%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2007-2018. All Rights Reserved.
%%
%% Licensed under the Apache License, Version 2.0 (the "License");
%% you may not use this file except in compliance with the License.
%% You may obtain a copy of the License at
%%
%% http://www.apache.org/licenses/LICENSE-2.0
%%
%% Unless required by applicable law or agreed to in writing, software
%% distributed under the License is distributed on an "AS IS" BASIS,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%%
%% %CopyrightEnd%
%%
%%
%%----------------------------------------------------------------------
%% Purpose: Handles tls1 encryption.
%%----------------------------------------------------------------------
-module(tls_v1).
-include("ssl_cipher.hrl").
-include("ssl_internal.hrl").
-include("ssl_record.hrl").
-export([master_secret/4, finished/5, certificate_verify/3, mac_hash/7, hmac_hash/3,
setup_keys/8, suites/1, prf/5,
ecc_curves/1, ecc_curves/2, oid_to_enum/1, enum_to_oid/1,
default_signature_algs/1, signature_algs/2,
default_signature_schemes/1, signature_schemes/2,
groups/1, groups/2, group_to_enum/1, enum_to_group/1]).
-type named_curve() :: sect571r1 | sect571k1 | secp521r1 | brainpoolP512r1 |
sect409k1 | sect409r1 | brainpoolP384r1 | secp384r1 |
sect283k1 | sect283r1 | brainpoolP256r1 | secp256k1 | secp256r1 |
sect239k1 | sect233k1 | sect233r1 | secp224k1 | secp224r1 |
sect193r1 | sect193r2 | secp192k1 | secp192r1 | sect163k1 |
sect163r1 | sect163r2 | secp160k1 | secp160r1 | secp160r2.
-type curves() :: [named_curve()].
-type group() :: secp256r1 | secp384r1 | secp521r1 | ffdhe2048 |
ffdhe3072 | ffdhe4096 | ffdhe6144 | ffdhe8192.
-type supported_groups() :: [group()].
-export_type([curves/0, named_curve/0, group/0, supported_groups/0]).
%%====================================================================
%% Internal application API
%%====================================================================
-spec master_secret(integer(), binary(), binary(), binary()) -> binary().
master_secret(PrfAlgo, PreMasterSecret, ClientRandom, ServerRandom) ->
%% RFC 2246 & 4346 && RFC 5246 - 8.1 %% master_secret = PRF(pre_master_secret,
%% "master secret", ClientHello.random +
%% ServerHello.random)[0..47];
prf(PrfAlgo, PreMasterSecret, <<"master secret">>,
[ClientRandom, ServerRandom], 48).
-spec finished(client | server, integer(), integer(), binary(), [binary()]) -> binary().
finished(Role, Version, PrfAlgo, MasterSecret, Handshake)
when Version == 1; Version == 2; PrfAlgo == ?MD5SHA ->
%% RFC 2246 & 4346 - 7.4.9. Finished
%% struct {
%% opaque verify_data[12];
%% } Finished;
%%
%% verify_data
%% PRF(master_secret, finished_label, MD5(handshake_messages) +
%% SHA-1(handshake_messages)) [0..11];
MD5 = crypto:hash(md5, Handshake),
SHA = crypto:hash(sha, Handshake),
prf(?MD5SHA, MasterSecret, finished_label(Role), [MD5, SHA], 12);
finished(Role, Version, PrfAlgo, MasterSecret, Handshake)
when Version == 3; Version == 4 ->
%% RFC 5246 - 7.4.9. Finished
%% struct {
%% opaque verify_data[12];
%% } Finished;
%%
%% verify_data
%% PRF(master_secret, finished_label, Hash(handshake_messages)) [0..11];
Hash = crypto:hash(mac_algo(PrfAlgo), Handshake),
prf(PrfAlgo, MasterSecret, finished_label(Role), Hash, 12).
-spec certificate_verify(md5sha | sha, integer(), [binary()]) -> binary().
certificate_verify(md5sha, _Version, Handshake) ->
MD5 = crypto:hash(md5, Handshake),
SHA = crypto:hash(sha, Handshake),
<<MD5/binary, SHA/binary>>;
certificate_verify(HashAlgo, _Version, Handshake) ->
crypto:hash(HashAlgo, Handshake).
