pk/dh.ml at main · gazagnaire.org/ocaml-crypto

upstream: https://github.com/mirage/mirage-crypto
ocaml-crypto / pk / dh.ml
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  1open Crypto.Uncommon
  2open Common
  3open Result.Syntax
  4
  5exception Invalid_key
  6
  7type group = {
  8  p : Z.t; (* The prime modulus *)
  9  gg : Z.t; (* Group generator *)
 10  q : Z.t option; (* `gg`'s order, maybe *)
 11}
 12
 13let group ~p ~gg ?q () =
 14  let* () =
 15    guard
 16      (Z.(p > zero && is_odd p) && Z_extra.pseudoprime p)
 17      (`Msg "invalid prime")
 18  in
 19  let* () = guard Z.(one < gg && gg < p) (`Msg "invalid generator") in
 20  Ok { p; gg; q }
 21
 22type secret = { group : group; x : Z.t }
 23
 24(*
 25 * Estimates of equivalent-strength exponent sizes for the moduli sizes.
 26 * 2048-8192 are taken from "Negotiated FF DHE Parameters for TLS."
 27 * Sizes above and below are further guesswork.
 28 *)
 29let exp_equivalent =
 30  [
 31    (1024, 180); (2048, 225); (3072, 275); (4096, 325); (6144, 375); (8192, 400);
 32  ]
 33
 34and exp_equivalent_max = 512
 35
 36let exp_size bits =
 37  try snd @@ List.find (fun (g, _) -> g >= bits) exp_equivalent
 38  with Not_found -> exp_equivalent_max
 39
 40let modulus_size { p; _ } = Z.numbits p
 41
 42(*
 43 * Current thinking:
 44 * g^y < 0 || g^y >= p : obviously not computed mod p
 45 * g^y = 0 || g^y = 1  : shared secret is 0, resp. 1
 46 * g^y = p - 1         : order of g^y is 2
 47 * g^y = g             : y mod (p-1) is 1
 48 *)
 49let bad_public_key { p; gg; _ } ggx =
 50  ggx <= Z.one || (ggx >= Z.(pred p)) || ggx = gg
 51
 52let valid_secret { p; _ } s = Z.(one < s && s < p)
 53
 54let key_of_secret_z ({ p; gg; _ } as group) x =
 55  if valid_secret group x then
 56    match Z.(powm_sec gg x p) with
 57    | ggx when bad_public_key group ggx -> raise_notrace Invalid_key
 58    | ggx -> ({ group; x }, Z_extra.to_octets_be ggx)
 59  else raise_notrace Invalid_key
 60
 61let key_of_secret group ~s =
 62  (* catches Invalid_private_key and re-raises with exception trace: *)
 63  try key_of_secret_z group (Z_extra.of_octets_be s)
 64  with Invalid_key -> raise Invalid_key
 65
 66(* XXX
 67 * - slightly weird distribution when bits > |q|
 68 * - exponentiation time
 69 *)
 70let rec gen_key ?g ?bits ({ p; q; _ } as group) =
 71  let pb = Z.numbits p in
 72  let s =
 73    imin
 74      (Option.value bits ~default:pb |> exp_size)
 75      (Option.fold ~none:pb ~some:Z.numbits q)
 76    |> Z_extra.gen_bits ?g ~msb:1
 77  in
 78  try key_of_secret_z group s with Invalid_key -> gen_key ?g ?bits group
 79
 80let shared { group; x } cs =
 81  match Z_extra.of_octets_be cs with
 82  | ggy when bad_public_key group ggy -> None
 83  | ggy -> Some (Z_extra.to_octets_be (Z.powm_sec ggy x group.p))
 84
 85(* Finds a safe prime with [p = 2q + 1] and [2^q = 1 mod p]. *)
 86let rec gen_group ?g ~bits () =
 87  let gg = Z.(~$2) and q, p = Z_extra.safe_prime ?g (imax bits 1) in
 88  if Z.(powm gg q p = one) then { p; gg; q = Some q } else gen_group ?g ~bits ()
 89
 90module Group = struct
 91  (* Safe-prime-style group: p = 2q + 1 && gg = 2 && gg^q = 1 mod p *)
 92  let s_group ~p =
 93    let p = Z_extra.of_octets_be p in
 94    { p; gg = Z.(~$2); q = Some Z.(pred p / ~$2) }
 95
 96  (* Any old group. *)
 97  let group ~p ~gg ~q =
 98    let f = Z_extra.of_octets_be in
 99    { p = f p; gg = f gg; q = Some (f q) }
100
101  (* RFC2409 *)
102
103  let oakley_1 =
104    (* 2^768 - 2 ^704 - 1 + 2^64 * { [2^638 pi] + 149686 } *)
105    s_group
106      ~p:
107        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x3A\x36\x20\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
108
109  let oakley_2 =
110    (* 2^1024 - 2^960 - 1 + 2^64 * { [2^894 pi] + 129093 }. *)
111    s_group
112      ~p:
113        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6x49\x28\x66\x51\xEC\xE6\x53\x81\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
114
115  (* RFC3526 *)
116
117  let oakley_5 =
118    (* 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 } *)
119    s_group
120      ~p:
121        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6\x49\x28\x66\x51\xEC\xE4\x5B\x3D\xC2\x00\x7C\xB8\xA1\x63\xBF\x05\x98\xDA\x48\x36\x1C\x55\xD3\x9A\x69\x16\x3F\xA8\xFD\x24\xCF\x5F\x83\x65\x5D\x23\xDC\xA3\xAD\x96\x1C\x62\xF3\x56\x20\x85\x52\xBB\x9E\xD5\x29\x07\x70\x96\x96\x6D\x67\x0C\x35\x4E\x4A\xBC\x98\x04\xF1\x74\x6C\x08\xCA\x23\x73\x27\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
122
123  let oakley_14 =
124    (* 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 } *)
125    s_group
126      ~p:
