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I'm looking for how to turn bytes into a signed int using lua 5.1.5, so far I've only been able to find solutions for lua 5.2 onward, and they are not backward compatible.
I have solutions for how to turn bytes into unsigned integers, like so:
payload_t.temperature=tonumber(utility.hex2str(string.sub(payload,32,33)),16)
First of all I'll assume that you actually have a byte string rather than a hex string given; if your string is a hex string, you can trivially convert it to a byte string using gsub:
function hex2bytes(str)
-- assert that it is indeed a string of hex digit pairs
assert(#str % 2 == 0 and not str:match"[^%x]")
return str:gsub("%x%x", function(hex) return tonumber(hex, 16) end)
end
Now, let's convert this byte string to an integer. I'll assume little endian (least significant byte first); should your string be big endian (most significant byte first) you'll have to reverse it using str:reverse() before you read it.
Reading an unsigned integer is pretty straightforward:
function bytes2uint(str)
local uint = 0
for i = 1, #str do
uint = uint + str:byte(i) * 0x100^(i-1)
end
return uint
end
I'll assume your integers are stored using Two's complement. In this case the higher 2^n values (equivalent to the first bit being set or the value being >= 2^(n-1)) the uint can take represent negative numbers, with the smallest value (2^(n-1)) representing the largest negative value (-2^(n-1)). Thus you can simply subtract the unsigned value from 2^n, the (exclusive) max value for the uint:
function bytes2int(str)
local uint = bytes2uint(str)
local max = 0x100 ^ #str
if uint >= max / 2 then
return uint - max
end
return uint
end
I am trying to write a PBKDF2 implementation in pure lua. I am writing it because I want to use it in a sandboxed lua environment that does not allow outside libraries. I had a look at the standard document from the IETF and had at it. Below is the code I have come up with:
do
package.preload["pbkdf2"] = function()
local hmac = require 'hmac'
local len = string.len
local gsub = string.gsub
local format = string.format
local byte = string.byte
local char = string.char
local concat = table.concat
local ceil = math.ceil
local function toBytes(str)
local tmp = {}
for i = 1, len(str) do
tmp[i] = byte(str, i)
end
return tmp
end
local function toString(bArray)
local tmp = {}
for i = 1, #bArray do
tmp[i] = char(bArray[i])
end
tmp = concat(tmp)
return tmp
end
-- transform a string of bytes in a string of hexadecimal digits
local function asHex(s)
local h = gsub(s, ".", function(c)
return format("%02x", byte(c))
end)
return h
end
local num2string = function(l, n)
local s = {}
for i = 1, n do
local idx = (n + 1) - i
s[idx] = char(l & 255)
l = l >> 8
end
s = concat(s)
return s
end
local buildBlock = function(hFun, password, salt, c, int)
local tmp
local tmp2
for i = 1, c do
if i == 1 then
print(int)
print(salt .. int)
-- PRF(password, salt || INT_32_BE(i)
-- return result of hash as a byte string
tmp = hmac.hash(hFun, password, salt .. num2string(int, 4), true)
else
-- returns result of hash as byte string
tmp2 = hmac.hash(hFun, password, tmp, true)
-- transform to byte arrays
tmp2 = toBytes(tmp2)
tmp = toBytes(tmp)
assert(#tmp == #tmp2)
-- apply XOR over bytes in both arrays
-- save results to final array
for j = 1, #tmp do
-- perform XOR operation on both elements in the respective arrays
tmp[j] = tmp[j] ~ tmp2[j]
end
-- transform back into byte string to pass to next hash
tmp = toString(tmp)
end
end
return tmp
end
local truncate = function(str, pos)
return string.sub(str, 1, pos)
end
local deriveKey = function(hFun, message, salt, c, dLen)
local hLen = hFun.outputSize
-- the derived key cannot be larger than (2^32 * hLen)
if dLen > (2^32) * hLen then error("The derived key cannot be larger than 2^32 times the output size of the hash function.") end
-- the block size is the desired key length divided by the output size of the underlying hash function, rounded up
local blockSize = ceil(dLen/hLen)
-- to store our blocks
local final = {}
for i = 1, blockSize do
-- lets make our blocks in here
final[i] = buildBlock(hFun, message, salt, c, i)
end
local result
if #final == 1 then
result = final[1] -- we only have one block
else
result = concat(final) -- turns final into a bytestring to be outputted
end
--if #result > dLen then truncate(final, dLen) end
assert(#result == dLen)
return asHex(result) -- outputs as a hex value
end
return {deriveKey = deriveKey}
end
end
This code is not getting the correct answers. Testing this code with test vectors provided here, assuming that the underlying PRF is HMAC-SHA256, the output is below:
key: "password"
salt: "salt"
c: 1
dkLen: 32
Got: 13463842ec330934dc124494b40d8baade465b72f3fcadad741f2d0e052fd2f5
Expected: 120fb6cffcf8b32c43e7225256c4f837a86548c92ccc35480805987cb70be17b
key: "password"
salt: "salt"
c: 2
dkLen: 32
Got: 8b82aed26f503effdbc6c14bc7f0338b2b90e387f14ac1f91f9ad74e618f9558
Expected: AE4D0C95AF6B46D32D0ADFF928F06DD02A303F8EF3C251DFD6E2D85A95474C43
I believe it may have something to do with the string to byte encoding, but I cannot pinpoint what exactly is causing the issue. When I was testing my HMAC code, I had to rely on online generators because I couldn't find vectors for HMAC-SHA224 and HMAC-SHA256. Some calculators would give me completely different output values for the same key, message combination. That could be because of how they are processing the inputs, but I am not sure. I would appreciate it if someone more experienced could help me out with this.
