diff --git a/onchain/permissionless-arbitration/offchain/.luarc.json b/onchain/permissionless-arbitration/offchain/.luarc.json
new file mode 100644
index 00000000..5f8d0ef7
--- /dev/null
+++ b/onchain/permissionless-arbitration/offchain/.luarc.json
@@ -0,0 +1,13 @@
+{
+    "$schema": "https://raw.githubusercontent.com/sumneko/vscode-lua/master/setting/schema.json",
+
+    "runtime.version": "Lua 5.4",
+
+    "diagnostics": {
+        "enable": true
+    },
+
+    "workspace.library": {
+      "runtime/lua": true
+    }
+}
diff --git a/onchain/permissionless-arbitration/offchain/cryptography/hash.lua b/onchain/permissionless-arbitration/offchain/cryptography/hash.lua
new file mode 100644
index 00000000..b05df9f1
--- /dev/null
+++ b/onchain/permissionless-arbitration/offchain/cryptography/hash.lua
@@ -0,0 +1,114 @@
+-- local keccak_bin = require "cartesi".keccak
+
+local function hex_from_bin(bin)
+    assert(bin:len() == 32)
+    return "0x" .. string.gsub(bin, ".", function(c)
+        return string.format("%02x", string.byte(c))
+    end)
+end
+
+-- local function keccak(...)
+--     return hex_from_bin(keccak_bin(...))
+-- end
+
+local function keccak(...)
+    local args = {...}
+    assert(#args > 0)
+    for _,v in ipairs(args) do
+        assert(v:len() == 66, "string not a hash: " .. v)
+    end
+    local args_str = table.concat(args, " ")
+
+
+    local cmd = string.format(
+        [[cast keccak $(cast --concat-hex %s)]],
+        args_str
+    )
+
+    local handle = io.popen(cmd)
+    assert(handle)
+
+    local digest = handle:read()
+    handle:close()
+    return digest
+end
+
+local internalized_hahes = {}
+local iterateds = {}
+
+local Hash = {}
+Hash.__index = Hash
+
+function Hash:from_digest(digest_hex)
+    assert(type(digest_hex) == "string", digest_hex:len() == 66)
+
+    local x = internalized_hahes[digest_hex]
+    if x then return x end
+
+    local h = {digest_hex = digest_hex}
+    iterateds[h] = {h}
+    setmetatable(h, self)
+    internalized_hahes[digest_hex] = h
+    return h
+end
+
+function Hash:from_digest_bin(digest_bin)
+    local digest_hex = hex_from_bin(digest_bin)
+    return self:from_digest(digest_hex)
+end
+
+function Hash:from_data(data)
+    local digest_hex = keccak(data)
+    return self:from_digest(digest_hex)
+end
+
+function Hash:join(other_hash)
+    assert(getmetatable(other_hash) == Hash)
+    local digest_hex = keccak(self.digest_hex, other_hash.digest_hex)
+    local ret = Hash:from_digest(digest_hex)
+    ret.left = self.digest_hex
+    ret.right = other_hash.digest_hex
+    return ret
+end
+
+function Hash:children()
+    local left, right= self.left, self.right
+    if left and right then
+        return true, left, right
+    else
+        return false
+    end
+end
+
+function Hash:iterated_merkle(level)
+    level = level + 1
+    local iterated = iterateds[self]
+
+    local ret = iterated[level]
+    if ret then return ret end
+
+    local i = #iterated -- at least 1
+    local highest_level = iterated[i]
+    while i < level do
+        highest_level = highest_level:join(highest_level)
+        i = i + 1
+        iterated[i] = highest_level
+    end
+
+    return highest_level
+end
+
+Hash.__tostring = function (x)
+    return x.digest_hex
+end
+
+local zero_bytes32 = "0x0000000000000000000000000000000000000000000000000000000000000000"
+local zero_hash = Hash:from_digest(zero_bytes32)
+
+Hash.zero = zero_hash
+
+function Hash:is_zero()
+    return self == zero_hash
+end
+
+return Hash
diff --git a/onchain/permissionless-arbitration/offchain/cryptography/merkle.lua b/onchain/permissionless-arbitration/offchain/cryptography/merkle.lua
new file mode 100644
index 00000000..8fabcaf4
--- /dev/null
+++ b/onchain/permissionless-arbitration/offchain/cryptography/merkle.lua
@@ -0,0 +1,144 @@
+local function ulte(a, b)
+    return a == b or math.ult(a, b)
+end
+
+local function is_pow2(x)
+    return x & (x-1) == 0
+end
+
+-- Returns number of leading zeroes of x. Shamelessly stolen from the book
+-- Hacker's Delight.
