forked from osmarks/potatOS
2135 lines
41 KiB
Lua
2135 lines
41 KiB
Lua
-- Elliptic curve cryptography library. This should probably be minified? Why does it have its own `irequire`?
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local preload = _G.package.preload
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local irequire = _G.require
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if type(irequire) ~= "function" then
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local loading = {}
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local loaded = {}
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irequire = function(name)
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local result = loaded[name]
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if result ~= nil then
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if result == loading then
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error("loop or previous error loading module '" .. name .. "'", 2)
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end
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return result
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end
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loaded[name] = loading
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local contents = preload[name]
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if contents then
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result = contents(name)
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else
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error("cannot load '" .. name .. "'", 2)
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end
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if result == nil then result = true end
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loaded[name] = result
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return result
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end
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end
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preload["fq"] = function(...)
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-- Fq Integer Arithmetic
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local bxor = bit32.bxor or bit.bxor
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local n = 0xffff
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local m = 0x10000
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local q = {1372, 62520, 47765, 8105, 45059, 9616, 65535, 65535, 65535, 65535, 65535, 65532}
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local qn = {1372, 62520, 47765, 8105, 45059, 9616, 65535, 65535, 65535, 65535, 65535, 65532, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
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local mt = {
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__tostring = function(a) return string.char(unpack(a)) end,
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__index = {
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toHex = function(self, s) return ("%02x"):rep(#self):format(unpack(self)) end,
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isEqual = function(self, t)
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if type(t) ~= "table" then return false end
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if #self ~= #t then return false end
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local ret = 0
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for i = 1, #self do
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ret = bit32.bor(ret, bxor(self[i], t[i]))
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end
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return ret == 0
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end
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}
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}
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local function eq(a, b)
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for i = 1, 12 do
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if a[i] ~= b[i] then
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return false
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end
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end
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return true
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end
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local function cmp(a, b)
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for i = 12, 1, -1 do
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if a[i] > b[i] then
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return 1
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elseif a[i] < b[i] then
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return -1
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end
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end
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return 0
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end
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local function cmp384(a, b)
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for i = 24, 1, -1 do
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if a[i] > b[i] then
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return 1
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elseif a[i] < b[i] then
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return -1
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end
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end
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return 0
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end
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local function bytes(x)
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local result = {}
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for i = 0, 11 do
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local m = x[i + 1] % 256
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result[2 * i + 1] = m
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result[2 * i + 2] = (x[i + 1] - m) / 256
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end
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return setmetatable(result, mt)
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end
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local function fromBytes(enc)
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local result = {}
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for i = 0, 11 do
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result[i + 1] = enc[2 * i + 1] % 256
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result[i + 1] = result[i + 1] + enc[2 * i + 2] * 256
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end
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return result
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end
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local function sub192(a, b)
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local r1 = a[1] - b[1]
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local r2 = a[2] - b[2]
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local r3 = a[3] - b[3]
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local r4 = a[4] - b[4]
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local r5 = a[5] - b[5]
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local r6 = a[6] - b[6]
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local r7 = a[7] - b[7]
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local r8 = a[8] - b[8]
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local r9 = a[9] - b[9]
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local r10 = a[10] - b[10]
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local r11 = a[11] - b[11]
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local r12 = a[12] - b[12]
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if r1 < 0 then
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r2 = r2 - 1
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r1 = r1 + m
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end
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if r2 < 0 then
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r3 = r3 - 1
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r2 = r2 + m
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end
