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@murbard
Created Nov 30, 2020
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(* Quick and dirty proof of concept *)
open Hacl_star
module Timelock : sig
type key = Z.t
type public
type secret
type proof
val generate: unit -> public * secret
val key_with_secret: secret -> time:Z.t -> value:Z.t -> key
val key_without_secret: public -> time:Z.t -> value:Z.t -> key * proof
val verify: public -> time:Z.t -> value:Z.t -> key -> proof -> bool
end = struct
type secret = {p : Z.t ; q : Z.t}
type public = Z.t (* RSA modulus = p * q*)
type proof = Z.t
type key = Z.t
let generate () =
let seed = Bytes.create 128 in
let _ = Hacl.RandomBuffer.randombytes seed in (*TODO don't ignore return value*)
let p = (seed |> Bytes.to_string |> Z.of_bits |> Z.nextprime) in
let _ = Hacl.RandomBuffer.randombytes seed in (*TODO don't ignore return value*)
let q = (seed |> Bytes.to_string |> Z.of_bits |> Z.nextprime) in
Z.(p * q), {p ; q}
let bytes_32 = Bytes.of_string "\032"
let hash_to_prime public time value key =
let s = String.concat "\xff\x00\xff\x00\xff\x00\xff\x00" (List.map Z.to_bits [public ; time ; value ; key]) in
let hash_ : Bytes.t = Bytes.create 32 in
Hacl.Blake2b_256.hash bytes_32 (Bytes.of_string s) hash_;
Z.(nextprime (of_bits (Bytes.to_string hash_)))
let key_with_secret secret ~time ~value =
let phi = Z.((secret.p - one) * (secret.q - one)) in
let e = Z.powm (Z.of_int 2) time phi in
Z.powm value e Z.(secret.p * secret.q)
let key_without_secret public ~time ~value =
let rec aux time v =
if time = Z.zero then v
else aux Z.(time - one) Z.((v * v) mod public)
in
let key = aux time value in
let l = hash_to_prime public time value key in
let pi = ref Z.one and r = ref Z.one in
for i = 1 to (Z.to_int time) do
pi := Z.(!pi * !pi mod public) ;
r := Z.(!r lsl 1);
if Z.(!r >= l) then (
pi := Z.(!pi * value mod public) ;
r := Z.(!r - l)
) else ()
done;
(key, !pi)
let verify public ~time ~value key proof =
let l = hash_to_prime public time value key in
let r = Z.(powm (of_int 2) time l) in
key = Z.((powm proof l public) * (powm value r public) mod public )
end
let main () =
let public,secret = Timelock.generate()
and value = Z.of_int 42
and time = Z.of_int 1000 in
let key = Timelock.key_with_secret secret ~time ~value
and same_key, proof = Timelock.key_without_secret public ~time ~value in
assert (key = same_key) ;
assert (Timelock.verify public ~time ~value key proof) ;
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