-spec setup_keys(integer(), integer(), binary(), binary(), binary(), integer(),
integer(), integer()) -> {binary(), binary(), binary(),
binary(), binary(), binary()}.
setup_keys(Version, _PrfAlgo, MasterSecret, ServerRandom, ClientRandom, HashSize,
KeyMatLen, IVSize)
when Version == 1 ->
%% RFC 2246 - 6.3. Key calculation
%% key_block = PRF(SecurityParameters.master_secret,
%% "key expansion",
%% SecurityParameters.server_random +
%% SecurityParameters.client_random);
%% Then the key_block is partitioned as follows:
%% client_write_MAC_secret[SecurityParameters.hash_size]
%% server_write_MAC_secret[SecurityParameters.hash_size]
%% client_write_key[SecurityParameters.key_material_length]
%% server_write_key[SecurityParameters.key_material_length]
%% client_write_IV[SecurityParameters.IV_size]
%% server_write_IV[SecurityParameters.IV_size]
WantedLength = 2 * (HashSize + KeyMatLen + IVSize),
KeyBlock = prf(?MD5SHA, MasterSecret, "key expansion",
[ServerRandom, ClientRandom], WantedLength),
<<ClientWriteMacSecret:HashSize/binary,
ServerWriteMacSecret:HashSize/binary,
ClientWriteKey:KeyMatLen/binary, ServerWriteKey:KeyMatLen/binary,
ClientIV:IVSize/binary, ServerIV:IVSize/binary>> = KeyBlock,
{ClientWriteMacSecret, ServerWriteMacSecret, ClientWriteKey,
ServerWriteKey, ClientIV, ServerIV};
%% TLS v1.1
setup_keys(Version, _PrfAlgo, MasterSecret, ServerRandom, ClientRandom, HashSize,
KeyMatLen, IVSize)
when Version == 2 ->
%% RFC 4346 - 6.3. Key calculation
%% key_block = PRF(SecurityParameters.master_secret,
%% "key expansion",
%% SecurityParameters.server_random +
%% SecurityParameters.client_random);
%% Then the key_block is partitioned as follows:
%% client_write_MAC_secret[SecurityParameters.hash_size]
%% server_write_MAC_secret[SecurityParameters.hash_size]
%% client_write_key[SecurityParameters.key_material_length]
%% server_write_key[SecurityParameters.key_material_length]
%%
%% RFC 4346 is incomplete, the client and server IVs have to
%% be generated just like for TLS 1.0
WantedLength = 2 * (HashSize + KeyMatLen + IVSize),
KeyBlock = prf(?MD5SHA, MasterSecret, "key expansion",
[ServerRandom, ClientRandom], WantedLength),
<<ClientWriteMacSecret:HashSize/binary,
ServerWriteMacSecret:HashSize/binary,
ClientWriteKey:KeyMatLen/binary, ServerWriteKey:KeyMatLen/binary,
ClientIV:IVSize/binary, ServerIV:IVSize/binary>> = KeyBlock,
{ClientWriteMacSecret, ServerWriteMacSecret, ClientWriteKey,
ServerWriteKey, ClientIV, ServerIV};
%% TLS v1.2
setup_keys(Version, PrfAlgo, MasterSecret, ServerRandom, ClientRandom, HashSize,
KeyMatLen, IVSize)
when Version == 3; Version == 4 ->
%% RFC 5246 - 6.3. Key calculation
%% key_block = PRF(SecurityParameters.master_secret,
%% "key expansion",
%% SecurityParameters.server_random +
%% SecurityParameters.client_random);
%% Then the key_block is partitioned as follows:
%% client_write_MAC_secret[SecurityParameters.hash_size]
%% server_write_MAC_secret[SecurityParameters.hash_size]
%% client_write_key[SecurityParameters.key_material_length]
%% server_write_key[SecurityParameters.key_material_length]
%% client_write_IV[SecurityParameters.fixed_iv_length]
%% server_write_IV[SecurityParameters.fixed_iv_length]
WantedLength = 2 * (HashSize + KeyMatLen + IVSize),
KeyBlock = prf(PrfAlgo, MasterSecret, "key expansion",
[ServerRandom, ClientRandom], WantedLength),
<<ClientWriteMacSecret:HashSize/binary,
ServerWriteMacSecret:HashSize/binary,
ClientWriteKey:KeyMatLen/binary, ServerWriteKey:KeyMatLen/binary,
ClientIV:IVSize/binary, ServerIV:IVSize/binary>> = KeyBlock,
{ClientWriteMacSecret, ServerWriteMacSecret, ClientWriteKey,
ServerWriteKey, ClientIV, ServerIV}.