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if r3 < 0 then
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r4 = r4 - 1
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r3 = r3 + m
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end
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if r4 < 0 then
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r5 = r5 - 1
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r4 = r4 + m
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end
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if r5 < 0 then
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r6 = r6 - 1
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r5 = r5 + m
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end
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if r6 < 0 then
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r7 = r7 - 1
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r6 = r6 + m
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end
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if r7 < 0 then
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r8 = r8 - 1
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r7 = r7 + m
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end
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if r8 < 0 then
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r9 = r9 - 1
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r8 = r8 + m
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end
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if r9 < 0 then
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r10 = r10 - 1
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r9 = r9 + m
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end
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if r10 < 0 then
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r11 = r11 - 1
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r10 = r10 + m
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end
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if r11 < 0 then
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r12 = r12 - 1
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r11 = r11 + m
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end
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local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
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return result
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end
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local function reduce(a)
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local result = {unpack(a)}
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if cmp(result, q) >= 0 then
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result = sub192(result, q)
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end
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return result
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end
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local function add(a, b)
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local r1 = a[1] + b[1]
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local r2 = a[2] + b[2]
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local r3 = a[3] + b[3]
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local r4 = a[4] + b[4]
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local r5 = a[5] + b[5]
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local r6 = a[6] + b[6]
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local r7 = a[7] + b[7]
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local r8 = a[8] + b[8]
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local r9 = a[9] + b[9]
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local r10 = a[10] + b[10]
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local r11 = a[11] + b[11]
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local r12 = a[12] + b[12]
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if r1 > n then
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r2 = r2 + 1
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r1 = r1 - m
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end
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if r2 > n then
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r3 = r3 + 1
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r2 = r2 - m
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end
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if r3 > n then
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r4 = r4 + 1
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r3 = r3 - m
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end
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if r4 > n then
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r5 = r5 + 1
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r4 = r4 - m
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end
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if r5 > n then
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r6 = r6 + 1
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r5 = r5 - m
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end
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if r6 > n then
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r7 = r7 + 1
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r6 = r6 - m
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end
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if r7 > n then
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r8 = r8 + 1
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r7 = r7 - m
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end
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if r8 > n then
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r9 = r9 + 1
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r8 = r8 - m
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end
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if r9 > n then
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r10 = r10 + 1
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r9 = r9 - m
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end
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if r10 > n then
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r11 = r11 + 1
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r10 = r10 - m
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end
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if r11 > n then
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r12 = r12 + 1
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r11 = r11 - m
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end
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local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
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return reduce(result)
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end
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local function sub(a, b)
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local result = sub192(a, b)
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if result[12] < 0 then
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result = add(result, q)
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end
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return result
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end
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local function add384(a, b)
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local r1 = a[1] + b[1]
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local r2 = a[2] + b[2]
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local r3 = a[3] + b[3]
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local r4 = a[4] + b[4]
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local r5 = a[5] + b[5]
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local r6 = a[6] + b[6]
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local r7 = a[7] + b[7]
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local r8 = a[8] + b[8]
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local r9 = a[9] + b[9]
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local r10 = a[10] + b[10]
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local r11 = a[11] + b[11]
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local r12 = a[12] + b[12]
