%% %% %CopyrightBegin% %% %% Copyright Ericsson AB 2004-2011. All Rights Reserved. %% %% The contents of this file are subject to the Erlang Public License, %% Version 1.1, (the "License"); you may not use this file except in %% compliance with the License. You should have received a copy of the %% Erlang Public License along with this software. If not, it can be %% retrieved online at http://www.erlang.org/. %% %% Software distributed under the License is distributed on an "AS IS" %% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See %% the License for the specific language governing rights and limitations %% under the License. %% %% %CopyrightEnd% %% %% %%---------------------------------------------------------------------- -module(ssh_test_lib). %% Note: This directive should only be used in test suites. -compile(export_all). -include_lib("public_key/include/public_key.hrl"). -include("test_server.hrl"). -include("test_server_line.hrl"). -define(TIMEOUT, 50000). connect(Options) -> connect(hostname(), inet_port(), Options). connect(Port, Options) when is_integer(Port) -> connect(hostname(), Port, Options); connect(any, Options) -> connect(hostname(), inet_port(), Options); connect(Host, Options) -> connect(Host, inet_port(), Options). connect(any, Port, Options) -> connect(hostname(), Port, Options); connect(Host, Port, Options) -> case ssh:connect(Host, Port, Options) of {ok, ConnectionRef} -> ConnectionRef; Error -> Error end. daemon(Options) -> daemon(any, inet_port(), Options). daemon(Port, Options) when is_integer(Port) -> daemon(any, Port, Options); daemon(Host, Options) -> daemon(Host, inet_port(), Options). daemon(Host, Port, Options) -> case ssh:daemon(Host, Port, Options) of {ok, Pid} when Host == any -> {Pid, hostname(), Port}; {ok, Pid} -> {Pid, Host, Port}; Error -> Error end. start_shell(Port, IOServer) -> spawn_link(?MODULE, init_shell, [Port, IOServer]). init_shell(Port, IOServer) -> Host = hostname(), UserDir = get_user_dir(), Options = [{user_interaction, false}, {silently_accept_hosts, true}] ++ UserDir, group_leader(IOServer, self()), loop_shell(Host, Port, Options). loop_shell(Host, Port, Options) -> ssh:shell(Host, Port, Options). start_io_server() -> spawn_link(?MODULE, init_io_server, [self()]). init_io_server(TestCase) -> process_flag(trap_exit, true), loop_io_server(TestCase, []). loop_io_server(TestCase, Buff0) -> receive {input, TestCase, Line} -> %io:format("~p~n",[{input, TestCase, Line}]), loop_io_server(TestCase, Buff0 ++ [Line]); {io_request, From, ReplyAs, Request} -> %io:format("request -> ~p~n",[Request]), {ok, Reply, Buff} = io_request(Request, TestCase, From, ReplyAs, Buff0), %io:format("reply -> ~p~n",[Reply]), io_reply(From, ReplyAs, Reply), loop_io_server(TestCase, Buff); {'EXIT',_, _} -> erlang:display('EXIT'), ok end. io_request({put_chars, Chars}, TestCase, _, _, Buff) -> reply(TestCase, Chars), {ok, ok, Buff}; io_request({put_chars, Enc, Chars}, TestCase, _, _, Buff) -> reply(TestCase, unicode:characters_to_binary(Chars,Enc,latin1)), {ok, ok, Buff}; io_request({get_line, _} = Request, _, From, ReplyAs, [] = Buff) -> erlang:send_after(1000, self(), {io_request, From, ReplyAs, Request}), {ok, [], Buff}; io_request({get_line, _Enc, _Prompt} = Request, _, From, ReplyAs, [] = Buff) -> erlang:send_after(1000, self(), {io_request, From, ReplyAs, Request}), {ok, [], Buff}; io_request({get_line, _Enc,_}, _, _, _, [Line | Buff]) -> {ok, Line, Buff}. io_reply(_, _, []) -> ok; io_reply(From, ReplyAs, Reply) -> From ! {io_reply, ReplyAs, Reply}. reply(_, []) -> ok; reply(TestCase, Result) -> TestCase ! Result. receive_exec_result(Msg) -> test_server:format("Expect data! ~p", [Msg]), receive {ssh_cm,_,{data,_,1, Data}} -> test_server:format("StdErr: ~p~n", [Data]), receive_exec_result(Msg); Msg -> test_server:format("1: Collected data ~p", [Msg]), expected; Other -> test_server:format("Other ~p", [Other]), {unexpected_msg, Other} end. receive_exec_end(ConnectionRef, ChannelId) -> Eof = {ssh_cm, ConnectionRef, {eof, ChannelId}}, ExitStatus = {ssh_cm, ConnectionRef, {exit_status, ChannelId, 0}}, Closed = {ssh_cm, ConnectionRef,{closed, ChannelId}}, case receive_exec_result(ExitStatus) of {unexpected_msg, Eof} -> %% Open ssh seems to not allways send these messages %% in the same order! test_server:format("2: Collected data ~p", [Eof]), case receive_exec_result(ExitStatus) of expected -> expected = receive_exec_result(Closed); {unexpected_msg, Closed} -> test_server:format("3: Collected data ~p", [Closed]) end; expected -> test_server:format("4: Collected data ~p", [ExitStatus]), expected = receive_exec_result(Eof), expected = receive_exec_result(Closed); Other -> test_server:fail({unexpected_msg, Other}) end. receive_exec_result(Data, ConnectionRef, ChannelId) -> Eof = {ssh_cm, ConnectionRef, {eof, ChannelId}}, Closed = {ssh_cm, ConnectionRef,{closed, ChannelId}}, expected = receive_exec_result(Data), expected = receive_exec_result(Eof), expected = receive_exec_result(Closed). inet_port()-> {ok, Socket} = gen_tcp:listen(0, [{reuseaddr, true}]), {ok, Port} = inet:port(Socket), gen_tcp:close(Socket), Port. %% copy private keys to given dir from ~/.ssh get_id_keys(DstDir) -> SrcDir = filename:join(os:getenv("HOME"), ".ssh"), RsaOk = copyfile(SrcDir, DstDir, "id_rsa"), DsaOk = copyfile(SrcDir, DstDir, "id_dsa"), case {RsaOk, DsaOk} of {{ok, _}, {ok, _}} -> {ok, both}; {{ok, _}, _} -> {ok, rsa}; {_, {ok, _}} -> {ok, dsa}; {Error, _} -> Error end. remove_id_keys(Dir) -> file:delete(filename:join(Dir, "id_rsa")), file:delete(filename:join(Dir, "id_dsa")). copyfile(SrcDir, DstDir, Fn) -> file:copy(filename:join(SrcDir, Fn), filename:join(DstDir, Fn)). failfun(_User, {authmethod,none}) -> ok; failfun(User, Reason) -> error_logger:format("~p failed XXX to login: ~p~n", [User, Reason]). hostname() -> {ok,Host} = inet:gethostname(), Host. known_hosts(BR) -> KnownHosts = ssh_file:file_name(user, "known_hosts", []), B = KnownHosts ++ "xxx", case BR of backup -> file:rename(KnownHosts, B); restore -> file:delete(KnownHosts), file:rename(B, KnownHosts) end. get_user_dir() -> case os:type() of {win32, _} -> [{user_dir, filename:join([os:getenv("HOME"), ".ssh"])}]; _ -> [] end. make_dsa_cert_files(Config) -> make_dsa_cert_files("", Config). make_dsa_cert_files(RoleStr, Config) -> CaInfo = {CaCert, _} = make_cert([{key, dsa}]), {Cert, CertKey} = make_cert([{key, dsa}, {issuer, CaInfo}]), CaCertFile = filename:join([?config(data_dir, Config), RoleStr, "dsa_cacerts.pem"]), CertFile = filename:join([?config(data_dir, Config), RoleStr, "dsa_cert.pem"]), KeyFile = filename:join([?config(data_dir, Config), RoleStr, "dsa_key.pem"]), der_to_pem(CaCertFile, [{'Certificate', CaCert, not_encrypted}]), der_to_pem(CertFile, [{'Certificate', Cert, not_encrypted}]), der_to_pem(KeyFile, [CertKey]), {CaCertFile, CertFile, KeyFile}. make_dsa_files(Config) -> make_dsa_files(Config, rfc4716_public_key). make_dsa_files(Config, Type) -> {DSA, EncodedKey} = ssh_test_lib:gen_dsa(128, 