+local function clz(x)
+    if x == 0 then return 64 end
+    local n = 0
+    if (x & 0xFFFFFFFF00000000) == 0 then n = n + 32; x = x << 32 end
+    if (x & 0xFFFF000000000000) == 0 then n = n + 16; x = x << 16 end
+    if (x & 0xFF00000000000000) == 0 then n = n +  8; x = x <<  8 end
+    if (x & 0xF000000000000000) == 0 then n = n +  4; x = x <<  4 end
+    if (x & 0xC000000000000000) == 0 then n = n +  2; x = x <<  2 end
+    if (x & 0x8000000000000000) == 0 then n = n +  1 end
+    return n
+end
+
+-- Returns number of trailing zeroes of x. Shamelessly stolen from the book
+-- Hacker's Delight.
+local function ctz(x)
+    x = x & (~x + 1)
+    return 63 - clz(x)
+end
+
+
+local Slice = {}
+Slice.__index = Slice
+
+function Slice:new(arr, start_idx_inc, end_idx_ex)
+    start_idx_inc = start_idx_inc or 1
+    end_idx_ex = end_idx_ex or #arr + 1
+    assert(start_idx_inc > 0)
+    assert(ulte(start_idx_inc, end_idx_ex))
+    assert(end_idx_ex <= #arr + 1)
+    local s = {
+        arr = arr,
+        start_idx_inc = start_idx_inc,
+        end_idx_ex = end_idx_ex,
+    }
+    setmetatable(s, self)
+    return s
+end
+
+function Slice:slice(si, ei)
+    assert(si > 0)
+    assert(ulte(si, ei))
+    local start_idx_inc = self.start_idx_inc + si - 1
+    local end_idx_ex = self.start_idx_inc + ei - 1
+    assert(ulte(end_idx_ex, self.end_idx_ex))
+    return Slice:new(self.arr, start_idx_inc, end_idx_ex)
+end
+
+function Slice:len()
+    return self.end_idx_ex - self.start_idx_inc
+end
+
+function Slice:get(idx)
+    idx = assert(math.tointeger(idx))
+    assert(idx > 0)
+    local i = self.start_idx_inc + idx - 1
+    assert(i < self.end_idx_ex)
+    return self.arr[i]
+end
+
+local function semi_sum(a, b)
+    assert(ulte(a, b))
+    return a + (b - a) // 2
+end
+
+function Slice:find_cell_containing(elem)
+    local l, r = 1, self:len()
+    while l < r do
+        local m = semi_sum(l, r)
+        if self:get(m).accumulated_count < elem then
+            l = m + 1
+        else
+            r = m
+        end
+    end
+    if l == self:len() then
+        assert(elem <= self:get(l).accumulated_count + 1)
+    end
+    return l
+end
+
+
+local MerkleBuilder = {}
+MerkleBuilder.__index = MerkleBuilder
+
+function MerkleBuilder:new()
+    local m = {
+        leafs = {}
+    }
+    setmetatable(m, self)
+    return m
+end
+
+function MerkleBuilder:add(hash, rep)
+    rep = rep or 1
+
+    local last_accumulated_count
+    if self.leafs[#self.leafs] then
+        last_accumulated_count = self.leafs[#self.leafs].accumulated_count
+    else
+        last_accumulated_count = 0
+    end
+
+    local accumulated_count = rep + last_accumulated_count
+
+    table.insert(self.leafs, {hash = hash, accumulated_count = accumulated_count})
+end
+
+local function merkle(leafs, log2size, stride)
+    local first_time =  stride * (1 << log2size) + 1
+    local last_time = (stride + 1) * (1 << log2size)
+
+    local first_cell = leafs:find_cell_containing(first_time)
+    local last_cell = leafs:find_cell_containing(last_time)
+
+    if first_cell == last_cell then
+        return leafs:get(first_cell).hash:iterated_merkle(log2size)
+    end
+
+    local slice = leafs:slice(first_cell, last_cell + 1)
+    local hash_left = merkle(slice, log2size - 1, 2 * stride)
+    local hash_right = merkle(slice, log2size - 1, 2 * stride + 1)
+
+    return hash_left:join(hash_right)
+end
+
+function MerkleBuilder:build()
+    local last = assert(self.leafs[#self.leafs])
+    local count = last.accumulated_count
+    assert(is_pow2(count))
+    local log2size = ctz(count)
+    return merkle(Slice:new(self.leafs), log2size, 0)
+end
+
+return MerkleBuilder