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local r13 = a[13] + b[13]
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local r14 = a[14] + b[14]
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local r15 = a[15] + b[15]
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local r16 = a[16] + b[16]
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local r17 = a[17] + b[17]
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local r18 = a[18] + b[18]
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local r19 = a[19] + b[19]
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local r20 = a[20] + b[20]
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local r21 = a[21] + b[21]
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local r22 = a[22] + b[22]
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local r23 = a[23] + b[23]
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local r24 = a[24] + b[24]
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if r1 > n then
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r2 = r2 + 1
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r1 = r1 - m
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end
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if r2 > n then
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r3 = r3 + 1
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r2 = r2 - m
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end
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if r3 > n then
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r4 = r4 + 1
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r3 = r3 - m
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end
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if r4 > n then
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r5 = r5 + 1
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r4 = r4 - m
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end
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if r5 > n then
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r6 = r6 + 1
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r5 = r5 - m
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end
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if r6 > n then
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r7 = r7 + 1
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r6 = r6 - m
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end
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if r7 > n then
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r8 = r8 + 1
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r7 = r7 - m
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end
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if r8 > n then
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r9 = r9 + 1
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r8 = r8 - m
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end
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if r9 > n then
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r10 = r10 + 1
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r9 = r9 - m
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end
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if r10 > n then
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r11 = r11 + 1
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r10 = r10 - m
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end
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if r11 > n then
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r12 = r12 + 1
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r11 = r11 - m
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end
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if r12 > n then
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r13 = r13 + 1
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r12 = r12 - m
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end
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if r13 > n then
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r14 = r14 + 1
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r13 = r13 - m
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end
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if r14 > n then
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r15 = r15 + 1
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r14 = r14 - m
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end
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if r15 > n then
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r16 = r16 + 1
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r15 = r15 - m
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end
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if r16 > n then
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r17 = r17 + 1
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r16 = r16 - m
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end
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if r17 > n then
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r18 = r18 + 1
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r17 = r17 - m
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end
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if r18 > n then
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r19 = r19 + 1
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r18 = r18 - m
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end
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if r19 > n then
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r20 = r20 + 1
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r19 = r19 - m
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end
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if r20 > n then
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r21 = r21 + 1
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r20 = r20 - m
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end
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if r21 > n then
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r22 = r22 + 1
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r21 = r21 - m
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end
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if r22 > n then
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r23 = r23 + 1
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r22 = r22 - m
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end
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if r23 > n then
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r24 = r24 + 1
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r23 = r23 - m
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end
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local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24}
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return result
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end
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local function sub384(a, b)
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local r1 = a[1] - b[1]
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local r2 = a[2] - b[2]
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local r3 = a[3] - b[3]
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local r4 = a[4] - b[4]
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local r5 = a[5] - b[5]
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local r6 = a[6] - b[6]
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local r7 = a[7] - b[7]
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local r8 = a[8] - b[8]
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local r9 = a[9] - b[9]
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local r10 = a[10] - b[10]
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local r11 = a[11] - b[11]
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local r12 = a[12] - b[12]
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local r13 = a[13] - b[13]
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local r14 = a[14] - b[14]
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local r15 = a[15] - b[15]
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local r16 = a[16] - b[16]
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local r17 = a[17] - b[17]
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local r18 = a[18] - b[18]
