wip

examples/kzg.ml

@@ -38,9 +38,9 @@ module ToyCurve = struct
       (`Quotient
         (Polynomial.create
            [|
-             Finite_field.(inj_ring (one fp));
-             Finite_field.(inj_ring (zero fp));
-             Finite_field.(inj_ring (one fp));
+             Finite_field.(one fp);
+             Finite_field.(zero fp);
+             Finite_field.(one fp);
            |]))
 
   let g1_x =
@@ -73,12 +73,12 @@ end
 module KZG :
   Polynomial_commitment
     with type common_input = kzg_common_input
-     and type polynomial = (finite_field, ring) typ Polynomial.t
+     and type polynomial = Finite_field.t Polynomial.t
      and type scalar = Finite_field.t
      and type evaluation = Finite_field.t
      and type commitment = Finite_field.t Elliptic_curve.elt = struct
   type common_input = kzg_common_input
-  type polynomial = (finite_field, ring) typ Polynomial.t
+  type polynomial = Finite_field.t Polynomial.t
   type scalar = Finite_field.t
   type evaluation = Finite_field.t
   type commitment = Finite_field.t Elliptic_curve.elt
@@ -87,21 +87,18 @@ module KZG :
   let commit c p =
     assert (Polynomial.degree p < Vector.length c.srs_g1);
     let f x p cm =
-      let n = Option.get Finite_field.(inj_prime_field (inj_field x)) in
+      let n = Option.get Finite_field.(inj_prime_field x) in
       Elliptic_curve.(add c.curve cm (mul c.curve ~n ~p))
     in
     let acc = Elliptic_curve.zero c.curve in
     Polynomial.fold_left2_vec ~f ~acc p c.srs_g1
 
   let prove c p x =
-    let y = Polynomial.(create [| eval p (Finite_field.inj_ring x) |]) in
+    let y = Polynomial.(create [| eval p x |]) in
     let n = Polynomial.(sub p y) in
     let d =
       Polynomial.create
-        [|
-          Finite_field.(inj_ring (one c.finite_field_generator));
-          Finite_field.(inj_ring (neg x));
-        |]
+        [| Finite_field.(one c.finite_field_generator); Finite_field.(neg x) |]
     in
     let q = Polynomial.div n d in
     commit c q
@@ -153,14 +150,14 @@ let c =
 let p =
   Polynomial.create
     [|
-      Finite_field.(inj_ring (random c.finite_field_generator));
-      Finite_field.(inj_ring (zero c.finite_field_generator));
-      Finite_field.(inj_ring (random c.finite_field_generator));
+      Finite_field.(random c.finite_field_generator);
+      Finite_field.(zero c.finite_field_generator);
+      Finite_field.(random c.finite_field_generator);
     |]
 
 let cm = KZG.commit c p
 let x = Finite_field.random c.finite_field_generator
-let y = Finite_field.inj_field (Polynomial.eval p (Finite_field.inj_ring x))
+let y = Polynomial.eval p x
 let pi = KZG.prove c p x
 
 let () =
@@ -170,8 +167,8 @@ let () =
 let p' =
   Polynomial.create
     [|
-      Finite_field.(inj_ring (random c.finite_field_generator));
-      Finite_field.(inj_ring (random c.finite_field_generator));
+      Finite_field.(random c.finite_field_generator);
+      Finite_field.(random c.finite_field_generator);
     |]
 
 let cm' = KZG.commit c p'
@@ -181,7 +178,7 @@ let rhs = KZG.commit c (Polynomial.add p p')
 (* KZG commitments are homomorphic *)
 let () = assert (Elliptic_curve.(equal lhs rhs))
 let x' = Finite_field.random c.finite_field_generator
-let y' = Finite_field.inj_field (Polynomial.eval p' (Finite_field.inj_ring x'))
+let y' = Polynomial.eval p' x'
 let pi' = KZG.prove c p' x'
 let () = assert (KZG.verify c cm' x' y' pi')
 

examples/number_fields.ml

@@ -22,10 +22,7 @@ let () = Printf.eprintf "%s\n" (Polynomial.to_string qq)
 let () = Printf.eprintf "%b\n" (Polynomial.is_irreducible q)
 let qmin : Integer.t Polynomial.t = Polynomial.minimal q
 let () = Printf.eprintf "%s\n" (Polynomial.to_string qmin)
-
-let inj_rat =
-  Polynomial.inj_base_ring ~inj:(fun x ->
-      x |> Integer.inj_rat |> Rational.inj_ring)
+let inj_rat = Polynomial.inj_base_ring ~inj:(fun x -> x |> Integer.inj_rat)
 
 let () =
   Printf.eprintf "%b\n"

