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<!DOCTYPE chapter SYSTEM "chapter.dtd">

<chapter>
  <header>
    <copyright>
      <year>2011</year><year>2018</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
    </copyright>
    <legalnotice>
      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.
    
    </legalnotice>

    <title>Getting Started</title>
    <prepared></prepared>
    <docno></docno>
    <date></date>
    <rev></rev>
    <file>using_public_key.xml</file>
  </header>

  <p>This section describes examples of how to use the 
    Public Key API. Keys and certificates used in the following 
    sections are generated only for testing the Public Key 
    application.</p>

    <p>Some shell printouts in the following examples
    are abbreviated for increased readability.</p>

     
  <section>
    <title>PEM Files</title>
    <p>Public-key data (keys, certificates, and so on) can be stored in 
    Privacy Enhanced Mail (PEM) format. 
    The PEM files have the following structure:</p>
    
    <code>
    &lt;text&gt;
    -----BEGIN &lt;SOMETHING&gt;-----
    &lt;Attribute&gt; : &lt;Value&gt;
    &lt;Base64 encoded DER data&gt;
    -----END &lt;SOMETHING&gt;-----
    &lt;text&gt;</code>
    
    <p>A file can contain several <c>BEGIN/END</c> blocks. Text lines between
    blocks are ignored. Attributes, if present, are ignored except
    for <c>Proc-Type</c> and <c>DEK-Info</c>, which are used when <c>DER</c> 
    data is encrypted.</p>

    <section>
      <title>DSA Private Key</title>
      <p>A DSA private key can look as follows:</p>
      <note><p>File handling is not done by the Public Key application.</p></note>
      
      <code>1> {ok, PemBin} = file:read_file("dsa.pem").
{ok,&lt;&lt;"-----BEGIN DSA PRIVATE KEY-----\nMIIBuw"...&gt;&gt;}</code>
      
      <p>The following PEM file has only one entry, a private DSA key:</p>
      <code>2> [DSAEntry] =  public_key:pem_decode(PemBin).
[{'DSAPrivateKey',&lt;&lt;48,130,1,187,2,1,0,2,129,129,0,183,
                    179,230,217,37,99,144,157,21,228,204,
		    162,207,61,246,...&gt;&gt;,
		    not_encrypted}]</code>
      
      <code>3> Key = public_key:pem_entry_decode(DSAEntry).
#'DSAPrivateKey'{version = 0,
                 p = 12900045185019966618...6593,
                 q = 1216700114794736143432235288305776850295620488937,
                 g = 10442040227452349332...47213,
                 y = 87256807980030509074...403143,
                 x = 510968529856012146351317363807366575075645839654}</code>
    </section>

    <section>
      <title>RSA Private Key with Password</title>
      <p>An RSA private key encrypted with a password can look as follows:</p>
      
      <code>1> {ok, PemBin} = file:read_file("rsa.pem").
{ok,&lt;&lt;"Bag Attribut"...&gt;&gt;}</code>

    <p>The following PEM file has only one entry, a private RSA key:</p>
    <code>2>[RSAEntry] = public_key:pem_decode(PemBin).
[{'RSAPrivateKey',&lt;&lt;224,108,117,203,152,40,15,77,128,126,
                    221,195,154,249,85,208,202,251,109,
                    119,120,57,29,89,19,9,...&gt;&gt;,
                  {"DES-EDE3-CBC",&lt;&lt;"kÙeø¼pµL"&gt;&gt;}}]</code>

    <p>In this following example, the password is <c>"abcd1234"</c>:</p>
    <code>3> Key = public_key:pem_entry_decode(RSAEntry, "abcd1234").
    #'RSAPrivateKey'{version = 'two-prime',
                 modulus = 1112355156729921663373...2737107,
                 publicExponent = 65537,
                 privateExponent = 58064406231183...2239766033,
                 prime1 = 11034766614656598484098...7326883017,
                 prime2 = 10080459293561036618240...77738643771,
                 exponent1 = 77928819327425934607...22152984217,
                 exponent2 = 36287623121853605733...20588523793,
                 coefficient = 924840412626098444...41820968343,
                 otherPrimeInfos = asn1_NOVALUE}</code>
    </section>
  
  <section>
    <title>X509 Certificates</title>
    <p>The following is an example of X509 certificates:</p>
    