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local r19 = a[19] - b[19]
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local r20 = a[20] - b[20]
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local r21 = a[21] - b[21]
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local r22 = a[22] - b[22]
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local r23 = a[23] - b[23]
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local r24 = a[24] - b[24]
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if r1 < 0 then
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r2 = r2 - 1
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r1 = r1 + m
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end
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if r2 < 0 then
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r3 = r3 - 1
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r2 = r2 + m
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end
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if r3 < 0 then
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r4 = r4 - 1
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r3 = r3 + m
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end
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if r4 < 0 then
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r5 = r5 - 1
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r4 = r4 + m
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end
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if r5 < 0 then
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r6 = r6 - 1
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r5 = r5 + m
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end
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if r6 < 0 then
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r7 = r7 - 1
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r6 = r6 + m
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end
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if r7 < 0 then
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r8 = r8 - 1
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r7 = r7 + m
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end
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if r8 < 0 then
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r9 = r9 - 1
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r8 = r8 + m
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end
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if r9 < 0 then
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r10 = r10 - 1
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r9 = r9 + m
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end
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if r10 < 0 then
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r11 = r11 - 1
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r10 = r10 + m
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end
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if r11 < 0 then
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r12 = r12 - 1
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r11 = r11 + m
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end
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if r12 < 0 then
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r13 = r13 - 1
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r12 = r12 + m
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end
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if r13 < 0 then
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r14 = r14 - 1
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r13 = r13 + m
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end
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if r14 < 0 then
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r15 = r15 - 1
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r14 = r14 + m
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end
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if r15 < 0 then
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r16 = r16 - 1
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r15 = r15 + m
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end
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if r16 < 0 then
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r17 = r17 - 1
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r16 = r16 + m
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end
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if r17 < 0 then
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r18 = r18 - 1
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r17 = r17 + m
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end
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if r18 < 0 then
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r19 = r19 - 1
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r18 = r18 + m
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end
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if r19 < 0 then
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r20 = r20 - 1
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r19 = r19 + m
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end
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if r20 < 0 then
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r21 = r21 - 1
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r20 = r20 + m
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end
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if r21 < 0 then
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r22 = r22 - 1
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r21 = r21 + m
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end
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if r22 < 0 then
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r23 = r23 - 1
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r22 = r22 + m
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end
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if r23 < 0 then
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r24 = r24 - 1
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r23 = r23 + m
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end
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local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24}
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return result
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end
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local function mul384(a, b)
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local a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12 = unpack(a)
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local b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12 = unpack(b)
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local r1 = a1 * b1
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local r2 = a1 * b2
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r2 = r2 + a2 * b1
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local r3 = a1 * b3
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r3 = r3 + a2 * b2
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r3 = r3 + a3 * b1
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local r4 = a1 * b4
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r4 = r4 + a2 * b3
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r4 = r4 + a3 * b2
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r4 = r4 + a4 * b1
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local r5 = a1 * b5
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r5 = r5 + a2 * b4
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r5 = r5 + a3 * b3
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r5 = r5 + a4 * b2
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r5 = r5 + a5 * b1
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local r6 = a1 * b6
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r6 = r6 + a2 * b5
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r6 = r6 + a3 * b4
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r6 = r6 + a4 * b3
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r6 = r6 + a5 * b2
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r6 = r6 + a6 * b1
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local r7 = a1 * b7