127        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6\x49\x28\x66\x51\xEC\xE4\x5B\x3D\xC2\x00\x7C\xB8\xA1\x63\xBF\x05\x98\xDA\x48\x36\x1C\x55\xD3\x9A\x69\x16\x3F\xA8\xFD\x24\xCF\x5F\x83\x65\x5D\x23\xDC\xA3\xAD\x96\x1C\x62\xF3\x56\x20\x85\x52\xBB\x9E\xD5\x29\x07\x70\x96\x96\x6D\x67\x0C\x35\x4E\x4A\xBC\x98\x04\xF1\x74\x6C\x08\xCA\x18\x21\x7C\x32\x90\x5E\x46\x2E\x36\xCE\x3B\xE3\x9E\x77\x2C\x18\x0E\x86\x03\x9B\x27\x83\xA2\xEC\x07\xA2\x8F\xB5\xC5\x5D\xF0\x6F\x4C\x52\xC9\xDE\x2B\xCB\xF6\x95\x58\x17\x18\x39\x95\x49\x7C\xEA\x95\x6A\xE5\x15\xD2\x26\x18\x98\xFA\x05\x10\x15\x72\x8E\x5A\x8A\xAC\xAA\x68\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
128
129  let oakley_15 =
130    (* 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 } *)
131    s_group
132      ~p:
133        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6\x49\x28\x66\x51\xEC\xE4\x5B\x3D\xC2\x00\x7C\xB8\xA1\x63\xBF\x05\x98\xDA\x48\x36\x1C\x55\xD3\x9A\x69\x16\x3F\xA8\xFD\x24\xCF\x5F\x83\x65\x5D\x23\xDC\xA3\xAD\x96\x1C\x62\xF3\x56\x20\x85\x52\xBB\x9E\xD5\x29\x07\x70\x96\x96\x6D\x67\x0C\x35\x4E\x4A\xBC\x98\x04\xF1\x74\x6C\x08\xCA\x18\x21\x7C\x32\x90\x5E\x46\x2E\x36\xCE\x3B\xE3\x9E\x77\x2C\x18\x0E\x86\x03\x9B\x27\x83\xA2\xEC\x07\xA2\x8F\xB5\xC5\x5D\xF0\x6F\x4C\x52\xC9\xDE\x2B\xCB\xF6\x95\x58\x17\x18\x39\x95\x49\x7C\xEA\x95\x6A\xE5\x15\xD2\x26\x18\x98\xFA\x05\x10\x15\x72\x8E\x5A\x8A\xAA\xC4\x2D\xAD\x33\x17\x0D\x04\x50\x7A\x33\xA8\x55\x21\xAB\xDF\x1C\xBA\x64\xEC\xFB\x85\x04\x58\xDB\xEF\x0A\x8A\xEA\x71\x57\x5D\x06\x0C\x7D\xB3\x97\x0F\x85\xA6\xE1\xE4\xC7\xAB\xF5\xAE\x8C\xDB\x09\x33\xD7\x1E\x8C\x94\xE0\x4A\x25\x61\x9D\xCE\xE3\xD2\x26\x1A\xD2\xEE\x6B\xF1\x2F\xFA\x06\xD9\x8A\x08\x64\xD8\x76\x02\x73\x3E\xC8\x6A\x64\x52\x1F\x2B\x18\x17\x7B\x20\x0C\xBB\xE1\x17\x57\x7A\x61\x5D\x6C\x77\x09\x88\xC0\xBA\xD9\x46\xE2\x08\xE2\x4F\xA0\x74\xE5\xAB\x31\x43\xDB\x5B\xFC\xE0\xFD\x10\x8E\x4B\x82\xD1\x20\xA9\x3A\xD2\xCA\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
134
135  let oakley_16 =
136    (* 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 } *)
137    s_group
138      ~p:
139        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6\x49\x28\x66\x51\xEC\xE4\x5B\x3D\xC2\x00\x7C\xB8\xA1\x63\xBF\x05\x98\xDA\x48\x36\x1C\x55\xD3\x9A\x69\x16\x3F\xA8\xFD\x24\xCF\x5F\x83\x65\x5D\x23\xDC\xA3\xAD\x96\x1C\x62\xF3\x56\x20\x85\x52\xBB\x9E\xD5\x29\x07\x70\x96\x96\x6D\x67\x0C\x35\x4E\x4A\xBC\x98\x04\xF1\x74\x6C\x08\xCA\x18\x21\x7C\x32\x90\x5E\x46\x2E\x36\xCE\x3B\xE3\x9E\x77\x2C\x18\x0E\x86\x03\x9B\x27\x83\xA2\xEC\x07\xA2\x8F\xB5\xC5\x5D\xF0\x6F\x4C\x52\xC9\xDE\x2B\xCB\xF6\x95\x58\x17\x18\x39\x95\x49\x7C\xEA\x95\x6A\xE5\x15\xD2\x26\x18\x98\xFA\x05\x10\x15\x72\x8E\x5A\x8A\xAA\xC4\x2D\xAD\x33\x17\x0D\x04\x50\x7A\x33\xA8\x55\x21\xAB\xDF\x1C\xBA\x64\xEC\xFB\x85\x04\x58\xDB\xEF\x0A\x8A\xEA\x71\x57\x5D\x06\x0C\x7D\xB3\x97\x0F\x85\xA6\xE1\xE4\xC7\xAB\xF5\xAE\x8C\xDB\x09\x33\xD7\x1E\x8C\x94\xE0\x4A\x25\x61\x9D\xCE\xE3\xD2\x26\x1A\xD2\xEE\x6B\xF1\x2F\xFA\x06\xD9\x8A\x08\x64\xD8\x76\x02\x73\x3E\xC8\x6A\x64\x52\x1F\x2B\x18\x17\x7B\x20\x0C\xBB\xE1\x17\x57\x7A\x61\x5D\x6C\x77\x09\x88\xC0\xBA\xD9\x46\xE2\x08\xE2\x4F\xA0\x74\xE5\xAB\x31\x43\xDB\x5B\xFC\xE0\xFD\x10\x8E\x4B\x82\xD1\x20\xA9\x21\x08\x01\x1A\x72\x3C\x12\xA7\x87\xE6\xD7\x88\x71\x9A\x10\xBD\xBA\x5B\x26\x99\xC3\x27\x18\x6A\xF4\xE2\x3C\x1A\x94\x68\x34\xB6\x15\x0B\xDA\x25\x83\xE9\xCA\x2A\xD4\x4C\xE8\xDB\xBB\xC2\xDB\x04\xDE\x8E\xF9\x2E\x8E\xFC\x14\x1F\xBE\xCA\xA6\x28\x7C\x59\x47\x4E\x6B\xC0\x5D\x99\xB2\x96\x4F\xA0\x90\xC3\xA2\x23\x3B\xA1\x86\x51\x5B\xE7\xED\x1F\x61\x29\x70\xCE\xE2\xD7\xAF\xB8\x1B\xDD\x76\x21\x70\x48\x1C\xD0\x06\x91\x27\xD5\xB0\x5A\xA9\x93\xB4\xEA\x98\x8D\x8F\xDD\xC1\x86\xFF\xB7\xDC\x90\xA6\xC0\x8F\x4D\xF4\x35\xC9\x34\x06\x31\x99\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
140
141  let oakley_17 =
142    (* 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 } *)
143    s_group
144      ~p:
145        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6\x49\x28\x66\x51\xEC\xE4\x5B\x3D\xC2\x00\x7C\xB8\xA1\x63\xBF\x05\x98\xDA\x48\x36\x1C\x55\xD3\x9A\x69\x16\x3F\xA8\xFD\x24\xCF\x5F\x83\x65\x5D\x23\xDC\xA3\xAD\x96\x1C\x62\xF3\x56\x20\x85\x52\xBB\x9E\xD5\x29\x07\x70\x96\x96\x6D\x67\x0C\x35\x4E\x4A\xBC\x98\x04\xF1\x74\x6C\x08\xCA\x18\x21\x7C\x32\x90\x5E\x46\x2E\x36\xCE\x3B\xE3\x9E\x77\x2C\x18\x0E\x86\x03\x9B\x27\x83\xA2\xEC\x07\xA2\x8F\xB5\xC5\x5D\xF0\x6F\x4C\x52\xC9\xDE\x2B\xCB\xF6\x95\x58\x17\x18\x39\x95\x49\x7C\xEA\x95\x6A\xE5\x15\xD2\x26\x18\x98\xFA\x05\x10\x15\x72\x8E\x5A\x8A\xAA\xC4\x2D\xAD\x33\x17\x0D\x04\x50\x7A\x33\xA8\x55\x21\xAB\xDF\x1C\xBA\x64\xEC\xFB\x85\x04\x58\xDB\xEF\x0A\x8A\xEA\x71\x57\x5D\x06\x0C\x7D\xB3\x97\x0F\x85