Lua RSA

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---      *** BitLibEmu for Lua ***            ---
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--- Author:  Martin Huesser                   ---
--- Date:    2008-06-16                       ---
--- License: You may use this code in your    ---
---          projects as long as this header  ---
---          stays intact.                    ---
-------------------------------------------------

local mod   = math.fmod
local floor = math.floor
bit = {}

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local function cap(x)
    return mod(x,4294967296)
end

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function bit.bnot(x)
    return 4294967295-cap(x)
end

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function bit.lshift(x,n)
    return cap(cap(x)*2^n)
end

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function bit.rshift(x,n)
    return floor(cap(x)/2^n)
end

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function bit.band(x,y)
    local z,i,j = 0,1
    for j = 0,31 do
        if (mod(x,2)==1 and mod(y,2)==1) then
            z = z + i
        end
        x = bit.rshift(x,1)
        y = bit.rshift(y,1)
        i = i*2
    end
    return z
end

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function bit.bor(x,y)
    local z,i,j = 0,1
    for j = 0,31 do
        if (mod(x,2)==1 or mod(y,2)==1) then
            z = z + i
        end
        x = bit.rshift(x,1)
        y = bit.rshift(y,1)
        i = i*2
    end
    return z
end

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function bit.bxor(x,y)
    local z,i,j = 0,1
    for j = 0,31 do
        if (mod(x,2)~=mod(y,2)) then
            z = z + i
        end
        x = bit.rshift(x,1)
        y = bit.rshift(y,1)
        i = i*2
    end
    return z
end





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---      *** BigInteger for Lua ***           ---
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--- Author:  Martin Huesser                   ---
--- Date:    2008-06-16                       ---
--- License: You may use this code in your    ---
---          projects as long as this header  ---
---          stays intact.                    ---
-------------------------------------------------

---------------------------------------
--- Lua 5.0/5.1/WoW Header ------------
---------------------------------------

local strlen  = string.len
local strchar = string.char
local strbyte = string.byte
local strsub  = string.sub
local max     = math.max
local min     = math.min
local floor   = math.floor
local ceil    = math.ceil
local mod     = math.fmod
local getn    = function(t) return #t end
local setn    = function() end
local tinsert = table.insert

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--- Helper Functions ------------------
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local function Digit(x,i)                   --returns i-th digit or zero
    local d = x[i]                      --if out of bounds
    if (d==nil) then
        return 0
    end
    return d
end

---------------------------------------

local function Clean(x)                     --remove leading zeros
    local i = getn(x)
    while (i>1 and x[i]==0) do
        x[i] = nil
        i = i-1
    end
    setn(x,i)
end

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--- String Conversion -----------------
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local function Hex(i)                       --convert number to ascii
    if (i>-1 and i<10) then
        return strchar(48+i)
    end
    if (i>9 and i<16) then
        return strchar(55+i)
    end
    return strchar(48)
end

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local function Dec(i)                       --convert ascii to number
    if (i==nil) then
        return 0
    end
    if (i>47 and i<58) then
        return i-48
    end
    if (i>64 and i<71) then
        return i-55
    end
    if (i>96 and i<103) then
        return i-87
    end
    return 0
end

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function BigInt_NumToHex(x)                 --convert number to hexstring
    local s,i,j,c = ""
    for i = 1,getn(x) do
        c = x[i]
        for j = 1,6 do
            s = Hex(mod(c,16))..s
            c = floor(c/16)
        end
    end
    i = 1
    while (i<strlen(s) and strbyte(s,i)==48) do
        i = i+1
    end
    return strsub(s,i)
end

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function BigInt_HexToNum(h)                 --convert hexstring to number
    local x,i,j = {}
    for i = 1,ceil(strlen(h)/6) do
        x[i] = 0
        for j = 1,6 do
            x[i] = 16*x[i]+Dec(strbyte(h,max(strlen(h)-6*i+j,0)))
        end
    end
    Clean(x)
    return x
end