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r7 = r7 + a2 * b6
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r7 = r7 + a3 * b5
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r7 = r7 + a4 * b4
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r7 = r7 + a5 * b3
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r7 = r7 + a6 * b2
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r7 = r7 + a7 * b1
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local r8 = a1 * b8
|
|
r8 = r8 + a2 * b7
|
|
r8 = r8 + a3 * b6
|
|
r8 = r8 + a4 * b5
|
|
r8 = r8 + a5 * b4
|
|
r8 = r8 + a6 * b3
|
|
r8 = r8 + a7 * b2
|
|
r8 = r8 + a8 * b1
|
|
|
|
local r9 = a1 * b9
|
|
r9 = r9 + a2 * b8
|
|
r9 = r9 + a3 * b7
|
|
r9 = r9 + a4 * b6
|
|
r9 = r9 + a5 * b5
|
|
r9 = r9 + a6 * b4
|
|
r9 = r9 + a7 * b3
|
|
r9 = r9 + a8 * b2
|
|
r9 = r9 + a9 * b1
|
|
|
|
local r10 = a1 * b10
|
|
r10 = r10 + a2 * b9
|
|
r10 = r10 + a3 * b8
|
|
r10 = r10 + a4 * b7
|
|
r10 = r10 + a5 * b6
|
|
r10 = r10 + a6 * b5
|
|
r10 = r10 + a7 * b4
|
|
r10 = r10 + a8 * b3
|
|
r10 = r10 + a9 * b2
|
|
r10 = r10 + a10 * b1
|
|
|
|
local r11 = a1 * b11
|
|
r11 = r11 + a2 * b10
|
|
r11 = r11 + a3 * b9
|
|
r11 = r11 + a4 * b8
|
|
r11 = r11 + a5 * b7
|
|
r11 = r11 + a6 * b6
|
|
r11 = r11 + a7 * b5
|
|
r11 = r11 + a8 * b4
|
|
r11 = r11 + a9 * b3
|
|
r11 = r11 + a10 * b2
|
|
r11 = r11 + a11 * b1
|
|
|
|
local r12 = a1 * b12
|
|
r12 = r12 + a2 * b11
|
|
r12 = r12 + a3 * b10
|
|
r12 = r12 + a4 * b9
|
|
r12 = r12 + a5 * b8
|
|
r12 = r12 + a6 * b7
|
|
r12 = r12 + a7 * b6
|
|
r12 = r12 + a8 * b5
|
|
r12 = r12 + a9 * b4
|
|
r12 = r12 + a10 * b3
|
|
r12 = r12 + a11 * b2
|
|
r12 = r12 + a12 * b1
|
|
|
|
local r13 = a2 * b12
|
|
r13 = r13 + a3 * b11
|
|
r13 = r13 + a4 * b10
|
|
r13 = r13 + a5 * b9
|
|
r13 = r13 + a6 * b8
|
|
r13 = r13 + a7 * b7
|
|
r13 = r13 + a8 * b6
|
|
r13 = r13 + a9 * b5
|
|
r13 = r13 + a10 * b4
|
|
r13 = r13 + a11 * b3
|
|
r13 = r13 + a12 * b2
|
|
|
|
local r14 = a3 * b12
|
|
r14 = r14 + a4 * b11
|
|
r14 = r14 + a5 * b10
|
|
r14 = r14 + a6 * b9
|
|
r14 = r14 + a7 * b8
|
|
r14 = r14 + a8 * b7
|
|
r14 = r14 + a9 * b6
|
|
r14 = r14 + a10 * b5
|
|
r14 = r14 + a11 * b4
|
|
r14 = r14 + a12 * b3
|
|
|
|
local r15 = a4 * b12
|
|
r15 = r15 + a5 * b11
|
|
r15 = r15 + a6 * b10
|
|
r15 = r15 + a7 * b9
|
|
r15 = r15 + a8 * b8
|
|
r15 = r15 + a9 * b7
|
|
r15 = r15 + a10 * b6
|
|
r15 = r15 + a11 * b5
|
|
r15 = r15 + a12 * b4
|
|
|
|
local r16 = a5 * b12
|
|
r16 = r16 + a6 * b11
|
|
r16 = r16 + a7 * b10
|
|
r16 = r16 + a8 * b9
|
|
r16 = r16 + a9 * b8
|
|
r16 = r16 + a10 * b7
|
|
r16 = r16 + a11 * b6
|
|
r16 = r16 + a12 * b5
|
|
|
|
local r17 = a6 * b12
|
|
r17 = r17 + a7 * b11
|
|
r17 = r17 + a8 * b10
|
|
r17 = r17 + a9 * b9
|
|
r17 = r17 + a10 * b8
|
|
r17 = r17 + a11 * b7
|
|
r17 = r17 + a12 * b6
|
|
|
|
local r18 = a7 * b12
|
|
r18 = r18 + a8 * b11
|
|
r18 = r18 + a9 * b10
|
|
r18 = r18 + a10 * b9
|
|
r18 = r18 + a11 * b8
|
|
r18 = r18 + a12 * b7
|
|
|
|
local r19 = a8 * b12
|
|
r19 = r19 + a9 * b11
|
|
r19 = r19 + a10 * b10
|
|
r19 = r19 + a11 * b9
|
|
r19 = r19 + a12 * b8
|
|
|
|
local r20 = a9 * b12
|
|
r20 = r20 + a10 * b11
|
|
r20 = r20 + a11 * b10
|
|
r20 = r20 + a12 * b9
|
|
|
|
local r21 = a10 * b12
|
|
r21 = r21 + a11 * b11
|
|
r21 = r21 + a12 * b10
|
|
|
|
local r22 = a11 * b12
|
|
r22 = r22 + a12 * b11
|
|
|
|
local r23 = a12 * b12
|
|
|
|
local r24 = 0
|
|
|
|
r2 = r2 + (r1 / m)
|
|
r2 = r2 - r2 % 1
|
|
r1 = r1 % m
|
|
r3 = r3 + (r2 / m)
|
|
r3 = r3 - r3 % 1
|
|
r2 = r2 % m
|
|
r4 = r4 + (r3 / m)
|
|
r4 = r4 - r4 % 1
|
|
r3 = r3 % m
|
|
r5 = r5 + (r4 / m)
|
|
r5 = r5 - r5 % 1
|
|
r4 = r4 % m
|
|
r6 = r6 + (r5 / m)
|
|
r6 = r6 - r6 % 1
|
|
r5 = r5 % m
|
|
r7 = r7 + (r6 / m)
|
|
r7 = r7 - r7 % 1
|
|
r6 = r6 % m
|
|
r8 = r8 + (r7 / m)
|
|
r8 = r8 - r8 % 1
|
|
r7 = r7 % m
|
|
r9 = r9 + (r8 / m)
|
|
r9 = r9 - r9 % 1
|
|
r8 = r8 % m
|
|
r10 = r10 + (r9 / m)
|
|
r10 = r10 - r10 % 1
|
|
r9 = r9 % m
|
|
r11 = r11 + (r10 / m)
|
|
r11 = r11 - r11 % 1
|
|
r10 = r10 % m
|
|
r12 = r12 + (r11 / m)
|
|
r12 = r12 - r12 % 1
|
|
r11 = r11 % m
|
|
r13 = r13 + (r12 / m)
|
|
r13 = r13 - r13 % 1
|
|
r12 = r12 % m
|
|
r14 = r14 + (r13 / m)
|
|
r14 = r14 - r14 % 1
|
|
r13 = r13 % m
|
|
r15 = r15 + (r14 / m)
|
|
r15 = r15 - r15 % 1
|
|
r14 = r14 % m
|
|
r16 = r16 + (r15 / m)
|
|
r16 = r16 - r16 % 1
|
|
r15 = r15 % m
|
|
r17 = r17 + (r16 / m)
|
|
r17 = r17 - r17 % 1
|
|
r16 = r16 % m
|
|
r18 = r18 + (r17 / m)
|
|
r18 = r18 - r18 % 1
|
|
r17 = r17 % m
|
|
r19 = r19 + (r18 / m)
|
|
r19 = r19 - r19 % 1
|
|
r18 = r18 % m
|
|
r20 = r20 + (r19 / m)
|
|
r20 = r20 - r20 % 1
|
|
r19 = r19 % m
|
|
r21 = r21 + (r20 / m)
|
|
r21 = r21 - r21 % 1
|
|
r20 = r20 % m
|
|
r22 = r22 + (r21 / m)
|
|
r22 = r22 - r22 % 1
|
|
r21 = r21 % m
|
|
r23 = r23 + (r22 / m)
|
|
r23 = r23 - r23 % 1
|
|
r22 = r22 % m
|
|
r24 = r24 + (r23 / m)
|
|
r24 = r24 - r24 % 1
|
|
r23 = r23 % m
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24}
|
|
|
|
return result
|
|
end
|
|
|
|
local function reduce384(a)
|
|
local result = {unpack(a)}
|
|
|
|
while cmp384(result, qn) >= 0 do
|
|
local qn = {unpack(qn)}
|
|
local qn2 = add384(qn, qn)
|
|
while cmp384(result, qn2) > 0 do
|
|
qn = qn2
|
|
qn2 = add384(qn2, qn2)
|
|
end
|
|
result = sub384(result, qn)
|
|
end
|
|
|
|
result = {unpack(result, 1, 12)}
|
|
|
|
return result
|
|
end
|
|
|
|
local function mul(a, b)
|
|
return reduce384(mul384(a, b))
|
|
end
|
|
|
|
return {
|
|
fromBytes = fromBytes,
|
|
bytes = bytes,
|
|
sub = sub,
|
|
mul = mul,
|
|
eq = eq,
|
|
cmp = cmp,
|
|
}
|
|
end
|
|
preload["fp"] = function(...)
|
|
-- Fp Integer Arithmetic
|
|
|
|
local n = 0xffff
|
|
local m = 0x10000
|
|
|
|
local p = {3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65533}
|
|
local p2 = {21845, 21845, 21845, 21845, 21845, 21845, 21845, 21845, 21845, 21845, 21845, 43690}
|
|
local r2 = {44014, 58358, 19452, 6484, 45852, 58974, 63348, 64806, 65292, 65454, 65508, 21512}
|
|
|
|
local function eq(a, b)
|
|
for i = 1, 12 do
|
|
if a[i] ~= b[i] then
|
|
return false
|
|
end
|
|
end
|
|
|
|
return true
|
|
end
|
|
|
|
local function reduce(a)
|
|
local r1 = a[1]
|
|
local r2 = a[2]
|
|
local r3 = a[3]
|
|
local r4 = a[4]
|
|
local r5 = a[5]
|
|
local r6 = a[6]
|
|
local r7 = a[7]
|
|
local r8 = a[8]
|
|
local r9 = a[9]
|
|
local r10 = a[10]
|
|
local r11 = a[11]
|
|
local r12 = a[12]
|
|
|
|
if r12 < 65533 or r12 == 65533 and r1 < 3 then
|
|
return {unpack(a)}
|
|
end
|
|
|
|
r1 = r1 - 3
|
|
r12 = r12 - 65533
|
|
|
|
if r1 < 0 then
|
|
r2 = r2 - 1
|
|
r1 = r1 + m
|
|
end
|
|
if r2 < 0 then
|
|
r3 = r3 - 1
|
|
r2 = r2 + m
|
|
end
|
|
if r3 < 0 then
|
|
r4 = r4 - 1
|
|
r3 = r3 + m
|
|
end
|
|
if r4 < 0 then
|
|
r5 = r5 - 1
|
|
r4 = r4 + m
|
|
end
|
|
if r5 < 0 then
|
|
r6 = r6 - 1
|
|
r5 = r5 + m
|
|
end
|
|
if r6 < 0 then
|
|
r7 = r7 - 1
|
|
r6 = r6 + m
|
|
end
|
|
if r7 < 0 then
|
|
r8 = r8 - 1
|
|
r7 = r7 + m
|
|
end
|
|
if r8 < 0 then
|
|
r9 = r9 - 1
|
|
r8 = r8 + m
|
|
end
|
|
if r9 < 0 then
|
|
r10 = r10 - 1
|
|
r9 = r9 + m
|
|
end
|
|
if r10 < 0 then
|
|
r11 = r11 - 1
|
|
r10 = r10 + m
|
|
end
|
|
if r11 < 0 then
|
|
r12 = r12 - 1
|
|
r11 = r11 + m
|
|
end
|
|
|
|
return {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
|
|
end
|
|
|
|
local function add(a, b)
|
|
local r1 = a[1] + b[1]
|
|
local r2 = a[2] + b[2]
|
|
local r3 = a[3] + b[3]
|
|
local r4 = a[4] + b[4]
|
|
local r5 = a[5] + b[5]
|
|
local r6 = a[6] + b[6]
|
|
local r7 = a[7] + b[7]
|
|
local r8 = a[8] + b[8]
|
|
local r9 = a[9] + b[9]
|
|
local r10 = a[10] + b[10]
|
|
local r11 = a[11] + b[11]
|
|
local r12 = a[12] + b[12]
|
|
|
|
if r1 > n then
|
|
r2 = r2 + 1
|
|
r1 = r1 - m
|
|
end
|
|
if r2 > n then
|
|
r3 = r3 + 1
|
|
r2 = r2 - m
|
|
end
|
|
if r3 > n then
|
|
r4 = r4 + 1
|
|
r3 = r3 - m
|
|
end
|
|
if r4 > n then
|
|
r5 = r5 + 1
|
|
r4 = r4 - m
|
|
end
|
|
if r5 > n then
|
|
r6 = r6 + 1
|
|
r5 = r5 - m
|
|
end
|
|
if r6 > n then
|
|
r7 = r7 + 1
|
|
r6 = r6 - m
|
|
end
|
|
if r7 > n then
|
|
r8 = r8 + 1
|
|
r7 = r7 - m
|
|
end
|
|
if r8 > n then
|
|
r9 = r9 + 1
|
|
r8 = r8 - m
|
|
end
|
|
if r9 > n then
|
|
r10 = r10 + 1
|
|
r9 = r9 - m
|
|
end
|
|
if r10 > n then
|
|
r11 = r11 + 1
|
|
r10 = r10 - m
|
|
end
|
|
if r11 > n then
|
|
r12 = r12 + 1
|
|
r11 = r11 - m
|
|
end
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
|
|
|
|
return reduce(result)
|
|
end
|
|
|
|
local function shr(a)
|
|
local r1 = a[1]
|
|
local r2 = a[2]
|
|
local r3 = a[3]
|
|
local r4 = a[4]
|
|
local r5 = a[5]
|
|
local r6 = a[6]
|
|
local r7 = a[7]
|
|
local r8 = a[8]
|
|
local r9 = a[9]
|
|
local r10 = a[10]
|
|
local r11 = a[11]
|