EDIT: This problem is solved. Seems that all that was needed was to pass int as a binary string of length 4. I updated the code with the fixes.
EDIT 2: I read the standard again to realize the solution was in my face the entire time (standard says to encode i as a 32-bit big endian integer).
The solution was to convert int to a binary string of length 4. Thanks to #EgorSkriptunoff for his insight.
I am trying to adapt the pure Lua implementation of the SecureHashAlgorithm found here for SHA2 512 instead of SHA2 256. When I try to use the adaptation, it does not give the correct answer.
Here is the adaptation:
--
-- UTILITY FUNCTIONS
--
-- transform a string of bytes in a string of hexadecimal digits
local function str2hexa (s)
local h = string.gsub(s, ".", function(c)
return string.format("%02x", string.byte(c))
end)
return h
end
-- transforms number 'l' into a big-endian sequence of 'n' bytes
--(coded as a string)
local function num2string(l, n)
local s = ""
for i = 1, n do
--most significant byte of l
local remainder = l % 256
s = string.char(remainder) .. s
--remove from l the bits we have already transformed
l = (l-remainder) / 256
end
return s
end
-- transform the big-endian sequence of eight bytes starting at
-- index 'i' in 's' into a number
local function s264num (s, i)
local n = 0
for i = i, i + 7 do
n = n*256 + string.byte(s, i)
end
return n
end
--
-- MAIN SECTION
--
-- FIRST STEP: INITIALIZE HASH VALUES
--(second 32 bits of the fractional parts of the square roots of the first 9th through 16th primes 23..53)
local HH = {}
local function initH512(H)
H = {0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179}
return H
end
-- SECOND STEP: INITIALIZE ROUND CONSTANTS
--(first 80 bits of the fractional parts of the cube roots of the first 80 primes 2..409)
local k = {
0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc, 0x3956c25bf348b538,
0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118, 0xd807aa98a3030242, 0x12835b0145706fbe,
0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2, 0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235,
0xc19bf174cf692694, 0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,
0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5, 0x983e5152ee66dfab,
0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4, 0xc6e00bf33da88fc2, 0xd5a79147930aa725,
0x06ca6351e003826f, 0x142929670a0e6e70, 0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed,
0x53380d139d95b3df, 0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b,
0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30, 0xd192e819d6ef5218,
0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8, 0x19a4c116b8d2d0c8, 0x1e376c085141ab53,
0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8, 0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373,
0x682e6ff3d6b2b8a3, 0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec,
0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b, 0xca273eceea26619c,
0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178, 0x06f067aa72176fba, 0x0a637dc5a2c898a6,
0x113f9804bef90dae, 0x1b710b35131c471b, 0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc,
0x431d67c49c100d4c, 0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817
}
-- THIRD STEP: PRE-PROCESSING (padding)
local function preprocess(toProcess, len)
--append a single '1' bit
--append K '0' bits, where K is the minimum number >= 0 such that L + 1 + K = 896mod1024
local extra = 128 - (len + 9) % 128
len = num2string(8 * len, 8)
toProcess = toProcess .. "\128" .. string.rep("\0", extra) .. len
assert(#toProcess % 128 == 0)
return toProcess
end
local function rrotate(rot, n)
return (rot >> n) | ((rot << 64 - n))