\xA6\xE1\xE4\xC7\xAB\xF5\xAE\x8C\xDB\x09\x33\xD7\x1E\x8C\x94\xE0\x4A\x25\x61\x9D\xCE\xE3\xD2\x26\x1A\xD2\xEE\x6B\xF1\x2F\xFA\x06\xD9\x8A\x08\x64\xD8\x76\x02\x73\x3E\xC8\x6A\x64\x52\x1F\x2B\x18\x17\x7B\x20\x0C\xBB\xE1\x17\x57\x7A\x61\x5D\x6C\x77\x09\x88\xC0\xBA\xD9\x46\xE2\x08\xE2\x4F\xA0\x74\xE5\xAB\x31\x43\xDB\x5B\xFC\xE0\xFD\x10\x8E\x4B\x82\xD1\x20\xA9\x21\x08\x01\x1A\x72\x3C\x12\xA7\x87\xE6\xD7\x88\x71\x9A\x10\xBD\xBA\x5B\x26\x99\xC3\x27\x18\x6A\xF4\xE2\x3C\x1A\x94\x68\x34\xB6\x15\x0B\xDA\x25\x83\xE9\xCA\x2A\xD4\x4C\xE8\xDB\xBB\xC2\xDB\x04\xDE\x8E\xF9\x2E\x8E\xFC\x14\x1F\xBE\xCA\xA6\x28\x7C\x59\x47\x4E\x6B\xC0\x5D\x99\xB2\x96\x4F\xA0\x90\xC3\xA2\x23\x3B\xA1\x86\x51\x5B\xE7\xED\x1F\x61\x29\x70\xCE\xE2\xD7\xAF\xB8\x1B\xDD\x76\x21\x70\x48\x1C\xD0\x06\x91\x27\xD5\xB0\x5A\xA9\x93\xB4\xEA\x98\x8D\x8F\xDD\xC1\x86\xFF\xB7\xDC\x90\xA6\xC0\x8F\x4D\xF4\x35\xC9\x34\x02\x84\x92\x36\xC3\xFA\xB4\xD2\x7C\x70\x26\xC1\xD4\xDC\xB2\x60\x26\x46\xDE\xC9\x75\x1E\x76\x3D\xBA\x37\xBD\xF8\xFF\x94\x06\xAD\x9E\x53\x0E\xE5\xDB\x38\x2F\x41\x30\x01\xAE\xB0\x6A\x53\xED\x90\x27\xD8\x31\x17\x97\x27\xB0\x86\x5A\x89\x18\xDA\x3E\xDB\xEB\xCF\x9B\x14\xED\x44\xCE\x6C\xBA\xCE\xD4\xBB\x1B\xDB\x7F\x14\x47\xE6\xCC\x25\x4B\x33\x20\x51\x51\x2B\xD7\xAF\x42\x6F\xB8\xF4\x01\x37\x8C\xD2\xBF\x59\x83\xCA\x01\xC6\x4B\x92\xEC\xF0\x32\xEA\x15\xD1\x72\x1D\x03\xF4\x82\xD7\xCE\x6E\x74\xFE\xF6\xD5\x5E\x70\x2F\x46\x98\x0C\x82\xB5\xA8\x40\x31\x90\x0B\x1C\x9E\x59\xE7\xC9\x7F\xBE\xC7\xE8\xF3\x23\xA9\x7A\x7E\x36\xCC\x88\xBE\x0F\x1D\x45\xB7\xFF\x58\x5A\xC5\x4B\xD4\x07\xB2\x2B\x41\x54\xAA\xCC\x8F\x6D\x7E\xBF\x48\xE1\xD8\x14\xCC\x5E\xD2\x0F\x80\x37\xE0\xA7\x97\x15\xEE\xF2\x9B\xE3\x28\x06\xA1\xD5\x8B\xB7\xC5\xDA\x76\xF5\x50\xAA\x3D\x8A\x1F\xBF\xF0\xEB\x19\xCC\xB1\xA3\x13\xD5\x5C\xDA\x56\xC9\xEC\x2E\xF2\x96\x32\x38\x7F\xE8\xD7\x6E\x3C\x04\x68\x04\x3E\x8F\x66\x3F\x48\x60\xEE\x12\xBF\x2D\x5B\x0B\x74\x74\xD6\xE6\x94\xF9\x1E\x6D\xCC\x40\x24\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
146
147  let oakley_18 =
148    (* 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 } *)
149    s_group
150      ~p:
151        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xC9\x0F\xDA\xA2\x21\x68\xC2\x34\xC4\xC6\x62\x8B\x80\xDC\x1C\xD1\x29\x02\x4E\x08\x8A\x67\xCC\x74\x02\x0B\xBE\xA6\x3B\x13\x9B\x22\x51\x4A\x08\x79\x8E\x34\x04\xDD\xEF\x95\x19\xB3\xCD\x3A\x43\x1B\x30\x2B\x0A\x6D\xF2\x5F\x14\x37\x4F\xE1\x35\x6D\x6D\x51\xC2\x45\xE4\x85\xB5\x76\x62\x5E\x7E\xC6\xF4\x4C\x42\xE9\xA6\x37\xED\x6B\x0B\xFF\x5C\xB6\xF4\x06\xB7\xED\xEE\x38\x6B\xFB\x5A\x89\x9F\xA5\xAE\x9F\x24\x11\x7C\x4B\x1F\xE6\x49\x28\x66\x51\xEC\xE4\x5B\x3D\xC2\x00\x7C\xB8\xA1\x63\xBF\x05\x98\xDA\x48\x36\x1C\x55\xD3\x9A\x69\x16\x3F\xA8\xFD\x24\xCF\x5F\x83\x65\x5D\x23\xDC\xA3\xAD\x96\x1C\x62\xF3\x56\x20\x85\x52\xBB\x9E\xD5\x29\x07\x70\x96\x96\x6D\x67\x0C\x35\x4E\x4A\xBC\x98\x04\xF1\x74\x6C\x08\xCA\x18\x21\x7C\x32\x90\x5E\x46\x2E\x36\xCE\x3B\xE3\x9E\x77\x2C\x18\x0E\x86\x03\x9B\x27\x83\xA2\xEC\x07\xA2\x8F\xB5\xC5\x5D\xF0\x6F\x4C\x52\xC9\xDE\x2B\xCB\xF6\x95\x58\x17\x18\x39\x95\x49\x7C\xEA\x95\x6A\xE5\x15\xD2\x26\x18\x98\xFA\x05\x10\x15\x72\x8E\x5A\x8A\xAA\xC4\x2D\xAD\x33\x17\x0D\x04\x50\x7A\x33\xA8\x55\x21\xAB\xDF\x1C\xBA\x64\xEC\xFB\x85\x04\x58\xDB\xEF\x0A\x8A\xEA\x71\x57\x5D\x06\x0C\x7D\xB3\x97\x0F\x85\xA6\xE1\xE4\xC7\xAB\xF5\xAE\x8C\xDB\x09\x33\xD7\x1E\x8C\x94\xE0\x4A\x25\x61\x9D\xCE\xE3\xD2\x26\x1A\xD2\xEE\x6B\xF1\x2F\xFA\x06\xD9\x8A\x08\x64\xD8\x76\x02\x73\x3E\xC8\x6A\x64\x52\x1F\x2B\x18\x17\x7B\x20\x0C\xBB\xE1\x17\x57\x7A\x61\x5D\x6C\x77\x09\x88\xC0\xBA\xD9\x46\xE2\x08\xE2\x4F\xA0\x74\xE5\xAB\x31\x43\xDB\x5B\xFC\xE0\xFD\x10\x8E\x4B\x82\xD1\x20\xA9\x21\x08\x01\x1A\x72\x3C\x12\xA7\x87\xE6\xD7\x88\x71\x9A\x10\xBD\xBA\x5B\x26\x99\xC3\x27\x18\x6A\xF4\xE2\x3C\x1A\x94\x68\x34\xB6\x15\x0B\xDA\x25\x83\xE9\xCA\x2A\xD4\x4C\xE8\xDB\xBB\xC2\xDB\x04\xDE\x8E\xF9\x2E\x8E\xFC\x14\x1F\xBE\xCA\xA6\x28\x7C\x59\x47\x4E\x6B\xC0\x5D\x99\xB2\x96\x4F\xA0\x90\xC3\xA2\x23\x3B\xA1\x86\x51\x5B\xE7\xED\x1F\x61\x29\x70\xCE\xE2\xD7\xAF\xB8\x1B\xDD\x76\x21\x70\x48\x1C\xD0\x06\x91\x27\xD5\xB0\x5A\xA9\x93\xB4\xEA\x98\x8D\x8F\xDD\xC1\x86\xFF\xB7\xDC\x90\xA6\xC0\x8F\x4D\xF4\x35\xC9\x34\x02\x84\x92\x36\xC3\xFA\xB4\xD2\x7C\x70\x26\xC1\xD4\xDC\xB2\x60\x26\x46\xDE\xC9\x75\x1E\x76\x3D\xBA\x37\xBD\xF8\xFF\x94\x06\xAD\x9E\x53\x0E\xE5\xDB\x38\x2F\x41\x30\x01\xAE\xB0\x6A\x53\xED\x90\x27\xD8\x31\x17\x97\x27\xB0\x86\x5A\x89\x18\xDA\x3E\xDB\xEB\xCF\x9B\x14\xED\x44\xCE\x6C\xBA\xCE\xD4\xBB\x1B\xDB\x7F\x14\x47\xE6\xCC\x25\x4B\x33\x20\x51\x51\x2B\xD7\xAF\x42\x6F\xB8\xF4\x01\x37\x8C\xD2\xBF\x59\x83\xCA\x01\xC6\x4B\x92\xEC\xF0\x32\xEA\x15\xD1\x72\x1D\x03\xF4\x82\xD7\xCE\x6E\x74\xFE\xF6\xD5\x5E\x70\x2F\x46\x98\x0C\x82\