|
local r12 = a[12]
|
|
|
|
r1 = r1 / 2
|
|
r1 = r1 - r1 % 1
|
|
r1 = r1 + (r2 % 2) * 0x8000
|
|
r2 = r2 / 2
|
|
r2 = r2 - r2 % 1
|
|
r2 = r2 + (r3 % 2) * 0x8000
|
|
r3 = r3 / 2
|
|
r3 = r3 - r3 % 1
|
|
r3 = r3 + (r4 % 2) * 0x8000
|
|
r4 = r4 / 2
|
|
r4 = r4 - r4 % 1
|
|
r4 = r4 + (r5 % 2) * 0x8000
|
|
r5 = r5 / 2
|
|
r5 = r5 - r5 % 1
|
|
r5 = r5 + (r6 % 2) * 0x8000
|
|
r6 = r6 / 2
|
|
r6 = r6 - r6 % 1
|
|
r6 = r6 + (r7 % 2) * 0x8000
|
|
r7 = r7 / 2
|
|
r7 = r7 - r7 % 1
|
|
r7 = r7 + (r8 % 2) * 0x8000
|
|
r8 = r8 / 2
|
|
r8 = r8 - r8 % 1
|
|
r8 = r8 + (r9 % 2) * 0x8000
|
|
r9 = r9 / 2
|
|
r9 = r9 - r9 % 1
|
|
r9 = r9 + (r10 % 2) * 0x8000
|
|
r10 = r10 / 2
|
|
r10 = r10 - r10 % 1
|
|
r10 = r10 + (r11 % 2) * 0x8000
|
|
r11 = r11 / 2
|
|
r11 = r11 - r11 % 1
|
|
r11 = r11 + (r12 % 2) * 0x8000
|
|
r12 = r12 / 2
|
|
r12 = r12 - r12 % 1
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
|
|
|
|
return result
|
|
end
|
|
|
|
local function sub192(a, b)
|
|
local r1 = a[1] - b[1]
|
|
local r2 = a[2] - b[2]
|
|
local r3 = a[3] - b[3]
|
|
local r4 = a[4] - b[4]
|
|
local r5 = a[5] - b[5]
|
|
local r6 = a[6] - b[6]
|
|
local r7 = a[7] - b[7]
|
|
local r8 = a[8] - b[8]
|
|
local r9 = a[9] - b[9]
|
|
local r10 = a[10] - b[10]
|
|
local r11 = a[11] - b[11]
|
|
local r12 = a[12] - b[12]
|
|
|
|
if r1 < 0 then
|
|
r2 = r2 - 1
|
|
r1 = r1 + m
|
|
end
|
|
if r2 < 0 then
|
|
r3 = r3 - 1
|
|
r2 = r2 + m
|
|
end
|
|
if r3 < 0 then
|
|
r4 = r4 - 1
|
|
r3 = r3 + m
|
|
end
|
|
if r4 < 0 then
|
|
r5 = r5 - 1
|
|
r4 = r4 + m
|
|
end
|
|
if r5 < 0 then
|
|
r6 = r6 - 1
|
|
r5 = r5 + m
|
|
end
|
|
if r6 < 0 then
|
|
r7 = r7 - 1
|
|
r6 = r6 + m
|
|
end
|
|
if r7 < 0 then
|
|
r8 = r8 - 1
|
|
r7 = r7 + m
|
|
end
|
|
if r8 < 0 then
|
|
r9 = r9 - 1
|
|
r8 = r8 + m
|
|
end
|
|
if r9 < 0 then
|
|
r10 = r10 - 1
|
|
r9 = r9 + m
|
|
end
|
|
if r10 < 0 then
|
|
r11 = r11 - 1
|
|
r10 = r10 + m
|
|
end
|
|
if r11 < 0 then
|
|
r12 = r12 - 1
|
|
r11 = r11 + m
|
|
end
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
|
|
|
|
return result
|
|
end
|
|
|
|
local function sub(a, b)
|
|
local r1 = a[1] - b[1]
|
|
local r2 = a[2] - b[2]
|
|
local r3 = a[3] - b[3]
|
|
local r4 = a[4] - b[4]
|
|
local r5 = a[5] - b[5]
|
|
local r6 = a[6] - b[6]
|
|
local r7 = a[7] - b[7]
|
|
local r8 = a[8] - b[8]
|
|
local r9 = a[9] - b[9]
|
|
local r10 = a[10] - b[10]
|
|
local r11 = a[11] - b[11]
|
|
local r12 = a[12] - b[12]
|
|
|
|
if r1 < 0 then
|
|
r2 = r2 - 1
|
|
r1 = r1 + m
|
|
end
|
|
if r2 < 0 then
|
|
r3 = r3 - 1
|
|
r2 = r2 + m
|
|
end
|
|
if r3 < 0 then
|
|
r4 = r4 - 1
|
|
r3 = r3 + m
|
|
end
|
|
if r4 < 0 then
|
|
r5 = r5 - 1
|
|
r4 = r4 + m
|
|
end
|
|
if r5 < 0 then
|
|
r6 = r6 - 1
|
|
r5 = r5 + m
|
|
end
|
|
if r6 < 0 then
|
|
r7 = r7 - 1
|
|
r6 = r6 + m
|
|
end
|
|
if r7 < 0 then
|
|
r8 = r8 - 1
|
|
r7 = r7 + m
|
|
end
|
|
if r8 < 0 then
|
|
r9 = r9 - 1
|
|
r8 = r8 + m
|
|
end
|
|
if r9 < 0 then
|
|
r10 = r10 - 1
|
|
r9 = r9 + m
|
|
end
|
|
if r10 < 0 then
|
|
r11 = r11 - 1
|
|
r10 = r10 + m
|
|
end
|
|
if r11 < 0 then
|
|
r12 = r12 - 1
|
|
r11 = r11 + m
|
|
end
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12}
|
|
|
|
if r12 < 0 then
|
|
result = add(result, p)
|
|
end
|
|
|
|
return result
|
|
end
|
|
|
|
local function add384(a, b)
|
|
local r1 = a[1] + b[1]
|
|
local r2 = a[2] + b[2]
|
|
local r3 = a[3] + b[3]
|
|
local r4 = a[4] + b[4]
|
|
local r5 = a[5] + b[5]
|
|
local r6 = a[6] + b[6]
|
|
local r7 = a[7] + b[7]
|
|
local r8 = a[8] + b[8]
|
|
local r9 = a[9] + b[9]
|
|
local r10 = a[10] + b[10]
|
|
local r11 = a[11] + b[11]
|
|
local r12 = a[12] + b[12]
|
|
local r13 = a[13] + b[13]
|
|
local r14 = a[14] + b[14]
|
|
local r15 = a[15] + b[15]
|
|
local r16 = a[16] + b[16]
|
|
local r17 = a[17] + b[17]
|
|
local r18 = a[18] + b[18]
|
|
local r19 = a[19] + b[19]
|
|
local r20 = a[20] + b[20]
|
|
local r21 = a[21] + b[21]
|
|
local r22 = a[22] + b[22]
|
|
local r23 = a[23] + b[23]
|
|
local r24 = a[24] + b[24]
|
|
|
|
if r1 > n then
|
|
r2 = r2 + 1
|
|
r1 = r1 - m
|
|
end
|
|
if r2 > n then
|
|
r3 = r3 + 1
|
|
r2 = r2 - m
|
|
end
|
|
if r3 > n then
|
|
r4 = r4 + 1
|
|
r3 = r3 - m
|
|
end
|
|
if r4 > n then
|
|
r5 = r5 + 1
|
|
r4 = r4 - m
|
|
end
|
|
if r5 > n then
|
|
r6 = r6 + 1
|
|
r5 = r5 - m
|
|
end
|
|
if r6 > n then
|
|
r7 = r7 + 1
|
|
r6 = r6 - m
|
|
end
|
|
if r7 > n then
|
|
r8 = r8 + 1
|
|
r7 = r7 - m
|
|
end
|
|
if r8 > n then
|
|
r9 = r9 + 1
|
|
r8 = r8 - m
|
|
end
|
|
if r9 > n then
|
|
r10 = r10 + 1
|
|
r9 = r9 - m
|
|
end
|
|
if r10 > n then
|
|
r11 = r11 + 1
|
|
r10 = r10 - m
|
|
end
|
|
if r11 > n then
|
|
r12 = r12 + 1
|
|
r11 = r11 - m
|
|
end
|
|
if r12 > n then
|
|
r13 = r13 + 1
|
|
r12 = r12 - m
|
|
end
|
|
if r13 > n then
|
|
r14 = r14 + 1
|
|
r13 = r13 - m
|
|
end
|
|
if r14 > n then
|
|
r15 = r15 + 1
|
|
r14 = r14 - m
|
|
end
|
|
if r15 > n then
|
|
r16 = r16 + 1
|
|
r15 = r15 - m
|
|
end
|
|
if r16 > n then
|
|
r17 = r17 + 1
|
|
r16 = r16 - m
|
|
end
|
|
if r17 > n then
|
|
r18 = r18 + 1
|
|
r17 = r17 - m
|
|
end
|
|
if r18 > n then
|
|
r19 = r19 + 1
|
|
r18 = r18 - m
|
|
end
|
|
if r19 > n then
|
|
r20 = r20 + 1
|
|
r19 = r19 - m
|
|
end
|
|
if r20 > n then
|
|
r21 = r21 + 1
|
|
r20 = r20 - m
|
|
end
|
|
if r21 > n then
|
|
r22 = r22 + 1
|
|
r21 = r21 - m
|
|
end
|
|
if r22 > n then
|
|
r23 = r23 + 1
|
|
r22 = r22 - m
|
|
end
|
|
if r23 > n then
|
|
r24 = r24 + 1
|
|
r23 = r23 - m
|
|
end
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24}
|
|
|
|
return result
|
|
end
|
|
|
|
local function mul384(a, b)
|
|
local a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12 = unpack(a)
|
|
local b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12 = unpack(b)
|
|
|
|
local r1 = a1 * b1
|
|
|
|
local r2 = a1 * b2
|
|
r2 = r2 + a2 * b1
|
|
|
|
local r3 = a1 * b3
|
|
r3 = r3 + a2 * b2
|
|
r3 = r3 + a3 * b1
|
|
|
|
local r4 = a1 * b4
|
|
r4 = r4 + a2 * b3
|
|
r4 = r4 + a3 * b2
|
|
r4 = r4 + a4 * b1
|
|
|
|
local r5 = a1 * b5
|
|
r5 = r5 + a2 * b4
|
|
r5 = r5 + a3 * b3
|
|
r5 = r5 + a4 * b2
|
|
r5 = r5 + a5 * b1
|
|
|
|
local r6 = a1 * b6
|
|
r6 = r6 + a2 * b5
|
|
r6 = r6 + a3 * b4
|
|
r6 = r6 + a4 * b3
|
|
r6 = r6 + a5 * b2
|
|
r6 = r6 + a6 * b1
|
|
|
|
local r7 = a1 * b7
|
|
r7 = r7 + a2 * b6
|
|
r7 = r7 + a3 * b5
|
|
r7 = r7 + a4 * b4
|
|
r7 = r7 + a5 * b3
|
|
r7 = r7 + a6 * b2
|
|
r7 = r7 + a7 * b1
|
|
|
|
local r8 = a1 * b8
|
|
r8 = r8 + a2 * b7
|
|
r8 = r8 + a3 * b6
|
|
r8 = r8 + a4 * b5
|
|
r8 = r8 + a5 * b4
|
|
r8 = r8 + a6 * b3
|
|
r8 = r8 + a7 * b2
|
|
r8 = r8 + a8 * b1
|
|
|
|
local r9 = a1 * b9
|
|
r9 = r9 + a2 * b8
|
|
r9 = r9 + a3 * b7
|
|
r9 = r9 + a4 * b6
|
|
r9 = r9 + a5 * b5
|
|
r9 = r9 + a6 * b4
|
|
r9 = r9 + a7 * b3
|
|
r9 = r9 + a8 * b2
|
|
r9 = r9 + a9 * b1
|
|
|
|
local r10 = a1 * b10
|
|
r10 = r10 + a2 * b9
|
|
r10 = r10 + a3 * b8
|
|
r10 = r10 + a4 * b7
|
|
r10 = r10 + a5 * b6
|
|
r10 = r10 + a6 * b5
|
|
r10 = r10 + a7 * b4
|
|
r10 = r10 + a8 * b3
|
|
r10 = r10 + a9 * b2
|
|
r10 = r10 + a10 * b1
|
|
|
|
local r11 = a1 * b11
|
|
r11 = r11 + a2 * b10
|
|
r11 = r11 + a3 * b9
|
|
r11 = r11 + a4 * b8
|
|
r11 = r11 + a5 * b7
|
|
r11 = r11 + a6 * b6
|
|
r11 = r11 + a7 * b5
|
|
r11 = r11 + a8 * b4
|
|
r11 = r11 + a9 * b3
|
|
r11 = r11 + a10 * b2
|
|
r11 = r11 + a11 * b1
|
|
|
|
local r12 = a1 * b12
|
|
r12 = r12 + a2 * b11
|
|
r12 = r12 + a3 * b10
|
|
r12 = r12 + a4 * b9
|
|
r12 = r12 + a5 * b8
|
|
r12 = r12 + a6 * b7
|
|
r12 = r12 + a7 * b6
|
|
r12 = r12 + a8 * b5
|
|
r12 = r12 + a9 * b4
|
|
r12 = r12 + a10 * b3
|
|
r12 = r12 + a11 * b2
|
|
r12 = r12 + a12 * b1
|
|
|
|
local r13 = a2 * b12
|
|
r13 = r13 + a3 * b11
|
|
r13 = r13 + a4 * b10
|
|
r13 = r13 + a5 * b9
|
|
r13 = r13 + a6 * b8
|
|
r13 = r13 + a7 * b7
|
|
r13 = r13 + a8 * b6
|
|
r13 = r13 + a9 * b5
|
|
r13 = r13 + a10 * b4
|
|
r13 = r13 + a11 * b3
|
|
r13 = r13 + a12 * b2
|
|
|
|
local r14 = a3 * b12
|
|
r14 = r14 + a4 * b11
|
|
r14 = r14 + a5 * b10
|
|
r14 = r14 + a6 * b9
|
|
r14 = r14 + a7 * b8
|
|
r14 = r14 + a8 * b7
|
|
r14 = r14 + a9 * b6
|
|
r14 = r14 + a10 * b5
|
|
r14 = r14 + a11 * b4
|
|
r14 = r14 + a12 * b3
|
|
|
|
local r15 = a4 * b12
|
|
r15 = r15 + a5 * b11
|
|
r15 = r15 + a6 * b10
|
|
r15 = r15 + a7 * b9
|
|
r15 = r15 + a8 * b8
|
|
r15 = r15 + a9 * b7
|
|
r15 = r15 + a10 * b6
|
|
r15 = r15 + a11 * b5
|
|
r15 = r15 + a12 * b4
|
|
|
|
local r16 = a5 * b12
|
|
r16 = r16 + a6 * b11
|
|
r16 = r16 + a7 * b10
|
|
r16 = r16 + a8 * b9
|
|
r16 = r16 + a9 * b8
|
|
r16 = r16 + a10 * b7
|
|
r16 = r16 + a11 * b6
|
|
r16 = r16 + a12 * b5
|
|
|
|
local r17 = a6 * b12
|
|
r17 = r17 + a7 * b11
|
|
r17 = r17 + a8 * b10
|
|
r17 = r17 + a9 * b9
|
|
r17 = r17 + a10 * b8