-spec mac_hash(integer(), binary(), integer(), integer(), tls_record:tls_version(),
integer(), binary()) -> binary().
mac_hash(Method, Mac_write_secret, Seq_num, Type, {Major, Minor},
Length, Fragment) ->
%% RFC 2246 & 4346 - 6.2.3.1.
%% HMAC_hash(MAC_write_secret, seq_num + TLSCompressed.type +
%% TLSCompressed.version + TLSCompressed.length +
%% TLSCompressed.fragment));
Mac = hmac_hash(Method, Mac_write_secret,
[<<?UINT64(Seq_num), ?BYTE(Type),
?BYTE(Major), ?BYTE(Minor), ?UINT16(Length)>>,
Fragment]),
Mac.
-spec suites(1|2|3|4) -> [ssl_cipher_format:cipher_suite()].
suites(Minor) when Minor == 1; Minor == 2 ->
[
?TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA,
?TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA,
?TLS_DHE_RSA_WITH_AES_256_CBC_SHA,
?TLS_DHE_DSS_WITH_AES_256_CBC_SHA,
?TLS_ECDH_ECDSA_WITH_AES_256_CBC_SHA,
?TLS_ECDH_RSA_WITH_AES_256_CBC_SHA,
?TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA,
?TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA,
?TLS_DHE_RSA_WITH_AES_128_CBC_SHA,
?TLS_DHE_DSS_WITH_AES_128_CBC_SHA,
?TLS_ECDH_ECDSA_WITH_AES_128_CBC_SHA,
?TLS_ECDH_RSA_WITH_AES_128_CBC_SHA
];
suites(3) ->
[?TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384,
?TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384,
?TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384,
?TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384,
?TLS_ECDH_ECDSA_WITH_AES_256_GCM_SHA384,
?TLS_ECDH_RSA_WITH_AES_256_GCM_SHA384,
?TLS_ECDH_ECDSA_WITH_AES_256_CBC_SHA384,
?TLS_ECDH_RSA_WITH_AES_256_CBC_SHA384,
?TLS_DHE_RSA_WITH_AES_256_GCM_SHA384,
?TLS_DHE_DSS_WITH_AES_256_GCM_SHA384,
?TLS_DHE_RSA_WITH_AES_256_CBC_SHA256,
?TLS_DHE_DSS_WITH_AES_256_CBC_SHA256,
?TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256,
?TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256,
?TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256,
?TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256,
?TLS_ECDH_ECDSA_WITH_AES_128_GCM_SHA256,
?TLS_ECDH_RSA_WITH_AES_128_GCM_SHA256,
?TLS_ECDH_ECDSA_WITH_AES_128_CBC_SHA256,
?TLS_ECDH_RSA_WITH_AES_128_CBC_SHA256,
?TLS_DHE_RSA_WITH_AES_128_GCM_SHA256,
?TLS_DHE_DSS_WITH_AES_128_GCM_SHA256,
?TLS_DHE_RSA_WITH_AES_128_CBC_SHA256,
?TLS_DHE_DSS_WITH_AES_128_CBC_SHA256
%% not supported
%% ?TLS_DH_RSA_WITH_AES_256_GCM_SHA384,
%% ?TLS_DH_DSS_WITH_AES_256_GCM_SHA384,
%% ?TLS_DH_RSA_WITH_AES_128_GCM_SHA256,
%% ?TLS_DH_DSS_WITH_AES_128_GCM_SHA256
] ++ suites(2);
suites(4) ->
[?TLS_AES_256_GCM_SHA384,
?TLS_AES_128_GCM_SHA256,
?TLS_CHACHA20_POLY1305_SHA256
%% Not supported
%% ?TLS_AES_128_CCM_SHA256,
%% ?TLS_AES_128_CCM_8_SHA256
] ++ suites(3).