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--- Math Functions --------------------
---------------------------------------

function BigInt_Add(x,y)                    --add numbers
    local z,l,i,r = {},max(getn(x),getn(y))
    z[1] = 0
    for i = 1,l do
        r = Digit(x,i)+Digit(y,i)+z[i]
        if (r>16777215) then
            z[i] = r-16777216
            z[i+1] = 1
        else
            z[i] = r
            z[i+1] = 0
        end
    end
    Clean(z)
    return z
end

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function BigInt_Sub(x,y)                    --subtract numbers
    local z,l,i,r = {},max(getn(x),getn(y))
    z[1] = 0
    for i = 1,l do
        r = Digit(x,i)-Digit(y,i)-z[i]
        if (r<0) then
            z[i] = r+16777216
            z[i+1] = 1
        else
            z[i] = r
            z[i+1] = 0
        end
    end
    if (z[l+1]==1) then
        return nil
    end
    Clean(z)
    return z
end

---------------------------------------

function BigInt_Mul(x,y)                    --multiply numbers
    local z,t,i,j,r = {},{}
    for i = getn(y),1,-1 do
        t[1] = 0
        for j = 1,getn(x) do
            r = x[j]*y[i]+t[j]
            t[j+1] = floor(r/16777216)
            t[j] = r-t[j+1]*16777216
        end
        tinsert(z,1,0)
        z = BigInt_Add(z,t)
    end
    Clean(z)
    return z
end

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local function Div2(x)                      --divide number by 2, (modifies
    local u,v,i = 0                     --passed number and returns
    for i = getn(x),1,-1 do                 --remainder)
        v = x[i]
        if (u==1) then
            x[i] = floor(v/2)+8388608
        else
            x[i] = floor(v/2)
        end
        u = mod(v,2)
    end
    Clean(x)
    return u
end

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local function SimpleDiv(x,y)                   --divide numbers, result
    local z,u,v,i,j = {},0                  --must fit into 1 digit!
    j = 16777216
    for i = 1,getn(y) do                    --This function is costly and
        z[i+1] = y[i]                   --may benefit most from an
    end                         --optimized algorithm!
    z[1] = 0
    for i = 23,0,-1 do
        j = j/2
        Div2(z)
        v = BigInt_Sub(x,z)
        if (v~=nil) then
            u = u+j
            x = v
        end
    end
    return u,x
end

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function BigInt_Div(x,y)                    --divide numbers
    local z,u,i,v = {},{},getn(x)
    for v = 1,min(getn(x),getn(y))-1 do
        tinsert(u,1,x[i])
        i = i - 1
    end
    while (i>0) do
        tinsert(u,1,x[i])
        i = i - 1
        v,u = SimpleDiv(u,y)
        tinsert(z,1,v)
    end
    Clean(z)
    return z,u
end

---------------------------------------

function BigInt_ModPower(b,e,m)                 --calculate b^e mod m
    local t,s,r = {},{1}
    for r = 1,getn(e) do
        t[r] = e[r]
    end
    repeat
        r = Div2(t)
        --print(getn(t))
        if (r==1) then
            r,s = BigInt_Div(BigInt_Mul(s,b),m)
        end
        r,b = BigInt_Div(BigInt_Mul(b,b),m)
    until (getn(t)==1 and t[1]==0)
    return s
end

---------------------------------------
--- ModPower Step Functions -----------
---------------------------------------

function BigInt_MP_StepInit(b,e,m)              --initialize nonblocking ModPower,
    local x,i = {b,{},m,{1},1}              --pass resulting table to StepExec!
    for i = 1,getn(e) do
        x[2][i] = e[i]
    end
    return x
end

