end

-- adding n 32bit numbers, cutting off the remainder (again)
local function w32_add_n (a,...)
    for i=1,select('#',...) do
        a = (a+select(i,...)) % 4294967296
    end
    return a
end
-- converting the number to a hexadecimal string
local function w32_to_hexstring (w) return format("%08x",w) end

-- calculating the SHA1 for some text
function sha1(msg)
    local H0,H1,H2,H3,H4 = 0x67452301,0xEFCDAB89,0x98BADCFE,0x10325476,0xC3D2E1F0
    local msg_len_in_bits = #msg * 8

    local first_append = char(0x80) -- append a '1' bit plus seven '0' bits

    local non_zero_message_bytes = #msg +1 +8 -- the +1 is the appended bit 1, the +8 are for the final appended length
    local current_mod = non_zero_message_bytes % 64
    local second_append = current_mod>0 and rep(char(0), 64 - current_mod) or ""

    -- now to append the length as a 64-bit number.
    local B1, R1 = modf(msg_len_in_bits  / 0x01000000)
    local B2, R2 = modf( 0x01000000 * R1 / 0x00010000)
    local B3, R3 = modf( 0x00010000 * R2 / 0x00000100)
    local B4      = 0x00000100 * R3

    local L64 = char( 0) .. char( 0) .. char( 0) .. char( 0) -- high 32 bits
                .. char(B1) .. char(B2) .. char(B3) .. char(B4) --  low 32 bits

    msg = msg .. first_append .. second_append .. L64

    assert(#msg % 64 == 0)

    local chunks = #msg / 64

    local W = { }
    local start, A, B, C, D, E, f, K, TEMP
    local chunk = 0

    while chunk < chunks do
        --
        -- break chunk up into W[0] through W[15]
        --
        start,chunk = chunk * 64 + 1,chunk + 1

        for t = 0, 15 do
            W[t] = bytes_to_w32(msg:byte(start, start + 3))
            start = start + 4
        end

        --
        -- build W[16] through W[79]
        --
        for t = 16, 79 do
            -- For t = 16 to 79 let Wt = S1(Wt-3 XOR Wt-8 XOR Wt-14 XOR Wt-16).
            W[t] = w32_rot(1, w32_xor_n(W[t-3], W[t-8], W[t-14], W[t-16]))
        end

        A,B,C,D,E = H0,H1,H2,H3,H4

        for t = 0, 79 do
            if t <= 19 then
                -- (B AND C) OR ((NOT B) AND D)
                f = w32_or(w32_and(B, C), w32_and(w32_not(B), D))
                K = 0x5A827999
            elseif t <= 39 then
                -- B XOR C XOR D
                f = w32_xor_n(B, C, D)
                K = 0x6ED9EBA1
            elseif t <= 59 then
                -- (B AND C) OR (B AND D) OR (C AND D
                f = w32_or3(w32_and(B, C), w32_and(B, D), w32_and(C, D))
                K = 0x8F1BBCDC
            else
                -- B XOR C XOR D
                f = w32_xor_n(B, C, D)
                K = 0xCA62C1D6
            end

            -- TEMP = S5(A) + ft(B,C,D) + E + Wt + Kt;
            A,B,C,D,E = w32_add_n(w32_rot(5, A), f, E, W[t], K),
                A, w32_rot(30, B), C, D
        end
        -- Let H0 = H0 + A, H1 = H1 + B, H2 = H2 + C, H3 = H3 + D, H4 = H4 + E.
        H0,H1,H2,H3,H4 = w32_add(H0, A),w32_add(H1, B),w32_add(H2, C),w32_add(H3, D),w32_add(H4, E)
    end
    local f = w32_to_hexstring
    return f(H0) .. f(H1) .. f(H2) .. f(H3) .. f(H4)
end

local function hex_to_binary(hex)
    return hex:gsub('..', function(hexval)
        return string.char(tonumber(hexval, 16))
    end)
end

function sha1_binary(msg)
    return hex_to_binary(sha1(msg))
end

local xor_with_0x5c = {}
local xor_with_0x36 = {}
-- building the lookuptables ahead of time (instead of littering the source code
-- with precalculated values)
for i=0,0xff do
    xor_with_0x5c[char(i)] = char(bxor(i,0x5c))
    xor_with_0x36[char(i)] = char(bxor(i,0x36))
end

local blocksize = 64 -- 512 bits

function hmac_sha1(key, text)
    assert(type(key)  == 'string', "key passed to hmac_sha1 should be a string")
    assert(type(text) == 'string', "text passed to hmac_sha1 should be a string")

    if #key > blocksize then
        key = sha1_binary(key)
    end

    local key_xord_with_0x36 = key:gsub('.', xor_with_0x36) .. string.rep(string.char(0x36), blocksize - #key)
    local key_xord_with_0x5c = key:gsub('.', xor_with_0x5c) .. string.rep(string.char(0x5c), blocksize - #key)

    return sha1(key_xord_with_0x5c .. sha1_binary(key_xord_with_0x36 .. text))
end

function hmac_sha1_binary(key, text)
    return hex_to_binary(hmac_sha1(key, text))
end