end
local function digestblock(msg, i, H)
local w = {}
for j = 1, 16 do w[j] = s264num(msg, i + (j - 1)*4) end
for j = 17, 80 do
local v = w[j - 15]
local s0 = rrotate(v, 1) ~ rrotate(v, 8) ~ (v >> 7)
v = w[j - 2]
w[j] = w[j - 16] + s0 + w[j - 7] + ((rrotate(v, 19) ~ rrotate(v, 61)) ~ (v >> 6))
end
local a, b, c, d, e, f, g, h = H[1], H[2], H[3], H[4], H[5], H[6], H[7], H[8]
for i = 1, 80 do
a, b, c, d, e, f, g, h = a , b , c , d , e , f , g , h
local s0 = rrotate(a, 28) ~ (rrotate(a, 34) ~ rrotate(a, 39))
local maj = ((a & b) ~ (a & c)) ~ (b & c)
local t2 = s0 + maj
local s1 = rrotate(e, 14) ~ (rrotate(e, 18) ~ rrotate(e, 41))
local ch = (e & f) ~ (~e & g)
local t1 = h + s1 + ch + k[i] + w[i]
h, g, f, e, d, c, b, a = g, f, e, d + t1, c, b, a, t1 + t2
end
H[1] = (H[1] + a)
H[2] = (H[2] + b)
H[3] = (H[3] + c)
H[4] = (H[4] + d)
H[5] = (H[5] + e)
H[6] = (H[6] + f)
H[7] = (H[7] + g)
H[8] = (H[8] + h)
end
local function finalresult512 (H)
-- Produce the final hash value:
return
str2hexa(num2string(H[1], 8)..num2string(H[2], 8)..num2string(H[3], 8)..num2string(H[4], 8)..
num2string(H[5], 8)..num2string(H[6], 8)..num2string(H[7], 8)..num2string(H[8], 8))
end
-- Returns the hash512 for the given string.
local function hash512 (msg)
msg = preprocess(msg, #msg)
local H = initH512(HH)
-- Process the message in successive 1024-bit (128 bytes) chunks:
for i = 1, #msg, 128 do
digestblock(msg, i, H)
end
return finalresult512(H)
end
Given hash512("a"):
Expect: 1f40fc92da241694750979ee6cf582f2d5d7d28e18335de05abc54d0560e0f5302860c652bf08d560252aa5e74210546f369fbbbce8c12cfc7957b2652fe9a75
Actual: e0b9623f2194cb81f2a62616a183edbe390be0d0b20430cadc3371efc237fa6bf7f8b48311f2fa249131c347fee3e8cde6acfdab286d648054541f92102cfc9c
I know that I am creating a message of the correct bit size (1024 bits) and also working in 1024-bit chunks, or at least I believe I am.
I am not sure if it has to do with the handling of the integers (the standard requires unsigned integers) or whether I made a mistake in one of the utility functions, or both. If it is indeed an issue with the handling of the integers, how would I go about taking care of the problem. I was able to resolve this when working on the 256-bit version of the adaptation by using mod 2^32 when working with numbers in the digestblock method. I attempted to do mod 2^64 and 2^63 with the 512-bit version and it does not correct the problem. I am stumped.
I should mention that I cannot use one of the many library implementations as I am using a sandboxed Lua that does not provide this access, which is why I need a pure lua implementation. Thanks in advance.
Unfortunately, after introducing integers in Lua 5.3 writing scripts for Lua becomes a more complicated task.
You must always think about transformations between integers and floating point numbers.
ALWAYS. Yes, that's boring.
One of your mistakes is an excellent example of this "dark corner of Lua".
local remainder = l % 256
s = string.char(remainder) .. s
--remove from l the bits we have already transformed
l = (l-remainder) / 256
Your value l is initially a 64-bit integer.
After cutting off its first byte l contains (64-8) = 56 bits, but now it's a floating point-number (with 53-bit precision, of course).
Possible solution: use l = l >> 8 or l = l // 256 instead of l = (l-remainder) / 256
Another mistake is using s264num(msg, i + (j - 1) * 4) instead of s264num(msg, i + (j - 1) * 8)
One more mistake is in the following line:
local extra = 128 - (len + 9) % 128
The correct code is
local extra = - (len + 17) % 128 + 8
(Please note that -a%m+b is not the same as b-a%m due to operator precedence)
After fixing these 3 mistakes your code works correctly.