---------------------------------------

function BigInt_MP_StepExec(x)                  --execute next calculation step,
    local r                         --finished if result~=nil.
    if (x[5]==1) then
        x[5] = 2
        r = Div2(x[2])
        if (r==1) then
            r,x[4] = BigInt_Div(BigInt_Mul(x[4],x[1]),x[3])
        end
        return nil
    end
    if (x[5]==2) then
        x[5] = 1
        r,x[1] = BigInt_Div(BigInt_Mul(x[1],x[1]),x[3])
        if (getn(x[2])==1 and x[2][1]==0) then
            x[5] = 0
            return x[4]
        end
        return nil
    end
    return nil
end

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-------------------------------------------------
---      *** SHA-1 algorithm for Lua ***      ---
-------------------------------------------------
--- Author:  Martin Huesser                   ---
--- Date:    2008-06-16                       ---
--- License: You may use this code in your    ---
---          projects as long as this header  ---
---          stays intact.                    ---
-------------------------------------------------

local strlen  = string.len
local strchar = string.char
local strbyte = string.byte
local strsub  = string.sub
local floor   = math.floor
local bnot    = bit.bnot
local band    = bit.band
local bor     = bit.bor
local bxor    = bit.bxor
local shl     = bit.lshift
local shr     = bit.rshift
local h0, h1, h2, h3, h4

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local function LeftRotate(val, nr)
    return shl(val, nr) + shr(val, 32 - nr)
end

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local function ToHex(num)
    local i, d
    local str = ""
    for i = 1, 8 do
        d = band(num, 15)
        if (d < 10) then
            str = strchar(d + 48) .. str
        else
            str = strchar(d + 87) .. str
        end
        num = floor(num / 16)
    end
    return str
end

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local function PreProcess(str)
    local bitlen, i
    local str2 = ""
    bitlen = strlen(str) * 8
    str = str .. strchar(128)
    i = 56 - band(strlen(str), 63)
    if (i < 0) then
        i = i + 64
    end
    for i = 1, i do
        str = str .. strchar(0)
    end
    for i = 1, 8 do
        str2 = strchar(band(bitlen, 255)) .. str2
        bitlen = floor(bitlen / 256)
    end
    return str .. str2
end

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local function MainLoop(str)
    local a, b, c, d, e, f, k, t
    local i, j
    local w = {}
    while (str ~= "") do
        for i = 0, 15 do
            w[i] = 0
            for j = 1, 4 do
                w[i] = w[i] * 256 + strbyte(str, i * 4 + j)
            end
        end
        for i = 16, 79 do
            w[i] = LeftRotate(bxor(bxor(w[i - 3], w[i - 8]), bxor(w[i - 14], w[i - 16])), 1)
        end
        a = h0
        b = h1
        c = h2
        d = h3
        e = h4
        for i = 0, 79 do
            if (i < 20) then
                f = bor(band(b, c), band(bnot(b), d))
                k = 1518500249
            elseif (i < 40) then
                f = bxor(bxor(b, c), d)
                k = 1859775393
            elseif (i < 60) then
                f = bor(bor(band(b, c), band(b, d)), band(c, d))
                k = 2400959708
            else
                f = bxor(bxor(b, c), d)
                k = 3395469782
            end
            t = LeftRotate(a, 5) + f + e + k + w[i]
            e = d
            d = c
            c = LeftRotate(b, 30)
            b = a
            a = t
        end
        h0 = band(h0 + a, 4294967295)
        h1 = band(h1 + b, 4294967295)
        h2 = band(h2 + c, 4294967295)
        h3 = band(h3 + d, 4294967295)
        h4 = band(h4 + e, 4294967295)
        str = strsub(str, 65)
    end
end

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function Sha1(str)
    str = PreProcess(str)
    h0  = 1732584193
    h1  = 4023233417
    h2  = 2562383102
    h3  = 0271733878
    h4  = 3285377520
    MainLoop(str)
    return  ToHex(h0) ..
        ToHex(h1) ..
        ToHex(h2) ..
        ToHex(h3) ..
        ToHex(h4)
end

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