xB5\xA8\x40\x31\x90\x0B\x1C\x9E\x59\xE7\xC9\x7F\xBE\xC7\xE8\xF3\x23\xA9\x7A\x7E\x36\xCC\x88\xBE\x0F\x1D\x45\xB7\xFF\x58\x5A\xC5\x4B\xD4\x07\xB2\x2B\x41\x54\xAA\xCC\x8F\x6D\x7E\xBF\x48\xE1\xD8\x14\xCC\x5E\xD2\x0F\x80\x37\xE0\xA7\x97\x15\xEE\xF2\x9B\xE3\x28\x06\xA1\xD5\x8B\xB7\xC5\xDA\x76\xF5\x50\xAA\x3D\x8A\x1F\xBF\xF0\xEB\x19\xCC\xB1\xA3\x13\xD5\x5C\xDA\x56\xC9\xEC\x2E\xF2\x96\x32\x38\x7F\xE8\xD7\x6E\x3C\x04\x68\x04\x3E\x8F\x66\x3F\x48\x60\xEE\x12\xBF\x2D\x5B\x0B\x74\x74\xD6\xE6\x94\xF9\x1E\x6D\xBE\x11\x59\x74\xA3\x92\x6F\x12\xFE\xE5\xE4\x38\x77\x7C\xB6\xA9\x32\xDF\x8C\xD8\xBE\xC4\xD0\x73\xB9\x31\xBA\x3B\xC8\x32\xB6\x8D\x9D\xD3\x00\x74\x1F\xA7\xBF\x8A\xFC\x47\xED\x25\x76\xF6\x93\x6B\xA4\x24\x66\x3A\xAB\x63\x9C\x5A\xE4\xF5\x68\x34\x23\xB4\x74\x2B\xF1\xC9\x78\x23\x8F\x16\xCB\xE3\x9D\x65\x2D\xE3\xFD\xB8\xBE\xFC\x84\x8A\xD9\x22\x22\x2E\x04\xA4\x03\x7C\x07\x13\xEB\x57\xA8\x1A\x23\xF0\xC7\x34\x73\xFC\x64\x6C\xEA\x30\x6B\x4B\xCB\xC8\x86\x2F\x83\x85\xDD\xFA\x9D\x4B\x7F\xA2\xC0\x87\xE8\x79\x68\x33\x03\xED\x5B\xDD\x3A\x06\x2B\x3C\xF5\xB3\xA2\x78\xA6\x6D\x2A\x13\xF8\x3F\x44\xF8\x2D\xDF\x31\x0E\xE0\x74\xAB\x6A\x36\x45\x97\xE8\x99\xA0\x25\x5D\xC1\x64\xF3\x1C\xC5\x08\x46\x85\x1D\xF9\xAB\x48\x19\x5D\xED\x7E\xA1\xB1\xD5\x10\xBD\x7E\xE7\x4D\x73\xFA\xF3\x6B\xC3\x1E\xCF\xA2\x68\x35\x90\x46\xF4\xEB\x87\x9F\x92\x40\x09\x43\x8B\x48\x1C\x6C\xD7\x88\x9A\x00\x2E\xD5\xEE\x38\x2B\xC9\x19\x0D\xA6\xFC\x02\x6E\x47\x95\x58\xE4\x47\x56\x77\xE9\xAA\x9E\x30\x50\xE2\x76\x56\x94\xDF\xC8\x1F\x56\xE8\x80\xB9\x6E\x71\x60\xC9\x80\xDD\x98\xED\xD3\xDF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
152
153  (* RFC5114 *)
154
155  (* 1024-bit, 160-bit subgroup *)
156  let rfc_5114_1 =
157    let p =
158      "\xB1\x0B\x8F\x96\xA0\x80\xE0\x1D\xDE\x92\xDE\x5E\xAE\x5D\x54\xEC\x52\xC9\x9F\xBC\xFB\x06\xA3\xC6\x9A\x6A\x9D\xCA\x52\xD2\x3B\x61\x60\x73\xE2\x86\x75\xA2\x3D\x18\x98\x38\xEF\x1E\x2E\xE6\x52\xC0\x13\xEC\xB4\xAE\xA9\x06\x11\x23\x24\x97\x5C\x3C\xD4\x9B\x83\xBF\xAC\xCB\xDD\x7D\x90\xC4\xBD\x70\x98\x48\x8E\x9C\x21\x9A\x73\x72\x4E\xFF\xD6\xFA\xE5\x64\x47\x38\xFA\xA3\x1A\x4F\xF5\x5B\xCC\xC0\xA1\x51\xAF\x5F\x0D\xC8\xB4\xBD\x45\xBF\x37\xDF\x36\x5C\x1A\x65\xE6\x8C\xFD\xA7\x6D\x4D\xA7\x08\xDF\x1F\xB2\xBC\x2E\x4A\x43\x71"
159    and gg =
160      "\xA4\xD1\xCB\xD5\xC3\xFD\x34\x12\x67\x65\xA4\x42\xEF\xB9\x99\x05\xF8\x10\x4D\xD2\x58\xAC\x50\x7F\xD6\x40\x6C\xFF\x14\x26\x6D\x31\x26\x6F\xEA\x1E\x5C\x41\x56\x4B\x77\x7E\x69\x0F\x55\x04\xF2\x13\x16\x02\x17\xB4\xB0\x1B\x88\x6A\x5E\x91\x54\x7F\x9E\x27\x49\xF4\xD7\xFB\xD7\xD3\xB9\xA9\x2E\xE1\x90\x9D\x0D\x22\x63\xF8\x0A\x76\xA6\xA2\x4C\x08\x7A\x09\x1F\x53\x1D\xBF\x0A\x01\x69\xB6\xA2\x8A\xD6\x62\xA4\xD1\x8E\x73\xAF\xA3\x2D\x77\x9D\x59\x18\xD0\x8B\xC8\x85\x8F\x4D\xCE\xF9\x7C\x2A\x24\\x85\x5E\x6E\xEB\x22\xB3\xB2\xE5"
161    and q =
162      "\xF5\x18\xAA\x87\x81\xA8\xDF\x27\x8A\xBA\x4E\x7D\x64\xB7\xCB\x9D\x49\x46\x23\x53"
163    in
164    group ~p ~gg ~q
165
166  (* 2048-bit, 224-bit subgroup *)
167  let rfc_5114_2 =
168    let p =
169      "\xAD\x10\x7E\x1E\x91\x23\xA9\xD0\xD6\x60\xFA\xA7\x95\x59\xC5\x1F\xA2\x0D\x64\xE5\x68\x3B\x9F\xD1\xB5\x4B\x15\x97\xB6\x1D\x0A\x75\xE6\xFA\x14\x1D\xF9\x5A\x56\xDB\xAF\x9A\x3C\x40\x7B\xA1\xDF\x15\xEB\x3D\x68\x8A\x30\x9C\x18\x0E\x1D\xE6\xB8\x5A\x12\x74\xA0\xA6\x6D\x3F\x81\x52\xAD\x6A\xC2\x12\x90\x37\xC9\xED\xEF\xDA\x4D\xF8\xD9\x1E\x8F\xEF\x55\xB7\x39\x4B\x7A\xD5\xB7\xD0\xB6\xC1\x22\x07\xC9\xF9\x8D\x11\xED\x34\xDB\xF6\xC6\xBA\x0B\x2C\x8B\xBC\x27\xBE\x6A\x00\xE0\xA0\xB9\xC4\x97\x08\xB3\xBF\x8A\x31\x70\x91\x88\x36\x81\x28\x61\x30\xBC\x89\x85\xDB\x16\x02\xE7\x14\x41\x5D\x93\x30\x27\x82\x73\xC7\xDE\x31\xEF\xDC\x73\x10\xF7\x12\x1F\xD5\xA0\x74\x15\x98\x7D\x9A\xDC\x0A\x48\x6D\xCD\xF9\x3A\xCC\x44\x32\x83\x87\x31\x5D\x75\xE1\x98\xC6\x41\xA4\x80\xCD\x86\xA1\xB9\xE5\x87\xE8\xBE\x60\xE6\x9C\xC9\x28\xB2\xB9\xC5\x21\x72\xE4\x13\x04\x2E\x9B\x23\xF1\x0B\x0E\x16\xE7\x97\x63\xC9\xB5\x3D\xCF\x4B\xA8\x0A\x29\xE3\xFB\x73\xC1\x6B\x8E\x75\xB9\x7E\xF3\x63\xE2\xFF\xA3\x1F\x71\xCF\x9D\xE5\x38\x4E\x71\xB8\x1C\x0A\xC4\xDF\xFE\x0C\x10\xE6\x4F"
170    and gg =
171      "\xAC\x40\x32\xEF\x4F\x2D\x9A\xE3\x9D\xF3\x0B\x5C\x8F\xFD\xAC\x50\x6C\xDE\xBE\x7B\x89\x99\x8C\xAF\x74\x86\x6A\x08\xCF\xE4\xFF\xE3\xA6\x82\x4A\x4E\x10\xB9\xA6\xF0\xDD\x92\x1F\x01\xA7\x0C\x4A\xFA\xAB\x73\x9D\x77\x00\xC2\x9F\x52\xC5\x7D\xB1\x7C\x62\x0A\x86\x52\xBE\x5E\x90\x01\xA8\xD6\x6A\xD7\xC1\x76\x69\x10\x19\x99\x02\x4A\xF4\xD0\x27\x27\x5A\xC1\x34\x8B\xB8\xA7\x62\xD0\x52\x1B\xC9\x8A\xE2\x47\x15\x04\x22\xEA\x1E\xD4\x09\x93\x9D\x54\xDA\x74\x60\xCD\xB5\xF6\xC6\xB2\x50\x71\x7C\xBE\xF1\x80\xEB\x34\x11\x8E\x98\xD1\x19\x52\x9A\x45\xD6\xF8\x34\x56\x6E\x30\x25\xE3\x16\xA3\x30\xEF\xBB\x77\xA8\x6F\x0C\x1A\xB1\x5B\x05\x1A\xE3\xD4\x28\xC8\xF8\xAC\xB7\x0A\x81\x37\x15\x0B\x8E\xEB\x10\xE1\x83\xED\xD1\x99\x63\xDD\xD9\xE2\x63\xE4\x77\x05\x89\xEF\x6A\xA2\x1E\x7F\x5F\x2F\xF3\x81\xB5\x39\xCC\xE3\x40\x9D\x13\xCD\x56\x6A\xFB\xB4\x8D\x6C\x01\x91\x81\xE1\xBC\xFE\x94\xB3\x02\x69\xED\xFE\x72\xFE\x9B\x6A\xA4\xBD\x7B\x5A\x0F\x1C\x71\xCF\xFF\x4C\x19\xC4\x18\xE1\xF6\xEC\x01\x79\x81\xBC\x08\x7F\x2A\x70\x65\xB3\x84\xB8\x90\xD3\x19\x1F\x2B\xFA"