I am using Lua on Redis and want to compare two signed 64-bit numbers, which are stored in two 8-byte/character strings.
How can I compare them using the libraries available in Redis?
http://redis.io/commands/EVAL#available-libraries
I'd like to know >/< and == checks. I think this probably involves pulling two 32-bit numbers for each 64-bit int, and doing some clever math on those, but I am not sure.
I have some code to make this less abstract. a0, a1, b0, b1 are all 32 bit numbers used to represent the msb & lsb's of two 64-bit signed int 64s:
-- ...
local comp_int64s = function (a0, a1, b0, b1)
local cmpres = 0
-- TOOD: Real comparison
return cmpres
end
local l, a0, a1, b0, b1
a0, l = bit.tobit(struct.unpack("I4", ARGV[1]))
a1, l = bit.tobit(struct.unpack("I4", ARGV[1], 5))
b0, l = bit.tobit(struct.unpack("I4", blob))
b1, l = bit.tobit(struct.unpack("I4", blob, 5))
print("Cmp result", comp_int64s(a0, a1, b0, b1))
EDIT: Added code
I came up with a method that looks like it's working. It's a little ugly though.
The first step is to compare top 32 bits as 2 compliment #’s
MSB sign bit stays, so numbers keep correct relations
-1 —> -1
0 —> 0
9223372036854775807 = 0x7fff ffff ffff ffff -> 0x7ffff ffff = 2147483647
So returning the result from the MSB's works unless they are equal, then the LSB's need to get checked.
I have a few cases to establish the some patterns:
-1 = 0xffff ffff ffff ffff
-2 = 0xffff ffff ffff fffe
32 bit is:
-1 -> 0xffff ffff = -1
-2 -> 0xffff fffe = -2
-1 > -2 would be like -1 > -2 : GOOD
And
8589934591 = 0x0000 0001 ffff ffff
8589934590 = 0x0000 0001 ffff fffe
32 bit is:
8589934591 -> ffff ffff = -1
8589934590 -> ffff fffe = -2
8589934591 > 8589934590 would be -1 > -2 : GOOD
The sign bit on MSB’s doesn’t matter b/c negative numbers have the same relationship between themselves as positive numbers. e.g regardless of sign bit, lsb values of 0xff > 0xfe, always.
What about if the MSB on the lower 32 bits is different?
0xff7f ffff 7fff ffff = -36,028,799,166,447,617
0xff7f ffff ffff ffff = -36,028,797,018,963,969
32 bit is:
-..799.. -> 0x7fff ffff = 2147483647
-..797.. -> 0xffff ffff = -1
-..799.. < -..797.. would be 2147483647 < -1 : BAD!
So we need to ignore the sign bit on the lower 32 bits. And since the relationships are the same for the LSBs regardless of sign, just using
the lowest 32 bits unsigned works for all cases.
This means I want signed for the MSB's and unsigned for the LSBs - so chaging I4 to i4 for the LSBs. Also making big endian official and using '>' on the struct.unpack calls:
-- ...
local comp_int64s = function (as0, au1, bs0, bu1)
if as0 > bs0 then
return 1
elseif as0 < bs0 then
return -1
else
-- msb's equal comparing lsbs - these are unsigned
if au1 > bu1 then
return 1
elseif au1 < bu1 then
return -1
else
return 0
end
end
end
local l, as0, au1, bs0, bu1
as0, l = bit.tobit(struct.unpack(">i4", ARGV[1]))
au1, l = bit.tobit(struct.unpack(">I4", ARGV[1], 5))
bs0, l = bit.tobit(struct.unpack(">i4", blob))
bu1, l = bit.tobit(struct.unpack(">I4", blob, 5))
print("Cmp result", comp_int64s(as0, au1, bs0, bu1))
Comparing is a simple string compare s1 == s2.
Greater than is when not s1 == s2 and i1 < i2.
Less than is the real work. string.byte allows to get single bytes as unsigned char. In case of unsigned integer, you would just have to check bytes-downwards: b1==b2 -> check next byte; through all bytes -> false (equal); b1>b2 -> false (greater than); b1<b2 -> true. Signed requires more steps: first check the sign bit (uppermost byte >127). If sign 1 is set but not sign 2, integer 1 is negative but not integer 2 -> true. The opposite would obviously result in false. When both signs are equal, you can do the unsigned processing.