examples/pohlig_hellman.ml

@@ -37,7 +37,7 @@ let pohlig_hellman_prime_power_order ~mul ~pow ~dlp_solve_prime ~base ~prime
 let pohlig_hellman ~order ~mul ~pow ~dlp_solve_prime ~base ~group_order h =
   let f base_order_factorization (prime, valuation) =
     let ord = Integer.(pow prime (of_int valuation)) in
-    let n = Integer.(divexact (to_integer group_order) ord) in
+    let n = Integer.(divexact group_order ord) in
     let*? intermediate_log =
       pohlig_hellman_prime_power_order ~mul ~pow ~dlp_solve_prime
         ~base:(pow base n) ~prime (pow h n) ~base_order_factorization
@@ -54,7 +54,7 @@ let pohlig_hellman ~order ~mul ~pow ~dlp_solve_prime ~base ~group_order h =
     else if dvdii (order base) (order h) = 0 then None
     else
       let factors = factor group_order in
-      let base_order = Integer.inj_unique_factorization_domain (order base) in
+      let base_order = order base in
       let logs = Array.map (f (factor base_order)) factors in
       if Array.for_all Option.is_some logs then
         let logs = Vector.of_array (Array.map Option.get logs) in
@@ -148,9 +148,7 @@ let rho_pollard_with_retries ~one ~mul ~pow ~class_x ~group_order ~base h =
 let zn_dlog ~base x =
   with_stack_clean_opt (fun () ->
       let modulo = Integer_mod.get_modulo base in
-      let group_order =
-        Integer.inj_unique_factorization_domain (eulerphi modulo)
-      in
+      let group_order = eulerphi modulo in
       let class_x x =
         Integer.(to_int (modulo (Integer_mod.lift x) (of_int 3)))
       in
@@ -177,10 +175,7 @@ let ell_solve_dlog ~ell ~base x =
         in
         Integer.(to_int (modulo h (of_int 3)))
       in
-      let group_order =
-        Integer.inj_unique_factorization_domain
-          (Elliptic_curve.order_elt ell base)
-      in
+      let group_order = Elliptic_curve.order_elt ell base in
       let mul = Elliptic_curve.add ell in
       let pow p n = Elliptic_curve.mul ell ~n ~p in
       pohlig_hellman

src/pari.ml

@@ -1,6 +1,6 @@
 include Pari_bindings
 
-type ('kind, 'structure) typ = gen
+type 'kind ty = gen
 
 let t = gen
 
@@ -16,7 +16,7 @@ type 'a polynomial = Polynomial of 'a
 type integer_mod = Integer_mod
 type finite_field = Finite_field
 type number_field = Number_field
-type elliptic_curve = Elliptic_curve
+type 'a elliptic_curve = Elliptic_curve of 'a
 
 let register_gc v =
   Gc.finalise_last (fun () -> pari_free Ctypes.(coerce gen (ptr void) v)) v
@@ -48,7 +48,7 @@ end
 module Rational = struct
   type t = gen
 
-  let[@inline] inj_ring x = Fun.id x
+  let of_int i = stoi (Signed.Long.of_int i)
   let[@inline] inj_real x = Fun.id x
   let[@inline] inj_complex x = Fun.id x
   let shift x s = mpshift x (Signed.Long.of_int s)
@@ -60,8 +60,6 @@ module Integer = struct
   let[@inline] inj_rat x = Fun.id x
   let[@inline] inj_real x = Fun.id x
   let[@inline] inj_complex x = Fun.id x
-  let[@inline] inj_unique_factorization_domain x = Fun.id x
-  let to_integer : gen -> t = Fun.id
   let equal x y = equalii x y = 1
   let of_int i = stoi (Signed.Long.of_int i)
   let to_int i = Signed.Long.to_int (itos i)
@@ -341,7 +339,6 @@ module Number_field = struct
   let discriminant nf = nf_get_disc nf
   let z_basis nf = nf_get_zk nf
   let elt a = Vector.(transpose_row (of_array a))
-  let inj_ring x = x
   let add nf a b = nfadd nf a b
   let mul nf a b = nfmul nf a b
 
@@ -362,12 +359,12 @@ module Number_field = struct
 end
 
 type 'a group_structure = {
-  mul : ('a, group) typ -> ('a, group) typ -> ('a, group) typ;
-  pow : ('a, group) typ -> Integer.t -> ('a, group) typ;
-  rand : unit -> ('a, group) typ;
-  hash : ('a, group) typ -> Unsigned.ULong.t;
-  equal : ('a, group) typ -> ('a, group) typ -> bool;
-  equal_identity : ('a, group) typ -> bool;
+  mul : 'a ty -> 'a ty -> 'a ty;
+  pow : 'a ty -> Integer.t -> 'a ty;
+  rand : unit -> 'a ty;
+  hash : 'a ty -> Unsigned.ULong.t;
+  equal : 'a ty -> 'a ty -> bool;
+  equal_identity : 'a ty -> bool;
   bb_group : bb_group Ctypes.structure option;
 }
 
@@ -381,9 +378,6 @@ end
 module Finite_field = struct
   type t = gen
 
-  let[@inline] inj_ring x = Fun.id x
-  let[@inline] inj_field x = Fun.id x
-
   let generator ~order =
     ff_primroot
       (ffgen order Signed.Long.zero)