signature_algs({3, 4}, HashSigns) ->
signature_algs({3, 3}, HashSigns);
signature_algs({3, 3}, HashSigns) ->
CryptoSupports = crypto:supports(),
Hashes = proplists:get_value(hashs, CryptoSupports),
PubKeys = proplists:get_value(public_keys, CryptoSupports),
Supported = lists:foldl(fun({Hash, dsa = Sign} = Alg, Acc) ->
case proplists:get_bool(dss, PubKeys)
andalso proplists:get_bool(Hash, Hashes)
andalso is_pair(Hash, Sign, Hashes)
of
true ->
[Alg | Acc];
false ->
Acc
end;
({Hash, Sign} = Alg, Acc) ->
case proplists:get_bool(Sign, PubKeys)
andalso proplists:get_bool(Hash, Hashes)
andalso is_pair(Hash, Sign, Hashes)
of
true ->
[Alg | Acc];
false ->
Acc
end
end, [], HashSigns),
lists:reverse(Supported).
default_signature_algs({3, 4}) ->
default_signature_algs({3, 3});
default_signature_algs({3, 3} = Version) ->
Default = [%% SHA2
{sha512, ecdsa},
{sha512, rsa},
{sha384, ecdsa},
{sha384, rsa},
{sha256, ecdsa},
{sha256, rsa},
{sha224, ecdsa},
{sha224, rsa},
%% SHA
{sha, ecdsa},
{sha, rsa},
{sha, dsa}],
signature_algs(Version, Default);
default_signature_algs(_) ->
undefined.
signature_schemes(Version, SignatureSchemes) when is_tuple(Version)
andalso Version >= {3, 3} ->
CryptoSupports = crypto:supports(),
Hashes = proplists:get_value(hashs, CryptoSupports),
PubKeys = proplists:get_value(public_keys, CryptoSupports),
Curves = proplists:get_value(curves, CryptoSupports),
Fun = fun (Scheme, Acc) ->
{Hash0, Sign0, Curve} =
ssl_cipher:scheme_to_components(Scheme),
Sign = case Sign0 of
rsa_pkcs1 -> rsa;
S -> S
end,
Hash = case Hash0 of
sha1 -> sha;
H -> H
end,
case proplists:get_bool(Sign, PubKeys)
andalso proplists:get_bool(Hash, Hashes)
andalso (Curve =:= undefined orelse
proplists:get_bool(Curve, Curves))
andalso is_pair(Hash, Sign, Hashes)
of
true ->
[Scheme | Acc];
false ->
Acc
end
end,
Supported = lists:foldl(Fun, [], SignatureSchemes),
lists:reverse(Supported);
signature_schemes(_, _) ->
[].
default_signature_schemes(Version) ->
Default = [
rsa_pkcs1_sha256,
rsa_pkcs1_sha384,
rsa_pkcs1_sha512,
ecdsa_secp256r1_sha256,
ecdsa_secp384r1_sha384,
ecdsa_secp521r1_sha512,
rsa_pss_rsae_sha256,
rsa_pss_rsae_sha384,
rsa_pss_rsae_sha512,
%% ed25519,
%% ed448,
rsa_pss_pss_sha256,
rsa_pss_pss_sha384,
rsa_pss_pss_sha512,
rsa_pkcs1_sha1,
ecdsa_sha1
],
signature_schemes(Version, Default).
%%--------------------------------------------------------------------
%%% Internal functions
%%--------------------------------------------------------------------
%%%% HMAC and the Pseudorandom Functions RFC 2246 & 4346 - 5.%%%%
hmac_hash(?NULL, _, _) ->
<<>>;
hmac_hash(Alg, Key, Value) ->
crypto:hmac(mac_algo(Alg), Key, Value).
mac_algo(?MD5) -> md5;
mac_algo(?SHA) -> sha;
mac_algo(?SHA256) -> sha256;
mac_algo(?SHA384) -> sha384;
mac_algo(?SHA512) -> sha512.
% First, we define a data expansion function, P_hash(secret, data) that
% uses a single hash function to expand a secret and seed into an
% arbitrary quantity of output:
%% P_hash(secret, seed) = HMAC_hash(secret, A(1) + seed) +
%% HMAC_hash(secret, A(2) + seed) +
%% HMAC_hash(secret, A(3) + seed) + ...
p_hash(Secret, Seed, WantedLength, Method) ->
p_hash(Secret, Seed, WantedLength, Method, 0, []).
p_hash(_Secret, _Seed, WantedLength, _Method, _N, [])
when WantedLength =< 0 ->
[];
p_hash(_Secret, _Seed, WantedLength, _Method, _N, [Last | Acc])
when WantedLength =< 0 ->
Keep = byte_size(Last) + WantedLength,
<<B:Keep/binary, _/binary>> = Last,
list_to_binary(lists:reverse(Acc, [B]));
p_hash(Secret, Seed, WantedLength, Method, N, Acc) ->
N1 = N+1,
Bin = hmac_hash(Method, Secret, [a(N1, Secret, Seed, Method), Seed]),
p_hash(Secret, Seed, WantedLength - byte_size(Bin), Method, N1, [Bin|Acc]).