172    and q =
173      "\x80\x1C\x0D\x34\xC5\x8D\x93\xFE\x99\x71\x77\x10\x1F\x80\x53\x5A\x47\x38\xCE\xBC\xBF\x38\x9A\x99\xB3\x63\x71\xEB"
174    in
175    group ~p ~gg ~q
176
177  (* 2048-bit, 256-bit subgroup *)
178  let rfc_5114_3 =
179    let p =
180      "\x87\xA8\xE6\x1D\xB4\xB6\x66\x3C\xFF\xBB\xD1\x9C\x65\x19\x59\x99\x8C\xEE\xF6\x08\x66\x0D\xD0\xF2\x5D\x2C\xEE\xD4\x43\x5E\x3B\x00\xE0\x0D\xF8\xF1\xD6\x19\x57\xD4\xFA\xF7\xDF\x45\x61\xB2\xAA\x30\x16\xC3\xD9\x11\x34\x09\x6F\xAA\x3B\xF4\x29\x6D\x83\x0E\x9A\x7C\x20\x9E\x0C\x64\x97\x51\x7A\xBD\x5A\x8A\x9D\x30\x6B\xCF\x67\xED\x91\xF9\xE6\x72\x5B\x47\x58\xC0\x22\xE0\xB1\xEF\x42\x75\xBF\x7B\x6C\x5B\xFC\x11\xD4\x5F\x90\x88\xB9\x41\xF5\x4E\xB1\xE5\x9B\xB8\xBC\x39\xA0\xBF\x12\x30\x7F\x5C\x4F\xDB\x70\xC5\x81\xB2\x3F\x76\xB6\x3A\xCA\xE1\xCA\xA6\xB7\x90\x2D\x52\x52\x67\x35\x48\x8A\x0E\xF1\x3C\x6D\x9A\x51\xBF\xA4\xAB\x3A\xD8\x34\x77\x96\x52\x4D\x8E\xF6\xA1\x67\xB5\xA4\x18\x25\xD9\x67\xE1\x44\xE5\x14\x05\x64\x25\x1C\xCA\xCB\x83\xE6\xB4\x86\xF6\xB3\xCA\x3F\x79\x71\x50\x60\x26\xC0\xB8\x57\xF6\x89\x96\x28\x56\xDE\xD4\x01\x0A\xBD\x0B\xE6\x21\xC3\xA3\x96\x0A\x54\xE7\x10\xC3\x75\xF2\x63\x75\xD7\x01\x41\x03\xA4\xB5\x43\x30\xC1\x98\xAF\x12\x61\x16\xD2\x27\x6E\x11\x71\x5F\x69\x38\x77\xFA\xD7\xEF\x09\xCA\xDB\x09\x4A\xE9\x1E\x1A\x15\x97"
181    and gg =
182      "\x3F\xB3\x2C\x9B\x73\x13\x4D\x0B\x2E\x77\x50\x66\x60\xED\xBD\x48\x4C\xA7\xB1\x8F\x21\xEF\x20\x54\x07\xF4\x79\x3A\x1A\x0B\xA1\x25\x10\xDB\xC1\x50\x77\xBE\x46\x3F\xFF\x4F\xED\x4A\xAC\x0B\xB5\x55\xBE\x3A\x6C\x1B\x0C\x6B\x47\xB1\xBC\x37\x73\xBF\x7E\x8C\x6F\x62\x90\x12\x28\xF8\xC2\x8C\xBB\x18\xA5\x5A\xE3\x13\x41\x00\x0A\x65\x01\x96\xF9\x31\xC7\x7A\x57\xF2\xDD\xF4\x63\xE5\xE9\xEC\x14\x4B\x77\x7D\xE6\x2A\xAA\xB8\xA8\x62\x8A\xC3\x76\xD2\x82\xD6\xED\x38\x64\xE6\x79\x82\x42\x8E\xBC\x83\x1D\x14\x34\x8F\x6F\x2F\x91\x93\xB5\x04\x5A\xF2\x76\x71\x64\xE1\xDF\xC9\x67\xC1\xFB\x3F\x2E\x55\xA4\xBD\x1B\xFF\xE8\x3B\x9C\x80\xD0\x52\xB9\x85\xD1\x82\xEA\x0A\xDB\x2A\x3B\x73\x13\xD3\xFE\x14\xC8\x48\x4B\x1E\x05\x25\x88\xB9\xB7\xD2\xBB\xD2\xDF\x01\x61\x99\xEC\xD0\x6E\x15\x57\xCD\x09\x15\xB3\x35\x3B\xBB\x64\xE0\xEC\x37\x7F\xD0\x28\x37\x0D\xF9\x2B\x52\xC7\x89\x14\x28\xCD\xC6\x7E\xB6\x18\x4B\x52\x3D\x1D\xB2\x46\xC3\x2F\x63\x07\x84\x90\xF0\x0E\xF8\xD6\x47\xD1\x48\xD4\x79\x54\x51\x5E\x23\x27\xCF\xEF\x98\xC5\x82\x66\x4B\x4C\x0F\x6C\xC4\x16\x59"
183    and q =
184      "\x8C\xF8\x36\x42\xA7\x09\xA0\x97\xB4\x47\x99\x76\x40\x12\x9D\xA2\x99\xB1\xA4\x7D\x1E\xB3\x75\x0B\xA3\x08\xB0\xFE\x64\xF5\xFB\xD3"
185    in
186    group ~p ~gg ~q
187
188  (* draft-ietf-tls-negotiated-ff-dhe-08 *)
189
190  let ffdhe2048 =
191    (* p = 2^2048 - 2^1984 + {[2^1918 * e] + 560316 } * 2^64 - 1 *)
192    (* The estimated symmetric-equivalent strength of this group is 103 bits.
193
194       Peers using ffdhe2048 that want to optimize their key exchange with a
195       short exponent (Section 5.2) should choose a secret key of at least
196       225 bits. *)
197    s_group
198      ~p:
199        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xAD\xF8\x54\x58\xA2\xBB\x4A\x9A\xAF\xDC\x56\x20\x27\x3D\x3C\xF1\xD8\xB9\xC5\x83\xCE\x2D\x36\x95\xA9\xE1\x36\x41\x14\x64\x33\xFB\xCC\x93\x9D\xCE\x24\x9B\x3E\xF9\x7D\x2F\xE3\x63\x63\x0C\x75\xD8\xF6\x81\xB2\x02\xAE\xC4\x61\x7A\xD3\xDF\x1E\xD5\xD5\xFD\x65\x61\x24\x33\xF5\x1F\x5F\x06\x6E\xD0\x85\x63\x65\x55\x3D\xED\x1A\xF3\xB5\x57\x13\x5E\x7F\x57\xC9\x35\x98\x4F\x0C\x70\xE0\xE6\x8B\x77\xE2\xA6\x89\xDA\xF3\xEF\xE8\x72\x1D\xF1\x58\xA1\x36\xAD\xE7\x35\x30\xAC\xCA\x4F\x48\x3A\x79\x7A\xBC\x0A\xB1\x82\xB3\x24\xFB\x61\xD1\x08\xA9\x4B\xB2\xC8\xE3\xFB\xB9\x6A\xDA\xB7\x60\xD7\xF4\x68\x1D\x4F\x42\xA3\xDE\x39\x4D\xF4\xAE\x56\xED\xE7\x63\x72\xBB\x19\x0B\x07\xA7\xC8\xEE\x0A\x6D\x70\x9E\x02\xFC\xE1\xCD\xF7\xE2\xEC\xC0\x34\x04\xCD\x28\x34\x2F\x61\x91\x72\xFE\x9C\xE9\x85\x83\xFF\x8E\x4F\x12\x32\xEE\xF2\x81\x83\xC3\xFE\x3B\x1B\x4C\x6F\xAD\x73\x3B\xB5\xFC\xBC\x2E\xC2\x20\x05\xC5\x8E\xF1\x83\x7D\x16\x83\xB2\xC6\xF3\x4A\x26\xC1\xB2\xEF\xFA\x88\x6B\x42\x38\x61\x28\x5C\x97\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
200
201  let ffdhe3072 =
202    (* p = 2^3072 - 2^3008 + {[2^2942 * e] + 2625351} * 2^64 -1 *)
203    (* The estimated symmetric-equivalent strength of this group is 125 bits.
