Lua适配SHA2-512算法实现结果不正确，求问题排查

我尝试将纯Lua实现的SHA2-256算法适配为SHA2-512，但修改后的代码无法输出正确的哈希结果。以下是我目前的适配代码（末尾存在截断）：

-- -- 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 = ini

关键错误点与修复方案 #

1. 消息字初始化的字节偏移错误
   SHA2-512的每个消息字是64位（8字节），但代码中沿用了SHA2-256的4字节偏移逻辑，导致读取的字节序列错误。修复：

for j = 1, 16 do
    w[j] = s264num(msg, i + (j - 1)*8) -- 将4改为8，对应64位字的字节长度
end

2. 64位旋转的溢出问题
   Lua默认位运算为32位，直接旋转64位数值会丢失高位，需要添加64位掩码确保数值完整性：

local function rrotate(rot, n)
    return ((rot >> n) | (rot << (64 - n))) & 0xffffffffffffffff
end

3. 哈希函数主体不完整
   代码末尾的hash512函数被截断，需要补全初始化和块循环逻辑：

-- Returns the hash512 for the given string.
local function hash512 (msg)
    msg = preprocess(msg, #msg)
    local H = initH512() -- 初始化哈希值
    -- 遍历每个128字节的消息块进行处理
    for i = 1, #msg, 128 do
        digestblock(msg, i, H)
    end
    return finalresult512(H) -- 返回最终哈希结果
end

4. 初始化函数的冗余参数
   initH512函数的参数H未被使用，可以简化为：

local function initH512()
    return {
        0x6a09e667f3bcc908, 0xbb67ae8584caa73b,
        0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1,
        0x510e527fade682d1, 0x9b05688c2b3e6c1f,
        0x1f83d9abfb41bd6b, 0x5be0cd19137e2179
    }
end

验证测试 #

修复后可以用标准测试向量验证，比如空字符串的SHA2-512结果应为：
cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e

调用print(hash512(""))应输出上述值。

内容的提问来源于stack exchange，提问作者O. Orum