      <code>1> {ok, PemBin} = file:read_file("cacerts.pem").
{ok,&lt;&lt;"-----BEGIN CERTIFICATE-----\nMIIC7jCCAl"...&gt;&gt;}</code>

      <p>The following file includes two certificates:</p>
      <code>2> [CertEntry1, CertEntry2] = public_key:pem_decode(PemBin).
[{'Certificate',&lt;&lt;48,130,2,238,48,130,2,87,160,3,2,1,2,2,
                  9,0,230,145,97,214,191,2,120,150,48,13,
                  ...&gt;&gt;,
                not_encrypted},
 {'Certificate',&lt;&lt;48,130,3,200,48,130,3,49,160,3,2,1,2,2,1,
                  1,48,13,6,9,42,134,72,134,247,...&gt;&gt;,
                not_encrypted}]</code>
      
      <p>Certificates can be decoded as usual:</p>
      <code>2> Cert = public_key:pem_entry_decode(CertEntry1).
#'Certificate'{
    tbsCertificate =
        #'TBSCertificate'{
            version = v3,serialNumber = 16614168075301976214,
            signature =
                #'AlgorithmIdentifier'{
                    algorithm = {1,2,840,113549,1,1,5},
                    parameters = &lt;&lt;5,0&gt;&gt;},
            issuer =
                {rdnSequence,
                    [[#'AttributeTypeAndValue'{
                          type = {2,5,4,3},
                          value = &lt;&lt;19,8,101,114,108,97,110,103,67,65&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,11},
                          value = &lt;&lt;19,10,69,114,108,97,110,103,32,79,84,80&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,10},
                          value = &lt;&lt;19,11,69,114,105,99,115,115,111,110,32,65,66&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,7},
                          value = &lt;&lt;19,9,83,116,111,99,107,104,111,108,109&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,6},
                          value = &lt;&lt;19,2,83,69&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {1,2,840,113549,1,9,1},
                          value = &lt;&lt;22,22,112,101,116,101,114,64,101,114,...&gt;&gt;}]]},
            validity =
                #'Validity'{
                    notBefore = {utcTime,"080109082929Z"},
                    notAfter = {utcTime,"080208082929Z"}},
            subject =
                {rdnSequence,
                    [[#'AttributeTypeAndValue'{
                          type = {2,5,4,3},
                          value = &lt;&lt;19,8,101,114,108,97,110,103,67,65&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,11},
                          value = &lt;&lt;19,10,69,114,108,97,110,103,32,79,84,80&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,10},
                          value = &lt;&lt;19,11,69,114,105,99,115,115,111,110,32,...&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,7},
                          value = &lt;&lt;19,9,83,116,111,99,107,104,111,108,...&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,6},
                          value = &lt;&lt;19,2,83,69&gt;&gt;}],
                     [#'AttributeTypeAndValue'{
                          type = {1,2,840,113549,1,9,1},
                          value = &lt;&lt;22,22,112,101,116,101,114,64,...&gt;&gt;}]]},
            subjectPublicKeyInfo =
                #'SubjectPublicKeyInfo'{
                    algorithm =
                        #'AlgorithmIdentifier'{
                            algorithm = {1,2,840,113549,1,1,1},
                            parameters = &lt;&lt;5,0&gt;&gt;},
                    subjectPublicKey =
                        {0,&lt;&lt;48,129,137,2,129,129,0,203,209,187,77,73,231,90,...&gt;&gt;}},
            issuerUniqueID = asn1_NOVALUE,
            subjectUniqueID = asn1_NOVALUE,
            extensions =
                [#'Extension'{
                     extnID = {2,5,29,19},
                     critical = true,
                     extnValue = [48,3,1,1,255]},
                 #'Extension'{
                     extnID = {2,5,29,15},
                     critical = false,
                     extnValue = [3,2,1,6]},
                 #'Extension'{
                     extnID = {2,5,29,14},
                     critical = false,
                     extnValue = [4,20,27,217,65,152,6,30,142|...]},
                 #'Extension'{
                     extnID = {2,5,29,17},
                     critical = false,
                     extnValue = [48,24,129,22,112,101,116,101|...]}]},
    signatureAlgorithm =
        #'AlgorithmIdentifier'{
            algorithm = {1,2,840,113549,1,1,5},
            parameters = &lt;&lt;5,0&gt;&gt;},
    signature =
    &lt;&lt;163,186,7,163,216,152,63,47,154,234,139,73,154,96,120,
    165,2,52,196,195,109,167,192,...&gt;&gt;}</code>