20), PKey = DSA#'DSAPrivateKey'.y, P = DSA#'DSAPrivateKey'.p, Q = DSA#'DSAPrivateKey'.q, G = DSA#'DSAPrivateKey'.g, Dss = #'Dss-Parms'{p=P, q=Q, g=G}, {ok, Hostname} = inet:gethostname(), {ok, {A, B, C, D}} = inet:getaddr(Hostname, inet), IP = lists:concat([A, ".", B, ".", C, ".", D]), Attributes = [], % Could be [{comment,"user@" ++ Hostname}], HostNames = [{hostnames,[IP, IP]}], PublicKey = [{{PKey, Dss}, Attributes}], KnownHosts = [{{PKey, Dss}, HostNames}], KnownHostsEnc = public_key:ssh_encode(KnownHosts, known_hosts), KnownHosts = public_key:ssh_decode(KnownHostsEnc, known_hosts), PublicKeyEnc = public_key:ssh_encode(PublicKey, Type), % PublicKey = public_key:ssh_decode(PublicKeyEnc, Type), SystemTmpDir = ?config(data_dir, Config), filelib:ensure_dir(SystemTmpDir), file:make_dir(SystemTmpDir), DSAFile = filename:join(SystemTmpDir, "ssh_host_dsa_key.pub"), file:delete(DSAFile), DSAPrivateFile = filename:join(SystemTmpDir, "ssh_host_dsa_key"), file:delete(DSAPrivateFile), KHFile = filename:join(SystemTmpDir, "known_hosts"), file:delete(KHFile), PemBin = public_key:pem_encode([EncodedKey]), file:write_file(DSAFile, PublicKeyEnc), file:write_file(KHFile, KnownHostsEnc), file:write_file(DSAPrivateFile, PemBin), ok. %%-------------------------------------------------------------------- %% Create and return a der encoded certificate %% Option Default %% ------------------------------------------------------- %% digest sha1 %% validity {date(), date() + week()} %% version 3 %% subject [] list of the following content %% {name, Name} %% {email, Email} %% {city, City} %% {state, State} %% {org, Org} %% {org_unit, OrgUnit} %% {country, Country} %% {serial, Serial} %% {title, Title} %% {dnQualifer, DnQ} %% issuer = {Issuer, IssuerKey} true (i.e. a ca cert is created) %% (obs IssuerKey migth be {Key, Password} %% key = KeyFile|KeyBin|rsa|dsa Subject PublicKey rsa or dsa generates key %% %% %% (OBS: The generated keys are for testing only) %% make_cert([{::atom(), ::term()}]) -> {Cert::binary(), Key::binary()} %%-------------------------------------------------------------------- make_cert(Opts) -> SubjectPrivateKey = get_key(Opts), {TBSCert, IssuerKey} = make_tbs(SubjectPrivateKey, Opts), Cert = public_key:pkix_sign(TBSCert, IssuerKey), true = verify_signature(Cert, IssuerKey, undef), %% verify that the keys where ok {Cert, encode_key(SubjectPrivateKey)}. %%-------------------------------------------------------------------- %% Writes cert files in Dir with FileName and FileName ++ Suffix %% write_cert(::string(), ::string(), {Cert,Key}) -> ok %%-------------------------------------------------------------------- write_cert(Dir, FileName, Suffix, {Cert, Key = {_,_,not_encrypted}}) when is_binary(Cert) -> ok = der_to_pem(filename:join(Dir, FileName), [{'Certificate', Cert, not_encrypted}]), ok = der_to_pem(filename:join(Dir, FileName ++ Suffix), [Key]). %%-------------------------------------------------------------------- %% Creates a rsa key (OBS: for testing only) %% the size are in bytes %% gen_rsa(::integer()) -> {::atom(), ::binary(), ::opaque()} %%-------------------------------------------------------------------- gen_rsa(Size) when is_integer(Size) -> Key = gen_rsa2(Size), {Key, encode_key(Key)}. %%-------------------------------------------------------------------- %% Creates