|
|
r17 = r17 + a11 * b7
|
|
r17 = r17 + a12 * b6
|
|
|
|
local r18 = a7 * b12
|
|
r18 = r18 + a8 * b11
|
|
r18 = r18 + a9 * b10
|
|
r18 = r18 + a10 * b9
|
|
r18 = r18 + a11 * b8
|
|
r18 = r18 + a12 * b7
|
|
|
|
local r19 = a8 * b12
|
|
r19 = r19 + a9 * b11
|
|
r19 = r19 + a10 * b10
|
|
r19 = r19 + a11 * b9
|
|
r19 = r19 + a12 * b8
|
|
|
|
local r20 = a9 * b12
|
|
r20 = r20 + a10 * b11
|
|
r20 = r20 + a11 * b10
|
|
r20 = r20 + a12 * b9
|
|
|
|
local r21 = a10 * b12
|
|
r21 = r21 + a11 * b11
|
|
r21 = r21 + a12 * b10
|
|
|
|
local r22 = a11 * b12
|
|
r22 = r22 + a12 * b11
|
|
|
|
local r23 = a12 * b12
|
|
|
|
local r24 = 0
|
|
|
|
r2 = r2 + (r1 / m)
|
|
r2 = r2 - r2 % 1
|
|
r1 = r1 % m
|
|
r3 = r3 + (r2 / m)
|
|
r3 = r3 - r3 % 1
|
|
r2 = r2 % m
|
|
r4 = r4 + (r3 / m)
|
|
r4 = r4 - r4 % 1
|
|
r3 = r3 % m
|
|
r5 = r5 + (r4 / m)
|
|
r5 = r5 - r5 % 1
|
|
r4 = r4 % m
|
|
r6 = r6 + (r5 / m)
|
|
r6 = r6 - r6 % 1
|
|
r5 = r5 % m
|
|
r7 = r7 + (r6 / m)
|
|
r7 = r7 - r7 % 1
|
|
r6 = r6 % m
|
|
r8 = r8 + (r7 / m)
|
|
r8 = r8 - r8 % 1
|
|
r7 = r7 % m
|
|
r9 = r9 + (r8 / m)
|
|
r9 = r9 - r9 % 1
|
|
r8 = r8 % m
|
|
r10 = r10 + (r9 / m)
|
|
r10 = r10 - r10 % 1
|
|
r9 = r9 % m
|
|
r11 = r11 + (r10 / m)
|
|
r11 = r11 - r11 % 1
|
|
r10 = r10 % m
|
|
r12 = r12 + (r11 / m)
|
|
r12 = r12 - r12 % 1
|
|
r11 = r11 % m
|
|
r13 = r13 + (r12 / m)
|
|
r13 = r13 - r13 % 1
|
|
r12 = r12 % m
|
|
r14 = r14 + (r13 / m)
|
|
r14 = r14 - r14 % 1
|
|
r13 = r13 % m
|
|
r15 = r15 + (r14 / m)
|
|
r15 = r15 - r15 % 1
|
|
r14 = r14 % m
|
|
r16 = r16 + (r15 / m)
|
|
r16 = r16 - r16 % 1
|
|
r15 = r15 % m
|
|
r17 = r17 + (r16 / m)
|
|
r17 = r17 - r17 % 1
|
|
r16 = r16 % m
|
|
r18 = r18 + (r17 / m)
|
|
r18 = r18 - r18 % 1
|
|
r17 = r17 % m
|
|
r19 = r19 + (r18 / m)
|
|
r19 = r19 - r19 % 1
|
|
r18 = r18 % m
|
|
r20 = r20 + (r19 / m)
|
|
r20 = r20 - r20 % 1
|
|
r19 = r19 % m
|
|
r21 = r21 + (r20 / m)
|
|
r21 = r21 - r21 % 1
|
|
r20 = r20 % m
|
|
r22 = r22 + (r21 / m)
|
|
r22 = r22 - r22 % 1
|
|
r21 = r21 % m
|
|
r23 = r23 + (r22 / m)
|
|
r23 = r23 - r23 % 1
|
|
r22 = r22 % m
|
|
r24 = r24 + (r23 / m)
|
|
r24 = r24 - r24 % 1
|
|
r23 = r23 % m
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24}
|
|
|
|
return result
|
|
end
|
|
|
|
local function REDC(T)
|
|
local m = {unpack(mul384({unpack(T, 1, 12)}, p2), 1, 12)}
|
|
local t = {unpack(add384(T, mul384(m, p)), 13, 24)}
|
|
|
|
return reduce(t)
|
|
end
|
|
|
|
local function mul(a, b)
|
|
return REDC(mul384(a, b))
|
|
end
|
|
|
|
local function sqr(a)
|
|
local a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12 = unpack(a)
|
|
|
|
local r1 = a1 * a1
|
|
|
|
local r2 = a1 * a2 * 2
|
|
|
|
local r3 = a1 * a3 * 2
|
|
r3 = r3 + a2 * a2
|
|
|
|
local r4 = a1 * a4 * 2
|
|
r4 = r4 + a2 * a3 * 2
|
|
|
|
local r5 = a1 * a5 * 2
|
|
r5 = r5 + a2 * a4 * 2
|
|
r5 = r5 + a3 * a3
|
|
|
|
local r6 = a1 * a6 * 2
|
|
r6 = r6 + a2 * a5 * 2
|
|
r6 = r6 + a3 * a4 * 2
|
|
|
|
local r7 = a1 * a7 * 2
|
|
r7 = r7 + a2 * a6 * 2
|
|
r7 = r7 + a3 * a5 * 2
|
|
r7 = r7 + a4 * a4
|
|
|
|
local r8 = a1 * a8 * 2
|
|
r8 = r8 + a2 * a7 * 2
|
|
r8 = r8 + a3 * a6 * 2
|
|
r8 = r8 + a4 * a5 * 2
|
|
|
|
local r9 = a1 * a9 * 2
|
|
r9 = r9 + a2 * a8 * 2
|
|
r9 = r9 + a3 * a7 * 2
|
|
r9 = r9 + a4 * a6 * 2
|
|
r9 = r9 + a5 * a5
|
|
|
|
local r10 = a1 * a10 * 2
|
|
r10 = r10 + a2 * a9 * 2
|
|
r10 = r10 + a3 * a8 * 2
|
|
r10 = r10 + a4 * a7 * 2
|
|
r10 = r10 + a5 * a6 * 2
|
|
|
|
local r11 = a1 * a11 * 2
|
|
r11 = r11 + a2 * a10 * 2
|
|
r11 = r11 + a3 * a9 * 2
|
|
r11 = r11 + a4 * a8 * 2
|
|
r11 = r11 + a5 * a7 * 2
|
|
r11 = r11 + a6 * a6
|
|
|
|
local r12 = a1 * a12 * 2
|
|
r12 = r12 + a2 * a11 * 2
|
|
r12 = r12 + a3 * a10 * 2
|
|
r12 = r12 + a4 * a9 * 2
|
|
r12 = r12 + a5 * a8 * 2
|
|
r12 = r12 + a6 * a7 * 2
|
|
|
|
local r13 = a2 * a12 * 2
|
|
r13 = r13 + a3 * a11 * 2
|
|
r13 = r13 + a4 * a10 * 2
|
|
r13 = r13 + a5 * a9 * 2
|
|
r13 = r13 + a6 * a8 * 2
|
|
r13 = r13 + a7 * a7
|
|
|
|
local r14 = a3 * a12 * 2
|
|
r14 = r14 + a4 * a11 * 2
|
|
r14 = r14 + a5 * a10 * 2
|
|
r14 = r14 + a6 * a9 * 2
|
|
r14 = r14 + a7 * a8 * 2
|
|
|
|
local r15 = a4 * a12 * 2
|
|
r15 = r15 + a5 * a11 * 2
|
|
r15 = r15 + a6 * a10 * 2
|
|
r15 = r15 + a7 * a9 * 2
|
|
r15 = r15 + a8 * a8
|
|
|
|
local r16 = a5 * a12 * 2
|
|
r16 = r16 + a6 * a11 * 2
|
|
r16 = r16 + a7 * a10 * 2
|
|
r16 = r16 + a8 * a9 * 2
|
|
|
|
local r17 = a6 * a12 * 2
|
|
r17 = r17 + a7 * a11 * 2
|
|
r17 = r17 + a8 * a10 * 2
|
|
r17 = r17 + a9 * a9
|
|
|
|
local r18 = a7 * a12 * 2
|
|
r18 = r18 + a8 * a11 * 2
|
|
r18 = r18 + a9 * a10 * 2
|
|
|
|
local r19 = a8 * a12 * 2
|
|
r19 = r19 + a9 * a11 * 2
|
|
r19 = r19 + a10 * a10
|
|
|
|
local r20 = a9 * a12 * 2
|
|
r20 = r20 + a10 * a11 * 2
|
|
|
|
local r21 = a10 * a12 * 2
|
|
r21 = r21 + a11 * a11
|
|
|
|
local r22 = a11 * a12 * 2
|
|
|
|
local r23 = a12 * a12
|
|
|
|
local r24 = 0
|
|
|
|
r2 = r2 + (r1 / m)
|
|
r2 = r2 - r2 % 1
|
|
r1 = r1 % m
|
|
r3 = r3 + (r2 / m)
|
|
r3 = r3 - r3 % 1
|
|
r2 = r2 % m
|
|
r4 = r4 + (r3 / m)
|
|
r4 = r4 - r4 % 1
|
|
r3 = r3 % m
|
|
r5 = r5 + (r4 / m)
|
|
r5 = r5 - r5 % 1
|
|
r4 = r4 % m
|
|
r6 = r6 + (r5 / m)
|
|
r6 = r6 - r6 % 1
|
|
r5 = r5 % m
|
|
r7 = r7 + (r6 / m)
|
|
r7 = r7 - r7 % 1
|
|
r6 = r6 % m
|
|
r8 = r8 + (r7 / m)
|
|
r8 = r8 - r8 % 1
|
|
r7 = r7 % m
|
|
r9 = r9 + (r8 / m)
|
|
r9 = r9 - r9 % 1
|
|
r8 = r8 % m
|
|
r10 = r10 + (r9 / m)
|
|
r10 = r10 - r10 % 1
|
|
r9 = r9 % m
|
|
r11 = r11 + (r10 / m)
|
|
r11 = r11 - r11 % 1
|
|
r10 = r10 % m
|
|
r12 = r12 + (r11 / m)
|
|
r12 = r12 - r12 % 1
|
|
r11 = r11 % m
|
|
r13 = r13 + (r12 / m)
|
|
r13 = r13 - r13 % 1
|
|
r12 = r12 % m
|
|
r14 = r14 + (r13 / m)
|
|
r14 = r14 - r14 % 1
|
|
r13 = r13 % m
|
|
r15 = r15 + (r14 / m)
|
|
r15 = r15 - r15 % 1
|
|
r14 = r14 % m
|
|
r16 = r16 + (r15 / m)
|
|
r16 = r16 - r16 % 1
|
|
r15 = r15 % m
|
|
r17 = r17 + (r16 / m)
|
|
r17 = r17 - r17 % 1
|
|
r16 = r16 % m
|
|
r18 = r18 + (r17 / m)
|
|
r18 = r18 - r18 % 1
|
|
r17 = r17 % m
|
|
r19 = r19 + (r18 / m)
|
|
r19 = r19 - r19 % 1
|
|
r18 = r18 % m
|
|
r20 = r20 + (r19 / m)
|
|
r20 = r20 - r20 % 1
|
|
r19 = r19 % m
|
|
r21 = r21 + (r20 / m)
|
|
r21 = r21 - r21 % 1
|
|
r20 = r20 % m
|
|
r22 = r22 + (r21 / m)
|
|
r22 = r22 - r22 % 1
|
|
r21 = r21 % m
|
|
r23 = r23 + (r22 / m)
|
|
r23 = r23 - r23 % 1
|
|
r22 = r22 % m
|
|
r24 = r24 + (r23 / m)
|
|
r24 = r24 - r24 % 1
|
|
r23 = r23 % m
|
|
|
|
local result = {r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24}
|
|
|
|
return REDC(result)
|
|
end
|
|
|
|
local function mont(a)
|
|
return mul(a, r2)
|
|
end
|
|
|
|
local function invMont(a)
|
|
local a = {unpack(a)}
|
|
|
|
for i = 13, 24 do
|
|
a[i] = 0
|
|
end
|
|
|
|
return REDC(a)
|
|
end
|
|
|
|
return {
|
|
eq = eq,
|
|
mul = mul,
|
|
sqr = sqr,
|
|
add = add,
|
|
sub = sub,
|
|
shr = shr,
|
|
mont = mont,
|
|
invMont = invMont,
|
|
sub192 = sub192
|
|
}
|
|
end
|
|
preload["empty"] = function(...)
|
|
|
|
end
|
|
preload["elliptic"] = function(...)
|
|
---- Elliptic Curve Arithmetic
|
|
|
|
---- About the Curve Itself
|
|
-- Field Size: 192 bits
|
|
-- Field Modulus (p): 65533 * 2^176 + 3
|
|
-- Equation: x^2 + y^2 = 1 + 108 * x^2 * y^2
|
|
-- Parameters: Edwards Curve with c = 1, and d = 108
|
|
-- Curve Order (n): 4 * 1569203598118192102418711808268118358122924911136798015831
|
|
-- Cofactor (h): 4
|
|
-- Generator Order (q): 1569203598118192102418711808268118358122924911136798015831
|
|
---- About the Curve's Security
|
|
-- Current best attack security: 94.822 bits (Pollard's Rho)
|
|
-- Rho Security: log2(0.884 * sqrt(q)) = 94.822
|
|
-- Transfer Security? Yes: p ~= q; k > 20
|
|
-- Field Discriminant Security? Yes: t = 67602300638727286331433024168; s = 2^2; |D| = 5134296629560551493299993292204775496868940529592107064435 > 2^100
|
|
-- Rigidity? A little, the parameters are somewhat small.
|
|
-- XZ/YZ Ladder Security? No: Single coordinate ladders are insecure, so they can't be used.
|
|
-- Small Subgroup Security? Yes: Secret keys are calculated modulo 4q.
|
|
-- Invalid Curve Security? Yes: Any point to be multiplied is checked beforehand.
|
|
-- Invalid Curve Twist Security? No: The curve is not protected against single coordinate ladder attacks, so don't use them.
|
|
-- Completeness? Yes: The curve is an Edwards Curve with non-square d and square a, so the curve is complete.
|
|
-- Indistinguishability? No: The curve does not support indistinguishability maps.
|
|
|
|
fp = irequire("fp")
|
|
|
|
local eq = fp.eq
|
|
local mul = fp.mul
|
|
local sqr = fp.sqr
|
|
local add = fp.add
|
|
local sub = fp.sub
|
|
local shr = fp.shr
|
|
local mont = fp.mont
|
|
local invMont = fp.invMont