204
205       Peers using ffdhe3072 that want to optimize their key exchange with a
206       short exponent (Section 5.2) should choose a secret key of at least
207       275 bits. *)
208    s_group
209      ~p:
210        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xAD\xF8\x54\x58\xA2\xBB\x4A\x9A\xAF\xDC\x56\x20\x27\x3D\x3C\xF1\xD8\xB9\xC5\x83\xCE\x2D\x36\x95\xA9\xE1\x36\x41\x14\x64\x33\xFB\xCC\x93\x9D\xCE\x24\x9B\x3E\xF9\x7D\x2F\xE3\x63\x63\x0C\x75\xD8\xF6\x81\xB2\x02\xAE\xC4\x61\x7A\xD3\xDF\x1E\xD5\xD5\xFD\x65\x61\x24\x33\xF5\x1F\x5F\x06\x6E\xD0\x85\x63\x65\x55\x3D\xED\x1A\xF3\xB5\x57\x13\x5E\x7F\x57\xC9\x35\x98\x4F\x0C\x70\xE0\xE6\x8B\x77\xE2\xA6\x89\xDA\xF3\xEF\xE8\x72\x1D\xF1\x58\xA1\x36\xAD\xE7\x35\x30\xAC\xCA\x4F\x48\x3A\x79\x7A\xBC\x0A\xB1\x82\xB3\x24\xFB\x61\xD1\x08\xA9\x4B\xB2\xC8\xE3\xFB\xB9\x6A\xDA\xB7\x60\xD7\xF4\x68\x1D\x4F\x42\xA3\xDE\x39\x4D\xF4\xAE\x56\xED\xE7\x63\x72\xBB\x19\x0B\x07\xA7\xC8\xEE\x0A\x6D\x70\x9E\x02\xFC\xE1\xCD\xF7\xE2\xEC\xC0\x34\x04\xCD\x28\x34\x2F\x61\x91\x72\xFE\x9C\xE9\x85\x83\xFF\x8E\x4F\x12\x32\xEE\xF2\x81\x83\xC3\xFE\x3B\x1B\x4C\x6F\xAD\x73\x3B\xB5\xFC\xBC\x2E\xC2\x20\x05\xC5\x8E\xF1\x83\x7D\x16\x83\xB2\xC6\xF3\x4A\x26\xC1\xB2\xEF\xFA\x88\x6B\x42\x38\x61\x1F\xCF\xDC\xDE\x35\x5B\x3B\x65\x19\x03\x5B\xBC\x34\xF4\xDE\xF9\x9C\x02\x38\x61\xB4\x6F\xC9\xD6\xE6\xC9\x07\x7A\xD9\x1D\x26\x91\xF7\xF7\xEE\x59\x8C\xB0\xFA\xC1\x86\xD9\x1C\xAE\xFE\x13\x09\x85\x13\x92\x70\xB4\x13\x0C\x93\xBC\x43\x79\x44\xF4\xFD\x44\x52\xE2\xD7\x4D\xD3\x64\xF2\xE2\x1E\x71\xF5\x4B\xFF\x5C\xAE\x82\xAB\x9C\x9D\xF6\x9E\xE8\x6D\x2B\xC5\x22\x36\x3A\x0D\xAB\xC5\x21\x97\x9B\x0D\xEA\xDA\x1D\xBF\x9A\x42\xD5\xC4\x48\x4E\x0A\xBC\xD0\x6B\xFA\x53\xDD\xEF\x3C\x1B\x20\xEE\x3F\xD5\x9D\x7C\x25\xE4\x1D\x2B\x66\xC6\x2E\x37\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
211
212  let ffdhe4096 =
213    (* p = 2^4096 - 2^4032 + {[2^3966 * e] + 5736041} * 2^64 - 1 *)
214    (* The estimated symmetric-equivalent strength of this group is 150 bits.
215
216       Peers using ffdhe4096 that want to optimize their key exchange with a
217       short exponent (Section 5.2) should choose a secret key of at least
218       325 bits. *)
219    s_group
220      ~p:
221        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xAD\xF8\x54\x58\xA2\xBB\x4A\x9A\xAF\xDC\x56\x20\x27\x3D\x3C\xF1\xD8\xB9\xC5\x83\xCE\x2D\x36\x95\xA9\xE1\x36\x41\x14\x64\x33\xFB\xCC\x93\x9D\xCE\x24\x9B\x3E\xF9\x7D\x2F\xE3\x63\x63\x0C\x75\xD8\xF6\x81\xB2\x02\xAE\xC4\x61\x7A\xD3\xDF\x1E\xD5\xD5\xFD\x65\x61\x24\x33\xF5\x1F\x5F\x06\x6E\xD0\x85\x63\x65\x55\x3D\xED\x1A\xF3\xB5\x57\x13\x5E\x7F\x57\xC9\x35\x98\x4F\x0C\x70\xE0\xE6\x8B\x77\xE2\xA6\x89\xDA\xF3\xEF\xE8\x72\x1D\xF1\x58\xA1\x36\xAD\xE7\x35\x30\xAC\xCA\x4F\x48\x3A\x79\x7A\xBC\x0A\xB1\x82\xB3\x24\xFB\x61\xD1\x08\xA9\x4B\xB2\xC8\xE3\xFB\xB9\x6A\xDA\xB7\x60\xD7\xF4\x68\x1D\x4F\x42\xA3\xDE\x39\x4D\xF4\xAE\x56\xED\xE7\x63\x72\xBB\x19\x0B\x07\xA7\xC8\xEE\x0A\x6D\x70\x9E\x02\xFC\xE1\xCD\xF7\xE2\xEC\xC0\x34\x04\xCD\x28\x34\x2F\x61\x91\x72\xFE\x9C\xE9\x85\x83\xFF\x8E\x4F\x12\x32\xEE\xF2\x81\x83\xC3\xFE\x3B\x1B\x4C\x6F\xAD\x73\x3B\xB5\xFC\xBC\x2E\xC2\x20\x05\xC5\x8E\xF1\x83\x7D\x16\x83\xB2\xC6\xF3\x4A\x26\xC1\xB2\xEF\xFA\x88\x6B\x42\x38\x61\x1F\xCF\xDC\xDE\x35\x5B\x3B\x65\x19\x03\x5B\xBC\x34\xF4\xDE\xF9\x9C\x02\x38\x61\xB4\x6F\xC9\xD6\xE6\xC9\x07\x7A\xD9\x1D\x26\x91\xF7\xF7\xEE\x59\x8C\xB0\xFA\xC1\x86\xD9\x1C\xAE\xFE\x13\x09\x85\x13\x92\x70\xB4\x13\x0C\x93\xBC\x43\x79\x44\xF4\xFD\x44\x52\xE2\xD7\x4D\xD3\x64\xF2\xE2\x1E\x71\xF5\x4B\xFF\x5C\xAE\x82\xAB\x9C\x9D\xF6\x9E\xE8\x6D\x2B\xC5\x22\x36\x3A\x0D\xAB\xC5\x21\x97\x9B\x0D\xEA\xDA\x1D\xBF\x9A\x42\xD5\xC4\x48\x4E\x0A\xBC\xD0\x6B\xFA\x53\xDD\xEF\x3C\x1B\x20\xEE\x3F\xD5\x9D\x7C\x25\xE4\x1D\x2B\x66\x9E\x1E\xF1\x6E\x6F\x52\xC3\x16\x4D\xF4\xFB\x79\x30\xE9\xE4\xE5\x88\x57\xB6\xAC\x7D\x5F\x42\xD6\x9F\x6D\x18\x77\x63\xCF\x1D\x55\x03\x40\x04\x87\xF5\x5B\xA5\x7E\x31\xCC\x7A\x71\x35\xC8\x86\xEF\xB4\x31\x8A\xED\x6A\x1E\x01\x2D\x9E\x68\x32\xA9\x07\x60\x0A\x91\x81\x30\xC4\x6D\xC7\x78\xF9\x71\xAD\x00\x38\x09\x29\x99\xA3\x33\xCB\x8B\x7A\x1A\x1D\xB9\x3D\x71\x40\x00\x3C\x2A\x4E\xCE\xA9\xF9\x8D\x0A\xCC\x0A\x82\x91\xCD\xCE\xC9\x7D\xCF\x8E\xC9\xB5\x5A\x7F\x88\xA4\x6B\x4D\xB5\xA8\x51\xF4\x41\x82\xE1\xC6\x8A\x00\x7E\x5E\x65\x5F\x6A\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
222
223  let ffdhe6144 =
224    (* p = 2^6144 - 2^6080 + {[2^6014 * e] + 15705020} * 2^64 - 1 *)
225    (* The estimated symmetric-equivalent strength of this group is 175 bits.