When you can pack more bytes to an integer, it's fine too, but you have to adjust the sign bit check. When you have LuaJIT, you can use the ffi library to cast your string into a byte array into an int64.
I need set some bits in ByteData at position counted in bits.
How I can do this?
Eg.
var byteData = new ByteData(1024);
var bitData = new BitData(byteData);
// Offset in bits: 387
// Number of bits: 5
// Value: 3
bitData.setBits(387, 5, 3);
Yes it is quite complicated. I dont know dart, but these are the general steps you need to take. I will label each variable as a letter and also use a more complicated example to show you what happens when the bits overflow.
1. Construct the BitData object with a ByteData object (A)
2. Call setBits(offset (B), bits (C), value (D));
I will use example values of:
A: 11111111 11111111 11111111 11111111
B: 7
C: 10
D: 00000000 11111111
3. Rather than using an integer with a fixed length of bits, you could
use another ByteData object (D) containing your bits you want to write.
Also create a mask (E) containing the significant bits.
e.g.
A: 11111111 11111111 11111111 11111111
D: 00000000 11111111
E: 00000011 11111111 (2^C - 1)
4. As an extra bonus step, we can make sure the insignificant
bits are really zero by ANDing with the bitmask.
D = D & E
D 00000000 11111111
E 00000011 11111111
5. Make sure D and E contain at least one full zero byte since we want
to shift them.
D 00000000 00000000 11111111
E 00000000 00000011 11111111
6. Work out these two integer values:
F = The extra bit offset for the start byte: B mod 8 (e.g. 7)
G = The insignificant bits: size(D) - C (e.g. 14)
7. H = G-F which should not be negative here. (e.g. 14-7 = 7)
8. Shift both D and E left by H bits.
D 00000000 01111111 10000000
E 00000001 11111111 10000000
9. Work out first byte number (J) floor(B / 8) e.g. 0
10. Read the value of A at this index out and let this be K
K = 11111111 11111111 11111111
11. AND the current (K) with NOT E to set zeros for the new bits.
Then you can OR the new bits over the top.
L = (K & !E) | D
K & !E = 11111110 00000000 01111111
L = 11111110 01111111 11111111
12. Write L to the same place you read it from.
There is no BitData class, so you'll have to do some of the bit-pushing yourself.
Find the corresponding byte offset, read in some bytes, mask out the existing bits and set the new ones at the correct bit offset, then write it back.
The real complexity comes when you need to store more bits than you can read/write in a single operation.
For endianness, if you are treating the memory as a sequence of bits with arbitrary width, I'd go for little-endian. Endianness only really makes sense for full-sized (2^n-bit, n > 3) integers. A 5 bit integer as the one you are storing can't have any endianness, and a 37 bit integer also won't have any natural way of expressing an endianness.
You can try something like this code (which can definitely be optimized more):
import "dart:typed_data";
void setBitData(ByteBuffer buffer, int offset, int length, int value) {
assert(value < (1 << length));
assert(offset + length < buffer.lengthInBytes * 8);
int byteOffset = offset >> 3;
int bitOffset = offset & 7;
if (length + bitOffset <= 32) {
ByteData data = new ByteData.view(buffer);
// Can update it one read/modify/write operation.
int mask = ((1 << length) - 1) << bitOffset;
int bits = data.getUint32(byteOffset, Endianness.LITTLE_ENDIAN);
bits = (bits & ~mask) | (value << bitOffset);
data.setUint32(byteOffset, bits, Endianness.LITTLE_ENDIAN);
return;
}
// Split the value into chunks of no more than 32 bits, aligned.
do {
int bits = (length > 32 ? 32 : length) - bitOffset;
setBitData(buffer, offset, bits, value & ((1 << bits) - 1));
offset += bits;
length -= bits;
value >>= bits;
bitOffset = 0;
} while (length > 0);
}
Example use:
main() {
var b = new Uint8List(32);
setBitData(b.buffer, 3, 8, 255);
print(b.map((v)=>v.toRadixString(16)));
setBitData(b.buffer, 13, 6*4, 0xffffff);
print(b.map((v)=>v.toRadixString(16)));
setBitData(b.buffer, 47, 21*4, 0xaaaaaaaaaaaaaaaaaaaaa);
print(b.map((v)=>v.toRadixString(16)));
}