|
|
local sub192 = fp.sub192
|
|
|
|
local bits = 192
|
|
local pMinusTwoBinary = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
|
|
local pMinusThreeOverFourBinary = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0}
|
|
local ZERO = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
|
|
local ONE = mont({1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
|
|
|
|
local p = mont({3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65533})
|
|
local G = {
|
|
mont({30457, 58187, 5603, 63215, 8936, 58151, 26571, 7272, 26680, 23486, 32353, 59456}),
|
|
mont({3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}),
|
|
mont({1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
|
|
}
|
|
local GTable = {G}
|
|
|
|
local d = mont({108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
|
|
|
|
local bxor = bit32.bxor or bit.bxor
|
|
local mt = {
|
|
__tostring = function(a) return string.char(unpack(a)) end,
|
|
__index = {
|
|
toHex = function(self, s) return ("%02x"):rep(#self):format(unpack(self)) end,
|
|
isEqual = function(self, t)
|
|
if type(t) ~= "table" then return false end
|
|
if #self ~= #t then return false end
|
|
local ret = 0
|
|
for i = 1, #self do
|
|
ret = bit32.bor(ret, bxor(self[i], t[i]))
|
|
end
|
|
return ret == 0
|
|
end
|
|
}
|
|
}
|
|
|
|
local function expMod(a, t)
|
|
local a = {unpack(a)}
|
|
local result = {unpack(ONE)}
|
|
|
|
for i = 1, bits do
|
|
if t[i] == 1 then
|
|
result = mul(result, a)
|
|
end
|
|
a = mul(a, a)
|
|
end
|
|
|
|
return result
|
|
end
|
|
|
|
-- We're using Projective Coordinates
|
|
-- For Edwards curves
|
|
-- The identity element is represented by (0:1:1)
|
|
local function pointDouble(P1)
|
|
local X1, Y1, Z1 = unpack(P1)
|
|
|
|
local b = add(X1, Y1)
|
|
local B = sqr(b)
|
|
local C = sqr(X1)
|
|
local D = sqr(Y1)
|
|
local E = add(C, D)
|
|
local H = sqr(Z1)
|
|
local J = sub(E, add(H, H))
|
|
local X3 = mul(sub(B, E), J)
|
|
local Y3 = mul(E, sub(C, D))
|
|
local Z3 = mul(E, J)
|
|
|
|
local P3 = {X3, Y3, Z3}
|
|
|
|
return P3
|
|
end
|
|
|
|
local function pointAdd(P1, P2)
|
|
local X1, Y1, Z1 = unpack(P1)
|
|
local X2, Y2, Z2 = unpack(P2)
|
|
|
|
local A = mul(Z1, Z2)
|
|
local B = sqr(A)
|
|
local C = mul(X1, X2)
|
|
local D = mul(Y1, Y2)
|
|
local E = mul(d, mul(C, D))
|
|
local F = sub(B, E)
|
|
local G = add(B, E)
|
|
local X3 = mul(A, mul(F, sub(mul(add(X1, Y1), add(X2, Y2)), add(C, D))))
|
|
local Y3 = mul(A, mul(G, sub(D, C)))
|
|
local Z3 = mul(F, G)
|
|
|
|
local P3 = {X3, Y3, Z3}
|
|
|
|
return P3
|
|
end
|
|
|
|
local function pointNeg(P1)
|
|
local X1, Y1, Z1 = unpack(P1)
|
|
|
|
local X3 = sub(p, X1)
|
|
local Y3 = {unpack(Y1)}
|
|
local Z3 = {unpack(Z1)}
|
|
|
|
local P3 = {X3, Y3, Z3}
|
|
|
|
return P3
|
|
end
|
|
|
|
local function pointSub(P1, P2)
|
|
return pointAdd(P1, pointNeg(P2))
|
|
end
|
|
|
|
local function pointScale(P1)
|
|
local X1, Y1, Z1 = unpack(P1)
|
|
|
|
local A = expMod(Z1, pMinusTwoBinary)
|
|
local X3 = mul(X1, A)
|
|
local Y3 = mul(Y1, A)
|
|
local Z3 = {unpack(ONE)}
|
|
|
|
local P3 = {X3, Y3, Z3}
|
|
|
|
return P3
|
|
end
|
|
|
|
local function pointEq(P1, P2)
|
|
local X1, Y1, Z1 = unpack(P1)
|
|
local X2, Y2, Z2 = unpack(P2)
|
|
|
|
local A1 = mul(X1, Z2)
|
|
local B1 = mul(Y1, Z2)
|
|
local A2 = mul(X2, Z1)
|
|
local B2 = mul(Y2, Z1)
|
|
|
|
return eq(A1, A2) and eq(B1, B2)
|
|
end
|
|
|
|
local function pointIsOnCurve(P1)
|
|
local X1, Y1, Z1 = unpack(P1)
|
|
|
|
local X12 = sqr(X1)
|
|
local Y12 = sqr(Y1)
|
|
local Z12 = sqr(Z1)
|
|
local Z14 = sqr(Z12)
|
|
local a = add(X12, Y12)
|
|
a = mul(a, Z12)
|
|
local b = mul(d, mul(X12, Y12))
|
|
b = add(Z14, b)
|
|
|
|
return eq(a, b)
|
|
end
|
|
|
|
local function mods(d)
|
|
-- w = 5
|
|
local result = d[1] % 32
|
|
|
|
if result >= 16 then
|
|
result = result - 32
|
|
end
|
|
|
|
return result
|
|
end
|
|
|
|
local function NAF(d)
|
|
local t = {}
|
|
local d = {unpack(d)}
|
|
|
|
while d[12] >= 0 and not eq(d, ZERO) do
|
|
if d[1] % 2 == 1 then
|
|
t[#t + 1] = mods(d)
|
|
d = sub192(d, {t[#t], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
|
|
else
|
|
t[#t + 1] = 0
|
|
end
|
|
|
|
d = shr(d)
|
|
end
|
|
|
|
return t
|
|
end
|
|
|
|
local function scalarMul(s, P1)
|
|
local naf = NAF(s)
|
|
local PTable = {P1}
|
|
local P2 = pointDouble(P1)
|
|
|
|
for i = 3, 31, 2 do
|
|
PTable[i] = pointAdd(PTable[i - 2], P2)
|
|
end
|
|
|
|
local Q = {{unpack(ZERO)}, {unpack(ONE)}, {unpack(ONE)}}
|
|
for i = #naf, 1, -1 do
|
|
Q = pointDouble(Q)
|
|
if naf[i] > 0 then
|
|
Q = pointAdd(Q, PTable[naf[i]])
|
|
elseif naf[i] < 0 then
|
|
Q = pointSub(Q, PTable[-naf[i]])
|
|
end
|
|
end
|
|
|
|
return Q
|
|
end
|
|
|
|
for i = 2, 196 do
|
|
GTable[i] = pointDouble(GTable[i - 1])
|
|
end
|
|
|
|
local function scalarMulG(s)
|
|
local result = {{unpack(ZERO)}, {unpack(ONE)}, {unpack(ONE)}}
|
|
local k = 1
|
|
|
|
for i = 1, 12 do
|
|
local w = s[i]
|
|
|
|
for j = 1, 16 do
|
|
if w % 2 == 1 then
|
|
result = pointAdd(result, GTable[k])
|
|
end
|
|
|
|
k = k + 1
|
|
|
|
w = w / 2
|
|
w = w - w % 1
|
|
end
|
|
end
|
|
|
|
return result
|
|
end
|
|
|
|
local function pointEncode(P1)
|
|
P1 = pointScale(P1)
|
|
|
|
local result = {}
|
|
local x, y = unpack(P1)
|
|
|
|
result[1] = x[1] % 2
|
|
|
|
for i = 1, 12 do
|
|
local m = y[i] % 256
|
|
result[2 * i] = m
|
|
result[2 * i + 1] = (y[i] - m) / 256
|
|
end
|
|
|
|
return setmetatable(result, mt)
|
|
end
|
|
|
|
local function pointDecode(enc)
|
|
local y = {}
|
|
for i = 1, 12 do
|
|
y[i] = enc[2 * i]
|
|
y[i] = y[i] + enc[2 * i + 1] * 256
|
|
end
|
|
|
|
local y2 = sqr(y)
|
|
local u = sub(y2, ONE)
|
|
local v = sub(mul(d, y2), ONE)
|
|
local u2 = sqr(u)
|
|
local u3 = mul(u, u2)
|
|
local u5 = mul(u3, u2)
|
|
local v3 = mul(v, sqr(v))
|
|
local w = mul(u5, v3)
|
|
local x = mul(u3, mul(v, expMod(w, pMinusThreeOverFourBinary)))
|
|
|
|
if x[1] % 2 ~= enc[1] then
|
|
x = sub(p, x)
|
|
end
|
|
|
|
local P3 = {x, y, {unpack(ONE)}}
|
|
|
|
return P3
|
|
end
|
|
|
|
return {
|
|
G = G,
|
|
pointAdd = pointAdd,
|
|
pointNeg = pointNeg,
|
|
pointSub = pointSub,
|
|
pointEq = pointEq,
|
|
pointIsOnCurve = pointIsOnCurve,
|
|
scalarMul = scalarMul,
|
|
scalarMulG = scalarMulG,
|
|
pointEncode = pointEncode,
|
|
pointDecode = pointDecode
|
|
}
|
|
end
|
|
preload["ecc"] = function(...)
|
|
local fq = irequire("fq")
|
|
local elliptic = irequire("elliptic")
|
|
local sha256 = require("sha256")
|
|
require("urandom")
|
|
|
|
local q = {1372, 62520, 47765, 8105, 45059, 9616, 65535, 65535, 65535, 65535, 65535, 65532}
|
|
|
|
local sLen = 24
|
|
local eLen = 24
|
|
|
|
local function hashModQ(sk)
|
|
local hash = sha256.hmac({0x00}, sk)
|
|
local x
|
|
repeat
|
|
hash = sha256.digest(hash)
|
|
x = fq.fromBytes(hash)
|
|
until fq.cmp(x, q) <= 0
|
|
|
|
return x
|
|
end
|
|
|
|
local function publicKey(sk)
|
|
local x = hashModQ(sk)
|
|
|
|
local Y = elliptic.scalarMulG(x)
|
|
local pk = elliptic.pointEncode(Y)
|
|
|
|
return pk
|
|
end
|
|
|
|
local function keypair()
|
|
local priv = os.urandom()
|
|
local pub = publicKey(priv)
|
|
return pub, priv
|
|
end
|
|
|
|
local function exchange(sk, pk)
|
|
local Y = elliptic.pointDecode(pk)
|
|
local x = hashModQ(sk)
|
|
|
|
local Z = elliptic.scalarMul(x, Y)
|
|
Z = elliptic.pointScale(Z)
|
|
|
|
local ss = fq.bytes(Z[2])
|
|
local ss = sha256.digest(ss)
|
|
|
|
return ss
|
|
end
|
|
|
|
local function sign(sk, message)
|
|
message = type(message) == "table" and string.char(unpack(message)) or message
|
|
sk = type(sk) == "table" and string.char(unpack(sk)) or sk
|
|
local epoch = tostring(os.epoch("utc"))
|
|
local x = hashModQ(sk)
|
|
local k = hashModQ(message .. epoch .. sk)
|
|
|
|
local R = elliptic.scalarMulG(k)
|
|
R = string.char(unpack(elliptic.pointEncode(R)))
|
|
local e = hashModQ(R .. message)
|
|
local s = fq.sub(k, fq.mul(x, e))
|
|
|
|
e = fq.bytes(e)
|
|
s = fq.bytes(s)
|
|
|
|
local sig = e
|
|
|
|
for i = 1, #s do
|
|
sig[#sig + 1] = s[i]
|
|
end
|
|
|
|
return sig
|
|
end
|
|
|
|
local function verify(pk, message, sig)
|
|
local Y = elliptic.pointDecode(pk)
|
|
local e = {unpack(sig, 1, eLen)}
|
|
local s = {unpack(sig, eLen + 1, eLen + sLen)}
|
|
|
|
e = fq.fromBytes(e)
|
|
s = fq.fromBytes(s)
|
|
|
|
local R = elliptic.pointAdd(elliptic.scalarMulG(s), elliptic.scalarMul(e, Y))
|
|
R = string.char(unpack(elliptic.pointEncode(R)))
|
|
local e2 = hashModQ(R .. message)
|
|
|
|
return fq.eq(e2, e)
|
|
end
|
|
|
|
return {
|
|
publicKey = publicKey,
|
|
exchange = exchange,
|
|
sign = sign,
|
|
verify = verify,
|
|
keypair = keypair
|
|
}
|
|
end
|
|
return irequire |