226
227       Peers using ffdhe6144 that want to optimize their key exchange with a
228       short exponent (Section 5.2) should choose a secret key of at least
229       375 bits. *)
230    s_group
231      ~p:
232        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xAD\xF8\x54\x58\xA2\xBB\x4A\x9A\xAF\xDC\x56\x20\x27\x3D\x3C\xF1\xD8\xB9\xC5\x83\xCE\x2D\x36\x95\xA9\xE1\x36\x41\x14\x64\x33\xFB\xCC\x93\x9D\xCE\x24\x9B\x3E\xF9\x7D\x2F\xE3\x63\x63\x0C\x75\xD8\xF6\x81\xB2\x02\xAE\xC4\x61\x7A\xD3\xDF\x1E\xD5\xD5\xFD\x65\x61\x24\x33\xF5\x1F\x5F\x06\x6E\xD0\x85\x63\x65\x55\x3D\xED\x1A\xF3\xB5\x57\x13\x5E\x7F\x57\xC9\x35\x98\x4F\x0C\x70\xE0\xE6\x8B\x77\xE2\xA6\x89\xDA\xF3\xEF\xE8\x72\x1D\xF1\x58\xA1\x36\xAD\xE7\x35\x30\xAC\xCA\x4F\x48\x3A\x79\x7A\xBC\x0A\xB1\x82\xB3\x24\xFB\x61\xD1\x08\xA9\x4B\xB2\xC8\xE3\xFB\xB9\x6A\xDA\xB7\x60\xD7\xF4\x68\x1D\x4F\x42\xA3\xDE\x39\x4D\xF4\xAE\x56\xED\xE7\x63\x72\xBB\x19\x0B\x07\xA7\xC8\xEE\x0A\x6D\x70\x9E\x02\xFC\xE1\xCD\xF7\xE2\xEC\xC0\x34\x04\xCD\x28\x34\x2F\x61\x91\x72\xFE\x9C\xE9\x85\x83\xFF\x8E\x4F\x12\x32\xEE\xF2\x81\x83\xC3\xFE\x3B\x1B\x4C\x6F\xAD\x73\x3B\xB5\xFC\xBC\x2E\xC2\x20\x05\xC5\x8E\xF1\x83\x7D\x16\x83\xB2\xC6\xF3\x4A\x26\xC1\xB2\xEF\xFA\x88\x6B\x42\x38\x61\x1F\xCF\xDC\xDE\x35\x5B\x3B\x65\x19\x03\x5B\xBC\x34\xF4\xDE\xF9\x9C\x02\x38\x61\xB4\x6F\xC9\xD6\xE6\xC9\x07\x7A\xD9\x1D\x26\x91\xF7\xF7\xEE\x59\x8C\xB0\xFA\xC1\x86\xD9\x1C\xAE\xFE\x13\x09\x85\x13\x92\x70\xB4\x13\x0C\x93\xBC\x43\x79\x44\xF4\xFD\x44\x52\xE2\xD7\x4D\xD3\x64\xF2\xE2\x1E\x71\xF5\x4B\xFF\x5C\xAE\x82\xAB\x9C\x9D\xF6\x9E\xE8\x6D\x2B\xC5\x22\x36\x3A\x0D\xAB\xC5\x21\x97\x9B\x0D\xEA\xDA\x1D\xBF\x9A\x42\xD5\xC4\x48\x4E\x0A\xBC\xD0\x6B\xFA\x53\xDD\xEF\x3C\x1B\x20\xEE\x3F\xD5\x9D\x7C\x25\xE4\x1D\x2B\x66\x9E\x1E\xF1\x6E\x6F\x52\xC3\x16\x4D\xF4\xFB\x79\x30\xE9\xE4\xE5\x88\x57\xB6\xAC\x7D\x5F\x42\xD6\x9F\x6D\x18\x77\x63\xCF\x1D\x55\x03\x40\x04\x87\xF5\x5B\xA5\x7E\x31\xCC\x7A\x71\x35\xC8\x86\xEF\xB4\x31\x8A\xED\x6A\x1E\x01\x2D\x9E\x68\x32\xA9\x07\x60\x0A\x91\x81\x30\xC4\x6D\xC7\x78\xF9\x71\xAD\x00\x38\x09\x29\x99\xA3\x33\xCB\x8B\x7A\x1A\x1D\xB9\x3D\x71\x40\x00\x3C\x2A\x4E\xCE\xA9\xF9\x8D\x0A\xCC\x0A\x82\x91\xCD\xCE\xC9\x7D\xCF\x8E\xC9\xB5\x5A\x7F\x88\xA4\x6B\x4D\xB5\xA8\x51\xF4\x41\x82\xE1\xC6\x8A\x00\x7E\x5E\x0D\xD9\x02\x0B\xFD\x64\xB6\x45\x03\x6C\x7A\x4E\x67\x7D\x2C\x38\x53\x2A\x3A\x23\xBA\x44\x42\xCA\xF5\x3E\xA6\x3B\xB4\x54\x32\x9B\x76\x24\xC8\x91\x7B\xDD\x64\xB1\xC0\xFD\x4C\xB3\x8E\x8C\x33\x4C\x70\x1C\x3A\xCD\xAD\x06\x57\xFC\xCF\xEC\x71\x9B\x1F\x5C\x3E\x4E\x46\x04\x1F\x38\x81\x47\xFB\x4C\xFD\xB4\x77\xA5\x24\x71\xF7\xA9\xA9\x69\x10\xB8\x55\x32\x2E\xDB\x63\x40\xD8\xA0\x0E\xF0\x92\x35\x05\x11\xE3\x0A\xBE\xC1\xFF\xF9\xE3\xA2\x6E\x7F\xB2\x9F\x8C\x18\x30\x23\xC3\x58\x7E\x38\xDA\x00\x77\xD9\xB4\x76\x3E\x4E\x4B\x94\xB2\xBB\xC1\x94\xC6\x65\x1E\x77\xCA\xF9\x92\xEE\xAA\xC0\x23\x2A\x28\x1B\xF6\xB3\xA7\x39\xC1\x22\x61\x16\x82\x0A\xE8\xDB\x58\x47\xA6\x7C\xBE\xF9\xC9\x09\x1B\x46\x2D\x53\x8C\xD7\x2B\x03\x74\x6A\xE7\x7F\x5E\x62\x29\x2C\x31\x15\x62\xA8\x46\x50\x5D\xC8\x2D\xB8\x54\x33\x8A\xE4\x9F\x52\x35\xC9\x5B\x91\x17\x8C\xCF\x2D\xD5\xCA\xCE\xF4\x03\xEC\x9D\x18\x10\xC6\x27\x2B\x04\x5B\x3B\x71\xF9\xDC\x6B\x80\xD6\x3F\xDD\x4A\x8E\x9A\xDB\x1E\x69\x62\xA6\x95\x26\xD4\x31\x61\xC1\xA4\x1D\x57\x0D\x79\x38\xDA\xD4\xA4\x0E\x32\x9C\xD0\xE4\x0E\x65\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
233
234  let ffdhe8192 =
235    (* p = 2^8192 - 2^8128 + {[2^8062 * e] + 10965728} * 2^64 - 1 *)
236    (* The estimated symmetric-equivalent strength of this group is 192 bits.