%% ... Where A(0) = seed
%% A(i) = HMAC_hash(secret, A(i-1))
%% a(0, _Secret, Seed, _Method) ->
%% Seed.
%% a(N, Secret, Seed, Method) ->
%% hmac_hash(Method, Secret, a(N-1, Secret, Seed, Method)).
a(0, _Secret, Seed, _Method) ->
Seed;
a(N, Secret, Seed0, Method) ->
Seed = hmac_hash(Method, Secret, Seed0),
a(N-1, Secret, Seed, Method).
split_secret(BinSecret) ->
%% L_S = length in bytes of secret;
%% L_S1 = L_S2 = ceil(L_S / 2);
%% The secret is partitioned into two halves (with the possibility of
%% one shared byte) as described above, S1 taking the first L_S1 bytes,
%% and S2 the last L_S2 bytes.
Length = byte_size(BinSecret),
Div = Length div 2,
EvenLength = Length - Div,
<<Secret1:EvenLength/binary, _/binary>> = BinSecret,
<<_:Div/binary, Secret2:EvenLength/binary>> = BinSecret,
{Secret1, Secret2}.
prf(?MD5SHA, Secret, Label, Seed, WantedLength) ->
%% PRF(secret, label, seed) = P_MD5(S1, label + seed) XOR
%% P_SHA-1(S2, label + seed);
{S1, S2} = split_secret(Secret),
LS = list_to_binary([Label, Seed]),
crypto:exor(p_hash(S1, LS, WantedLength, ?MD5),
p_hash(S2, LS, WantedLength, ?SHA));
prf(MAC, Secret, Label, Seed, WantedLength) ->
%% PRF(secret, label, seed) = P_SHA256(secret, label + seed);
LS = list_to_binary([Label, Seed]),
p_hash(Secret, LS, WantedLength, MAC).
%%%% Misc help functions %%%%
finished_label(client) ->
<<"client finished">>;
finished_label(server) ->
<<"server finished">>.
is_pair(sha, dsa, _) ->
true;
is_pair(_, dsa, _) ->
false;
is_pair(Hash, ecdsa, Hashs) ->
AtLeastSha = Hashs -- [md2,md4,md5],
lists:member(Hash, AtLeastSha);
is_pair(Hash, rsa, Hashs) ->
AtLeastMd5 = Hashs -- [md2,md4],
lists:member(Hash, AtLeastMd5).
%% list ECC curves in preferred order
-spec ecc_curves(1..3 | all) -> [named_curve()].
ecc_curves(all) ->
[sect571r1,sect571k1,secp521r1,brainpoolP512r1,
sect409k1,sect409r1,brainpoolP384r1,secp384r1,
sect283k1,sect283r1,brainpoolP256r1,secp256k1,secp256r1,
sect239k1,sect233k1,sect233r1,secp224k1,secp224r1,
sect193r1,sect193r2,secp192k1,secp192r1,sect163k1,
sect163r1,sect163r2,secp160k1,secp160r1,secp160r2];
ecc_curves(Minor) ->
TLSCurves = ecc_curves(all),
ecc_curves(Minor, TLSCurves).
-spec ecc_curves(1..3, [named_curve()]) -> [named_curve()].
ecc_curves(_Minor, TLSCurves) ->
CryptoCurves = crypto:ec_curves(),
lists:foldr(fun(Curve, Curves) ->
case proplists:get_bool(Curve, CryptoCurves) of
true -> [pubkey_cert_records:namedCurves(Curve)|Curves];
false -> Curves
end
end, [], TLSCurves).
-spec groups(4 | all) -> [group()].
groups(all) ->
[secp256r1,
secp384r1,
secp521r1,
ffdhe2048,
ffdhe3072,
ffdhe4096,
ffdhe6144,
ffdhe8192];
groups(Minor) ->
TLSGroups = groups(all),
groups(Minor, TLSGroups).