      <p>Parts of certificates can be decoded with
      <c>public_key:der_decode/2</c>, using the ASN.1 type of that part.
      However, an application-specific certificate extension requires 
      application-specific ASN.1 decode/encode-functions.
      In the recent example, the first value of <c>rdnSequence</c> is 
      of ASN.1 type <c>'X520CommonName'. ({2,5,4,3} = ?id-at-commonName)</c>:</p>
      
      <code>public_key:der_decode('X520CommonName', &lt;&lt;19,8,101,114,108,97,110,103,67,65&gt;&gt;).
{printableString,"erlangCA"}</code>

      <p>However, certificates can also be decoded using <c>pkix_decode_cert/2</c>, 
      which can customize and recursively decode standard parts of a certificate:</p>

      <code>3>{_, DerCert, _} = CertEntry1.</code>

      <code>4> public_key:pkix_decode_cert(DerCert, otp).
#'OTPCertificate'{
    tbsCertificate =
        #'OTPTBSCertificate'{
            version = v3,serialNumber = 16614168075301976214,
            signature =
                #'SignatureAlgorithm'{
                    algorithm = {1,2,840,113549,1,1,5},
                    parameters = 'NULL'},
            issuer =
                {rdnSequence,
                    [[#'AttributeTypeAndValue'{
                          type = {2,5,4,3},
                          value = {printableString,"erlangCA"}}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,11},
                          value = {printableString,"Erlang OTP"}}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,10},
                          value = {printableString,"Ericsson AB"}}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,7},
                          value = {printableString,"Stockholm"}}],
                     [#'AttributeTypeAndValue'{type = {2,5,4,6},value = "SE"}],
                     [#'AttributeTypeAndValue'{
                          type = {1,2,840,113549,1,9,1},
                          value = "peter@erix.ericsson.se"}]]},
            validity =
                #'Validity'{
                    notBefore = {utcTime,"080109082929Z"},
                    notAfter = {utcTime,"080208082929Z"}},
            subject =
                {rdnSequence,
                    [[#'AttributeTypeAndValue'{
                          type = {2,5,4,3},
                          value = {printableString,"erlangCA"}}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,11},
                          value = {printableString,"Erlang OTP"}}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,10},
                          value = {printableString,"Ericsson AB"}}],
                     [#'AttributeTypeAndValue'{
                          type = {2,5,4,7},
                          value = {printableString,"Stockholm"}}],
                     [#'AttributeTypeAndValue'{type = {2,5,4,6},value = "SE"}],
                     [#'AttributeTypeAndValue'{
                          type = {1,2,840,113549,1,9,1},
                          value = "peter@erix.ericsson.se"}]]},
            subjectPublicKeyInfo =
                #'OTPSubjectPublicKeyInfo'{
                    algorithm =
                        #'PublicKeyAlgorithm'{
                            algorithm = {1,2,840,113549,1,1,1},
                            parameters = 'NULL'},
                    subjectPublicKey =
                        #'RSAPublicKey'{
                            modulus =
                                1431267547247997...37419,
                            publicExponent = 65537}},
            issuerUniqueID = asn1_NOVALUE,
            subjectUniqueID = asn1_NOVALUE,
            extensions =
                [#'Extension'{
                     extnID = {2,5,29,19},
                     critical = true,
                     extnValue =
                         #'BasicConstraints'{
                             cA = true,pathLenConstraint = asn1_NOVALUE}},
                 #'Extension'{
                     extnID = {2,5,29,15},
                     critical = false,
                     extnValue = [keyCertSign,cRLSign]},
                 #'Extension'{
                     extnID = {2,5,29,14},
                     critical = false,
                     extnValue = [27,217,65,152,6,30,142,132,245|...]},
                 #'Extension'{
                     extnID = {2,5,29,17},
                     critical = false,
                     extnValue = [{rfc822Name,"peter@erix.ericsson.se"}]}]},
    signatureAlgorithm =
        #'SignatureAlgorithm'{
            algorithm = {1,2,840,113549,1,1,5},
            parameters = 'NULL'},
    signature =
         &lt;&lt;163,186,7,163,216,152,63,47,154,234,139,73,154,96,120,
           165,2,52,196,195,109,167,192,...&gt;&gt;}</code>