237
238       Peers using ffdhe8192 that want to optimize their key exchange with a
239       short exponent (Section 5.2) should choose a secret key of at least
240       400 bits. *)
241    s_group
242      ~p:
243        "\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xAD\xF8\x54\x58\xA2\xBB\x4A\x9A\xAF\xDC\x56\x20\x27\x3D\x3C\xF1\xD8\xB9\xC5\x83\xCE\x2D\x36\x95\xA9\xE1\x36\x41\x14\x64\x33\xFB\xCC\x93\x9D\xCE\x24\x9B\x3E\xF9\x7D\x2F\xE3\x63\x63\x0C\x75\xD8\xF6\x81\xB2\x02\xAE\xC4\x61\x7A\xD3\xDF\x1E\xD5\xD5\xFD\x65\x61\x24\x33\xF5\x1F\x5F\x06\x6E\xD0\x85\x63\x65\x55\x3D\xED\x1A\xF3\xB5\x57\x13\x5E\x7F\x57\xC9\x35\x98\x4F\x0C\x70\xE0\xE6\x8B\x77\xE2\xA6\x89\xDA\xF3\xEF\xE8\x72\x1D\xF1\x58\xA1\x36\xAD\xE7\x35\x30\xAC\xCA\x4F\x48\x3A\x79\x7A\xBC\x0A\xB1\x82\xB3\x24\xFB\x61\xD1\x08\xA9\x4B\xB2\xC8\xE3\xFB\xB9\x6A\xDA\xB7\x60\xD7\xF4\x68\x1D\x4F\x42\xA3\xDE\x39\x4D\xF4\xAE\x56\xED\xE7\x63\x72\xBB\x19\x0B\x07\xA7\xC8\xEE\x0A\x6D\x70\x9E\x02\xFC\xE1\xCD\xF7\xE2\xEC\xC0\x34\x04\xCD\x28\x34\x2F\x61\x91\x72\xFE\x9C\xE9\x85\x83\xFF\x8E\x4F\x12\x32\xEE\xF2\x81\x83\xC3\xFE\x3B\x1B\x4C\x6F\xAD\x73\x3B\xB5\xFC\xBC\x2E\xC2\x20\x05\xC5\x8E\xF1\x83\x7D\x16\x83\xB2\xC6\xF3\x4A\x26\xC1\xB2\xEF\xFA\x88\x6B\x42\x38\x61\x1F\xCF\xDC\xDE\x35\x5B\x3B\x65\x19\x03\x5B\xBC\x34\xF4\xDE\xF9\x9C\x02\x38\x61\xB4\x6F\xC9\xD6\xE6\xC9\x07\x7A\xD9\x1D\x26\x91\xF7\xF7\xEE\x59\x8C\xB0\xFA\xC1\x86\xD9\x1C\xAE\xFE\x13\x09\x85\x13\x92\x70\xB4\x13\x0C\x93\xBC\x43\x79\x44\xF4\xFD\x44\x52\xE2\xD7\x4D\xD3\x64\xF2\xE2\x1E\x71\xF5\x4B\xFF\x5C\xAE\x82\xAB\x9C\x9D\xF6\x9E\xE8\x6D\x2B\xC5\x22\x36\x3A\x0D\xAB\xC5\x21\x97\x9B\x0D\xEA\xDA\x1D\xBF\x9A\x42\xD5\xC4\x48\x4E\x0A\xBC\xD0\x6B\xFA\x53\xDD\xEF\x3C\x1B\x20\xEE\x3F\xD5\x9D\x7C\x25\xE4\x1D\x2B\x66\x9E\x1E\xF1\x6E\x6F\x52\xC3\x16\x4D\xF4\xFB\x79\x30\xE9\xE4\xE5\x88\x57\xB6\xAC\x7D\x5F\x42\xD6\x9F\x6D\x18\x77\x63\xCF\x1D\x55\x03\x40\x04\x87\xF5\x5B\xA5\x7E\x31\xCC\x7A\x71\x35\xC8\x86\xEF\xB4\x31\x8A\xED\x6A\x1E\x01\x2D\x9E\x68\x32\xA9\x07\x60\x0A\x91\x81\x30\xC4\x6D\xC7\x78\xF9\x71\xAD\x00\x38\x09\x29\x99\xA3\x33\xCB\x8B\x7A\x1A\x1D\xB9\x3D\x71\x40\x00\x3C\x2A\x4E\xCE\xA9\xF9\x8D\x0A\xCC\x0A\x82\x91\xCD\xCE\xC9\x7D\xCF\x8E\xC9\xB5\x5A\x7F\x88\xA4\x6B\x4D\xB5\xA8\x51\xF4\x41\x82\xE1\xC6\x8A\x00\x7E\x5E\x0D\xD9\x02\x0B\xFD\x64\xB6\x45\x03\x6C\x7A\x4E\x67\x7D\x2C\x38\x53\x2A\x3A\x23\xBA\x44\x42\xCA\xF5\x3E\xA6\x3B\xB4\x54\x32\x9B\x76\x24\xC8\x91\x7B\xDD\x64\xB1\xC0\xFD\x4C\xB3\x8E\x8C\x33\x4C\x70\x1C\x3A\xCD\xAD\x06\x57\xFC\xCF\xEC\x71\x9B\x1F\x5C\x3E\x4E\x46\x04\x1F\x38\x81\x47\xFB\x4C\xFD\xB4\x77\xA5\x24\x71\xF7\xA9\xA9\x69\x10\xB8\x55\x32\x2E\xDB\x63\x40\xD8\xA0\x0E\xF0\x92\x35\x05\x11\xE3\x0A\xBE\xC1\xFF\xF9\xE3\xA2\x6E\x7F\xB2\x9F\x8C\x18\x30\x23\xC3\x58\x7E\x38\xDA\x00\x77\xD9\xB4\x76\x3E\x4E\x4B\x94\xB2\xBB\xC1\x94\xC6\x65\x1E\x77\xCA\xF9\x92\xEE\xAA\xC0\x23\x2A\x28\x1B\xF6\xB3\xA7\x39\xC1\x22\x61\x16\x82\x0A\xE8\xDB\x58\x47\xA6\x7C\xBE\xF9\xC9\x09\x1B\x46\x2D\x53\x8C\xD7\x2B\x03\x74\x6A\xE7\x7F\x5E\x62\x29\x2C\x31\x15\x62\xA8\x46\x50\x5D\xC8\x2D\xB8\x54\x33\x8A\xE4\x9F\x52\x35\xC9\x5B\x91\x17\x8C\xCF\x2D\xD5\xCA\xCE\xF4\x03\xEC\x9D\x18\x10\xC6\x27\x2B\x04\x5B\x3B\x71\xF9\xDC\x6B\x80\xD6\x3F\xDD\x4A\x8E\x9A\xDB\x1E\x69\x62\xA6\x95\x26\xD4\x31\x61\xC1\xA4\x1D\x57\x0D\x79\x38\xDA\xD4\xA4\x0E\x32\x9C\xCF\xF4\x6A\xAA\x36\xAD\x00\x4C\xF6\x00\xC8\x38\x1E\x42\x5A\x31\xD9\x51\xAE\x64\xFD\xB2\x3F\xCE\xC9\x50\x9D\x43\x68\x7F\xEB\x69\xED\xD1\xCC\x5E\x0B\x8C\xC3\xBD\xF6\x4B\x10\xEF\x86\xB6\x31\x42\xA3\xAB\x88\x29\x55\x5B\x2F\x74\x7C\x93\x26\x65\xCB\x2C\x0F\x1C\xC0\x1B\xD7\x02\x29\x38\x88\x39\xD2\xAF\x05\xE4\x54\x50\x4A\xC7\x8B\x75\x82\x82\x28\x46\xC0\xBA\x35\xC3\x5F\x5C\x59\x16\x0C\xC0\x46\xFD\x82\x51\x54\x1F\xC6\x8C\x9C\x86\xB0\x22\xBB\x70\x99\x87\x6A\x46\x0E\x74\x51\xA8\xA9\x31\x09\x70\x3F\xEE\x1C\x21\x7E\x6C\x38\x26\xE5\x2C\x51\xAA\x69\x1E\x0E\x42\x3C\xFC\x99\xE9\xE3\x16\x50\xC1\x21\x7B\x62\x48\x16\xCD\xAD\x9A\x95\xF9\xD5\xB8\x01\x94\x88\xD9\xC0\xA0\xA1\xFE\x30\x75\xA5\x77\xE2\x31\x83\xF8\x1D\x4A\x3F\x2F\xA4\x57\x1E\xFC\x8C\xE0\xBA\x8A\x4F\xE8\xB6\x85\x5D\xFE\x72\xB0\xA6\x6E\xDE\xD2\xFB\xAB\xFB\xE5\x8A\x30\xFA\xFA\xBE\x1C\x5D\x71\xA8\x7E\x2F\x74\x1E\xF8\xC1\xFE\x86\xFE\xA6\xBB\xFD\xE5\x30\x67\x7F\x0D\x97\xD1\x1D\x49\xF7\xA8\x44\x3D\x08\x22\xE5\x06\xA9\xF4\x61\x4E\x01\x1E\x2A\x94\x83\x8F\xF8\x8C\xD6\x8C\x8B\xB7\xC5\xC6\x42\x4C\xFF\xFF\xFF\xFF\xFF\xFF\xFF\xFF"
244end