test: manual rsa

src/management.ml

@@ -33,15 +33,17 @@
    do we re-implement crypto
    or do we re-use secmodules with IPC on a Unix domain socket *)
 
+(*
 type key =
   | Eddsa of Mirage_crypto_ec.Ed25519.(priv * pub)
   | Rsa of Mirage_crypto_pk.Rsa.(priv * pub)
+  *)
 
 let eddsa_online_key_device =
   let finally _key = () in
   Vif.Device.v ~name:"eddsa_online_key" ~finally [] @@ fun () ->
   (* [Mirage_crypto_rng_miou_unix.(initialize (module Pfortuna))] is already done by [Vif.run] *)
-  Eddsa (Mirage_crypto_ec.Ed25519.generate ())
+  Mirage_crypto_ec.Ed25519.generate ()
 
 let rsa_denomination_key_device =
   let finally _key = () in
@@ -49,4 +51,58 @@ let rsa_denomination_key_device =
   let open Mirage_crypto_pk.Rsa in
   let rsa_keysize = 2048 in
   let priv = generate ~bits:rsa_keysize () in
-  Rsa (priv, pub_of_priv priv)
+  (priv, pub_of_priv priv)
+
+(* full-domain-hash ; not impl *)
+let fdh m = Fun.id m
+
+let mod_inverse a n =
+  let open Z in
+  (* extended Euclidean algorithm: returns (g, x, y) s.t. ax + by = g = gcd(a,b) *)
+  let rec extended_gcd a b =
+    if equal b zero then (a, one, zero)
+    else
+      let q, r = ediv_rem a b in
+      let g, x1, y1 = extended_gcd b r in
+      (g, y1, sub x1 (mul q y1))
+  in
+  (* modular inverse of a modulo n, if it exists *)
+  let mod_inverse a n =
+    let g, x, _ = extended_gcd a n in
+    if not (equal g one) then Fmt.failwith "no inverse"
+    else
+      (* normalize result into [0, n-1] *)
+      erem (add x n) n
+  in
+  mod_inverse a n
+
+let test =
+  let finally _key = () in
+  Vif.Device.v ~name:"test" ~finally
+    [ Vif.Device.value rsa_denomination_key_device ]
+  @@ fun (priv, pub) ->
+  let { e; n } : Mirage_crypto_pk.Rsa.pub = pub in
+  let d = priv.d in
+  (* client *)
+  let m = "uhuh ~~!" |> Z.of_bits in
+  let f = fdh m in
+  assert (Z.lt f n);
+  (* random blinding factor *)
+  (* should be in Z_n *)
+  let b = "qwertyuiop" |> Z.of_bits in
+  assert (Z.(lt (abs b) n));
+  let b_inv = mod_inverse b n in
+  assert (Z.(equal Z.one (b * b_inv mod n)));
+  let f' = Z.(f * powm b e n mod n) in
+  Fmt.pr "@. ok step 1. @.";
+  (* server *)
+  let s' = Z.(powm f' d n) in
+  Fmt.pr "@. ok step 2. @.";
+  (* client *)
+  let s = Z.(s' * b_inv mod n) in
+  let m' = Z.(powm s e n) in
+  Fmt.pr "m : `%s`@." (Z.to_string m);
+  Fmt.pr "m': `%s`@." (Z.to_string m');
+  let msg_txt = Z.to_bits m' in
+  Fmt.pr "msg_txt: `%s`@." msg_txt;
+  fun _key -> ()