      <p>This call is equivalent to <c>public_key:pem_entry_decode(CertEntry1)</c>:</p>
      <code>5> public_key:pkix_decode_cert(DerCert, plain).
#'Certificate'{ ...}</code>
  </section>

  <section>
    <title>Encoding Public-Key Data to PEM Format</title>

    <p>If you have public-key data and want to create a PEM file
    this can be done by calling functions
    <c>public_key:pem_entry_encode/2</c> and <c>pem_encode/1</c> and 
    saving the result to a file. For example, assume that you have 
    <c>PubKey = 'RSAPublicKey'{}</c>. Then you can create a PEM-"RSA PUBLIC KEY" 
    file (ASN.1 type <c>'RSAPublicKey'</c>) or a PEM-"PUBLIC KEY" file
    (<c>'SubjectPublicKeyInfo'</c> ASN.1 type).</p>

    <p>The second element of the PEM-entry is the ASN.1 <c>DER</c> encoded
    key data:</p>

    <code>1> PemEntry = public_key:pem_entry_encode('RSAPublicKey', RSAPubKey).
{'RSAPublicKey', &lt;&lt;48,72,...&gt;&gt;, not_encrypted}

2> PemBin = public_key:pem_encode([PemEntry]).
&lt;&lt;"-----BEGIN RSA PUBLIC KEY-----\nMEgC...&gt;&gt;

3> file:write_file("rsa_pub_key.pem", PemBin).
ok</code>

    <p>or:</p>

    <code>1> PemEntry = public_key:pem_entry_encode('SubjectPublicKeyInfo', RSAPubKey).
{'SubjectPublicKeyInfo', &lt;&lt;48,92...&gt;&gt;, not_encrypted}

2> PemBin = public_key:pem_encode([PemEntry]).
&lt;&lt;"-----BEGIN PUBLIC KEY-----\nMFw...&gt;&gt;

3> file:write_file("pub_key.pem", PemBin).
ok</code>

  </section>
</section>

<section>
      <title>RSA Public-Key Cryptography</title>
       <p>Suppose you have the following private key and a corresponding public key:</p>
       <list type="bulleted">
	 <item><c>PrivateKey = #'RSAPrivateKey{}'</c> and 
	 the plaintext <c>Msg = binary()</c></item>
	 <item><c>PublicKey = #'RSAPublicKey'{}</c>
	 </item>
       </list>
       <p>Then you can proceed as follows:</p>

       <p>Encrypt with the private key:</p>
       <code>RsaEncrypted = public_key:encrypt_private(Msg, PrivateKey),
Msg = public_key:decrypt_public(RsaEncrypted, PublicKey),</code>

       <p>Encrypt with the public key:</p>
       <code>RsaEncrypted = public_key:encrypt_public(Msg, PublicKey),
Msg = public_key:decrypt_private(RsaEncrypted, PrivateKey),</code>

      <note><p>You normally do only one of the encrypt or decrypt operations, 
      and the peer does the other. This normaly used in legacy applications
      as a primitive digital signature.
      </p></note>

  </section>

  <section>
    <title>Digital Signatures</title>

    <p>Suppose you have the following private key and a corresponding public key:</p>
    
    <list type="bulleted">
       <item><c>PrivateKey = #'RSAPrivateKey{}'</c> or
       <c>#'DSAPrivateKey'{}</c> and the plaintext <c>Msg = binary()</c></item>
       <item><c>PublicKey = #'RSAPublicKey'{}</c> or
       <c>{integer(), #'DssParams'{}}</c></item>
     </list>
     <p>Then you can proceed as follows:</p>

    <code>Signature = public_key:sign(Msg, sha, PrivateKey),
true = public_key:verify(Msg, sha, Signature, PublicKey),</code>

    <note><p>You normally do only one of the sign or verify operations,
    and the peer does the other.</p></note>

    <p>It can be appropriate to calculate the message digest before
    calling <c>sign</c> or <c>verify</c>, and then use <c>none</c> as 
    second argument:</p>

    <code>Digest = crypto:sha(Msg),
Signature = public_key:sign(Digest, none, PrivateKey),
true = public_key:verify(Digest, none, Signature, PublicKey),</code>
    