a dsa key (OBS: for testing only) %% the sizes are in bytes %% gen_dsa(::integer()) -> {::atom(), ::binary(), ::opaque()} %%-------------------------------------------------------------------- gen_dsa(LSize,NSize) when is_integer(LSize), is_integer(NSize) -> Key = gen_dsa2(LSize, NSize), {Key, encode_key(Key)}. %%-------------------------------------------------------------------- %% Verifies cert signatures %% verify_signature(::binary(), ::tuple()) -> ::boolean() %%-------------------------------------------------------------------- verify_signature(DerEncodedCert, DerKey, _KeyParams) -> Key = decode_key(DerKey), case Key of #'RSAPrivateKey'{modulus=Mod, publicExponent=Exp} -> public_key:pkix_verify(DerEncodedCert, #'RSAPublicKey'{modulus=Mod, publicExponent=Exp}); #'DSAPrivateKey'{p=P, q=Q, g=G, y=Y} -> public_key:pkix_verify(DerEncodedCert, {Y, #'Dss-Parms'{p=P, q=Q, g=G}}) end. %%%%%%%%%%%%%%%%%%%%%%%%% Implementation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% get_key(Opts) -> case proplists:get_value(key, Opts) of undefined -> make_key(rsa, Opts); rsa -> make_key(rsa, Opts); dsa -> make_key(dsa, Opts); Key -> Password = proplists:get_value(password, Opts, no_passwd), decode_key(Key, Password) end. decode_key({Key, Pw}) -> decode_key(Key, Pw); decode_key(Key) -> decode_key(Key, no_passwd). decode_key(#'RSAPublicKey'{} = Key,_) -> Key; decode_key(#'RSAPrivateKey'{} = Key,_) -> Key; decode_key(#'DSAPrivateKey'{} = Key,_) -> Key; decode_key(PemEntry = {_,_,_}, Pw) -> public_key:pem_entry_decode(PemEntry, Pw); decode_key(PemBin, Pw) -> [KeyInfo] = public_key:pem_decode(PemBin), decode_key(KeyInfo, Pw). encode_key(Key = #'RSAPrivateKey'{}) -> {ok, Der} = 'OTP-PUB-KEY':encode('RSAPrivateKey', Key), {'RSAPrivateKey', list_to_binary(Der), not_encrypted}; encode_key(Key = #'DSAPrivateKey'{}) -> {ok, Der} = 'OTP-PUB-KEY':encode('DSAPrivateKey', Key), {'DSAPrivateKey', list_to_binary(Der), not_encrypted}. make_tbs(SubjectKey, Opts) -> Version = list_to_atom("v"++integer_to_list(proplists:get_value(version, Opts, 3))), IssuerProp = proplists:get_value(issuer, Opts, true), {Issuer, IssuerKey} = issuer(IssuerProp, Opts, SubjectKey), {Algo, Parameters} = sign_algorithm(IssuerKey, Opts), SignAlgo = #'SignatureAlgorithm'{algorithm = Algo, parameters = Parameters}, Subject = case IssuerProp of true -> %% Is a Root Ca Issuer; _ -> subject(proplists:get_value(subject, Opts),false) end, {#'OTPTBSCertificate'{serialNumber = trunc(random:uniform()*100000000)*10000 + 1, signature = SignAlgo, issuer = Issuer, validity = validity(Opts), subject = Subject, subjectPublicKeyInfo = publickey(SubjectKey), version = Version, extensions = extensions(Opts) }, IssuerKey}. issuer(true, Opts, SubjectKey) -> %% Self signed {subject(proplists:get_value(subject, Opts), true), SubjectKey}; issuer({Issuer, IssuerKey}, _Opts, _SubjectKey) when is_binary(Issuer) -> {issuer_der(Issuer), decode_key(IssuerKey)}; issuer({File, IssuerKey}, _Opts, _SubjectKey) when is_list(File) -> {ok, [{cert, Cert, _}|_]} = pem_to_der(File), {issuer_der(Cert), decode_key(IssuerKey)}. issuer_der(Issuer) -> Decoded = public_key:pkix_decode_cert(Issuer, otp), #'OTPCertificate'{tbsCertificate=Tbs} = Decoded, #'OTPTBSCertificate'{subject=Subject} = Tbs, Subject. subject(undefined, IsRootCA) -> User = if IsRootCA -> "RootCA"; true -> os:getenv("USER") end, Opts = [{email, User ++ "@erlang.org"}, {name, User}, {city, "Stockholm"}, {country, "SE"}, {org, "erlang"}, {org_unit, "testing dep"}], subject(Opts); subject(Opts, _) -> subject(Opts). subject(SubjectOpts) when is_list(SubjectOpts) -> Encode = fun(Opt) -> {Type,Value} = subject_enc(Opt), [#'AttributeTypeAndValue'{type=Type, value=Value}] end, {rdnSequence, [Encode(Opt) || Opt <- SubjectOpts]}. %% Fill in the blanks subject_enc({name, Name}) -> {?'id-at-commonName', {printableString, Name}}; subject_enc({email, Email}) -> {?'id-emailAddress', Email}; subject_enc({city, City}) -> {?'id-at-localityName', {printableString, City}}; subject_enc({state, State}) -> {?'id-at-stateOrProvinceName', {printableString, State}}; subject_enc({org, Org}) -> {?'id-at-organizationName', {printableString, Org}}; subject_enc({org_unit, OrgUnit}) -> {?'id-at-organizationalUnitName', {printableString, OrgUnit}}; subject_enc({country, Country}) -> {?'id-at-countryName', Country}; subject_enc({serial, Serial}) -> {?'id-at-serialNumber', Serial}; subject_enc({title, Title}) -> {?'id-at-title', {printableString, Title}}; subject_enc({dnQualifer, DnQ}) -> {?'id-at-dnQualifier', DnQ}; subject_enc(Other) -> Other. extensions(Opts) -> case proplists:get_value(extensions, Opts, []) of false -> asn1_NOVALUE; Exts -> lists:flatten([extension(Ext) || Ext <- default_extensions(Exts)]) end. default_extensions(Exts) -> Def = [{key_usage,undefined}, {subject_altname, undefined}, {issuer_altname, undefined}, {basic_constraints, default}, {name_constraints, undefined}, {policy_constraints, undefined}, {ext_key_usage, undefined}, {inhibit_any, undefined}, {auth_key_id, undefined}, {subject_key_id, undefined}, {policy_mapping, undefined}], Filter = fun({Key, _}, D) -> lists:keydelete(Key, 1, D) end, Exts ++ lists:foldl(Filter, Def, Exts). extension({_, undefined}) -> []; extension({basic_constraints, Data}) -> case Data of default -> #'Extension'{extnID = ?'id-ce-basicConstraints', extnValue = #'BasicConstraints'{cA=true}, critical=true}; false -> []; Len when is_integer(Len) -> #'Extension'{extnID = ?'id-ce-basicConstraints', extnValue = #'BasicConstraints'{cA=true, pathLenConstraint=Len}, critical=true}; _ -> #'Extension'{extnID = ?'id-ce-basicConstraints', extnValue = Data} end; extension({Id, Data, Critical}) -> #'Extension'{extnID = Id, extnValue = Data, critical = Critical}. publickey(#'RSAPrivateKey'{modulus=N, publicExponent=E}) -> Public = #'RSAPublicKey'{modulus=N, publicExponent=E}, Algo = #'PublicKeyAlgorithm'{algorithm= ?rsaEncryption, parameters='NULL'}, #'OTPSubjectPublicKeyInfo'{algorithm = Algo, subjectPublicKey = Public}; publickey(#'DSAPrivateKey'{p=P, q=Q, g=G, y=Y}) -> Algo = #'PublicKeyAlgorithm'{algorithm= ?'id-dsa', parameters={params, #'Dss-Parms'{p=P, q=Q, g=G}}}, #'OTPSubjectPublicKeyInfo'{algorithm = Algo, subjectPublicKey = Y}. validity(Opts) -> DefFrom0 = calendar:gregorian_days_to_date(calendar:date_to_gregorian_days(date())-1), DefTo0 = calendar:gregorian_days_to_date(calendar:date_to_gregorian_days(date())+7), {DefFrom, DefTo} = proplists:get_value(validity, Opts, {DefFrom0, DefTo0}), Format = fun({Y,M,D}) -> lists:flatten(io_lib:format("~w~2..0w~2..0w000000Z",[Y,M,D])) end, #'Validity'{notBefore={generalTime, Format(DefFrom)}, notAfter ={generalTime, Format(DefTo)}}. sign_algorithm(#'RSAPrivateKey'{}, Opts) -> Type = case proplists:get_value(digest, Opts, sha1) of sha1 -> ?'sha1WithRSAEncryption'; sha512 -> ?'sha512WithRSAEncryption'; sha384 -> ?'sha384WithRSAEncryption'; sha256 -> ?'sha256WithRSAEncryption'; md5 -> ?'md5WithRSAEncryption'; md2 -> ?'md2WithRSAEncryption' end, {Type, 'NULL'}; sign_algorithm(#'DSAPrivateKey'{p=P, q=Q, g=G}, _Opts) -> {?'id-dsa-with-sha1', {params,#'Dss-Parms'{p=P, q=Q, g=G}}}. make_key(rsa, _Opts) -> %% (OBS: for testing only) gen_rsa2(64); make_key(dsa, _Opts) -> gen_dsa2(128, 20). %% Bytes i.e. {1024, 160} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% RSA key generation (OBS: for testing only) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -define(SMALL_PRIMES, [65537,97,89,83,79,73,71,67,61,59,53, 47,43,41,37,31,29,23,19,17,13,11,7,5,3]). gen_rsa2(Size) -> P = prime(Size), Q = prime(Size), N = P*Q, Tot = (P - 1) * (Q - 1), [E|_] = lists:dropwhile(fun(Candidate) -> (Tot rem Candidate) == 0 end, ?SMALL_PRIMES), {D1,D2} = extended_gcd(E, Tot), D = erlang:max(D1,D2), case D < E of true -> gen_rsa2(Size); false -> {Co1,Co2} = extended_gcd(Q, P), Co = erlang:max(Co1,Co2), #'RSAPrivateKey'{version = 'two-prime', modulus = N, publicExponent = E, privateExponent = D, prime1 = P, prime2 = Q, exponent1 = D rem (P-1), exponent2 = D rem (Q-1), coefficient = Co } end. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% DSA key generation (OBS: for testing only) %% See http://en.wikipedia.org/wiki/Digital_Signature_Algorithm %% and the fips_186-3.pdf %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% gen_dsa2(LSize, NSize) -> Q = prime(NSize), %% Choose N-bit prime Q X0 = prime(LSize), P0 = prime((LSize div 2) +1), %% Choose L-bit prime modulus P such that p-1 is a multiple of q. case dsa_search(X0 div (2*Q*P0), P0, Q, 1000) of error -> gen_dsa2(LSize, NSize); P -> G = crypto:mod_exp(2, (P-1) div Q, P), % Choose G a number whose multiplicative order modulo p is q. %% such that This may be done by setting g = h^(p-1)/q mod p, commonly h=2 is used. X = prime(20), %% Choose x by some random method, where 0 < x < q. Y = crypto:mod_exp(G, X, P), %% Calculate y = g^x mod p. #'DSAPrivateKey'{version=0, p=P, q=Q, g=G, y=Y, x=X} end. %% See fips_186-3.pdf dsa_search(T, P0, Q, Iter) when Iter > 0 -> P = 2*T*Q*P0 + 1, case is_prime(crypto:mpint(P), 50) of true -> P; false -> dsa_search(T+1, P0, Q, Iter-1) end; dsa_search(_,_,_,_) -> error. %%%%%%% Crypto Math %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% prime(ByteSize) -> Rand = odd_rand(ByteSize), crypto:erlint(prime_odd(Rand, 0)). prime_odd(Rand, N) -> case is_prime(Rand, 50) of true -> Rand; false -> NotPrime = crypto:erlint(Rand), prime_odd(crypto:mpint(NotPrime+2), N+1) end. %% see http://en.wikipedia.org/wiki/Fermat_primality_test is_prime(_, 0) -> true; is_prime(Candidate, Test) -> CoPrime = odd_rand(<<0,0,0,4, 10000:32>>, Candidate), case crypto:mod_exp(CoPrime, Candidate, Candidate) of CoPrime -> is_prime(Candidate, Test-1); _ -> false end. odd_rand(Size) -> Min = 1 bsl (Size*8-1), Max = (1 bsl (Size*8))-1, odd_rand(crypto:mpint(Min), crypto:mpint(Max)). odd_rand(Min,Max) -> Rand = <> = crypto:rand_uniform(Min,Max), BitSkip = (Sz+4)*8-1, case Rand of Odd = <<_:BitSkip, 1:1>> -> Odd; Even = <<_:BitSkip, 0:1>> -> crypto:mpint(crypto:erlint(Even)+1) end. extended_gcd(A, B) -> case A rem B of 0 -> {0, 1}; N -> {X, Y} = extended_gcd(B, N), {Y, X-Y*(A div B)} end. pem_to_der(File) -> {ok, PemBin} = file:read_file(File), public_key:pem_decode(PemBin). der_to_pem(File, Entries) -> PemBin = public_key:pem_encode(Entries), file:write_file(File, PemBin).