%%
-spec groups(4, [group()]) -> [group()].
groups(_Minor, TLSGroups) ->
%% TODO: Adding FFDHE groups to crypto?
CryptoGroups = crypto:ec_curves() ++ [ffdhe2048,ffdhe3072,ffdhe4096,ffdhe6144,ffdhe8192],
lists:filter(fun(Group) -> proplists:get_bool(Group, CryptoGroups) end, TLSGroups).
group_to_enum(secp256r1) -> 23;
group_to_enum(secp384r1) -> 24;
group_to_enum(secp521r1) -> 25;
group_to_enum(ffdhe2048) -> 256;
group_to_enum(ffdhe3072) -> 257;
group_to_enum(ffdhe4096) -> 258;
group_to_enum(ffdhe6144) -> 259;
group_to_enum(ffdhe8192) -> 260.
enum_to_group(23) -> secp256r1;
enum_to_group(24) -> secp384r1;
enum_to_group(25) -> secp521r1;
enum_to_group(256) -> ffdhe2048;
enum_to_group(257) -> ffdhe3072;
enum_to_group(258) -> ffdhe4096;
enum_to_group(259) -> ffdhe6144;
enum_to_group(260) -> ffdhe8192;
enum_to_group(_) -> undefined.
%% ECC curves from draft-ietf-tls-ecc-12.txt (Oct. 17, 2005)
oid_to_enum(?sect163k1) -> 1;
oid_to_enum(?sect163r1) -> 2;
oid_to_enum(?sect163r2) -> 3;
oid_to_enum(?sect193r1) -> 4;
oid_to_enum(?sect193r2) -> 5;
oid_to_enum(?sect233k1) -> 6;
oid_to_enum(?sect233r1) -> 7;
oid_to_enum(?sect239k1) -> 8;
oid_to_enum(?sect283k1) -> 9;
oid_to_enum(?sect283r1) -> 10;
oid_to_enum(?sect409k1) -> 11;
oid_to_enum(?sect409r1) -> 12;
oid_to_enum(?sect571k1) -> 13;
oid_to_enum(?sect571r1) -> 14;
oid_to_enum(?secp160k1) -> 15;
oid_to_enum(?secp160r1) -> 16;
oid_to_enum(?secp160r2) -> 17;
oid_to_enum(?secp192k1) -> 18;
oid_to_enum(?secp192r1) -> 19;
oid_to_enum(?secp224k1) -> 20;
oid_to_enum(?secp224r1) -> 21;
oid_to_enum(?secp256k1) -> 22;
oid_to_enum(?secp256r1) -> 23;
oid_to_enum(?secp384r1) -> 24;
oid_to_enum(?secp521r1) -> 25;
oid_to_enum(?brainpoolP256r1) -> 26;
oid_to_enum(?brainpoolP384r1) -> 27;
oid_to_enum(?brainpoolP512r1) -> 28.
enum_to_oid(1) -> ?sect163k1;
enum_to_oid(2) -> ?sect163r1;
enum_to_oid(3) -> ?sect163r2;
enum_to_oid(4) -> ?sect193r1;
enum_to_oid(5) -> ?sect193r2;
enum_to_oid(6) -> ?sect233k1;
enum_to_oid(7) -> ?sect233r1;
enum_to_oid(8) -> ?sect239k1;
enum_to_oid(9) -> ?sect283k1;
enum_to_oid(10) -> ?sect283r1;
enum_to_oid(11) -> ?sect409k1;
enum_to_oid(12) -> ?sect409r1;
enum_to_oid(13) -> ?sect571k1;
enum_to_oid(14) -> ?sect571r1;
enum_to_oid(15) -> ?secp160k1;
enum_to_oid(16) -> ?secp160r1;
enum_to_oid(17) -> ?secp160r2;
enum_to_oid(18) -> ?secp192k1;
enum_to_oid(19) -> ?secp192r1;
enum_to_oid(20) -> ?secp224k1;
enum_to_oid(21) -> ?secp224r1;
enum_to_oid(22) -> ?secp256k1;
enum_to_oid(23) -> ?secp256r1;
enum_to_oid(24) -> ?secp384r1;
enum_to_oid(25) -> ?secp521r1;
enum_to_oid(26) -> ?brainpoolP256r1;
enum_to_oid(27) -> ?brainpoolP384r1;
enum_to_oid(28) -> ?brainpoolP512r1;
enum_to_oid(_) ->
undefined.