  </section>
  
 <section>
   <marker id="verify_hostname"></marker>
   <title>Verifying a certificate hostname</title>
   <section>
     <title>Background</title>
     <p>When a client checks a server certificate there are a number of checks available like
     checks that the certificate is not revoked, not forged or not out-of-date.
     </p>
     <p>There are however attacks that are not detected by those checks. Suppose a bad guy has
     succeded with a DNS infection. Then the client could belive it is connecting to one host but
     ends up at another but evil one. Though it is evil, it could have a perfectly legal
     certificate! The certificate has a valid signature, it is not revoked, the certificate chain
     is not faked and has a trusted root and so on.
     </p>
     <p>To detect that the server is not the intended one, the client must additionaly perform
     a <i>hostname verification</i>. This procedure is described in
     <url href="https://tools.ietf.org/html/rfc6125">RFC 6125</url>. The idea is that the certificate
     lists the hostnames it could be fetched from. This is checked by the certificate issuer when
     the certificate is signed. So if the certificate is issued by a trusted root the client 
     could trust the host names signed in it.
     </p>
     <p>There is a default hostname matching procedure defined in
     <url href="https://tools.ietf.org/html/rfc6125#section/6">RFC 6125, section 6</url>
     as well as protocol dependent variations defined in
     <url href="https://tools.ietf.org/html/rfc6125#appendix-B">RFC 6125 appendix B</url>.
     The default procedure is implemented in
     <seemfa marker="public_key:public_key#pkix_verify_hostname/2">public_key:pkix_verify_hostname/2,3</seemfa>.
     It is possible for a client to hook in modified rules using the options list.
     </p>
     <p>Some terminology is needed: the certificate presents hostname(s) on which it is valid.
     Those are called <i>Presented IDs</i>. The hostname(s) the client belives it connects to
     are called <i>Reference IDs</i>. The matching rules aims to verify that there is at least
     one of the Reference IDs that matches one of the Presented IDs. If not, the verification fails.
     </p>
     <p>The IDs contains normal fully qualified domain names like e.g <c>foo.example.com</c>,
     but IP addresses are not recommended. The rfc describes why this is not recommended as well
     as security considerations about how to aquire the Reference IDs.
     </p>
     <p>Internationalized domain names are not supported.
     </p>
   </section>
   <section>
     <title>The verification process</title>
     <p>Traditionally the Presented IDs were found in the <c>Subject</c> certificate field as <c>CN</c>
     names. This is still quite common. When printing a certificate they show up as:
     </p>
     <code>
 $ openssl x509 -text &lt; cert.pem
 ...
 Subject: C=SE, CN=example.com, CN=*.example.com, O=erlang.org
 ...
     </code>
     <p>The example <c>Subject</c> field has one C, two CN and one O part. It is only the
     CN (Common Name) that is used by hostname verification. The two other (C and O) is not used
     here even when they contain a domain name like the O part. The C and O parts are defined
     elsewhere and meaningful only for other functions.
     </p>
     <p>In the example the Presented IDs are <c>example.com</c> as well as hostnames matching
     <c>*.example.com</c>. For example <c>foo.example.com</c> and <c>bar.example.com</c> both
     matches but not <c>foo.bar.example.com</c>. The name <c>erlang.org</c> matches neither
     since it is not a CN.
     </p>
     <p>In case where the Presented IDs are fetched from the <c>Subject</c> certificate field, the
     names may contain wildcard characters. The function handles this as defined in
     <url href="https://tools.ietf.org/html/rfc6125#section-6.4.3">chapter 6.4.3 in RFC 6125</url>.
     </p>
     <p>There may only be one wildcard character and that is in the first label, for example:
     <c>*.example.com</c>. This matches <c>foo.example.com</c> but neither <c>example.com</c> nor
     <c>foo.bar.example.com</c>.
     </p>
     <p>There may be label characters before or/and after the wildcard. For example:
     <c>a*d.example.com</c> matches <c>abcd.example.com</c> and <c>ad.example.com</c>,
     but not <c>ab.cd.example.com</c>.
     </p>
     <p>In the previous example there is no indication of which protocols are expected. So a client
     has no indication of whether it is a web server, an ldap server or maybe a sip server it is
     connected to.
     There are fields in the certificate that can indicate this. To be more exact, the rfc
     introduces the usage of the <c>X509v3 Subject Alternative Name</c> in the <c>X509v3 extensions</c>
     field:
     </p>
     <code>
 $ openssl x509 -text &lt; cert.pem
 ...
 X509v3 extensions:
     X509v3 Subject Alternative Name:
         DNS:kb.example.org, URI:https://www.example.org
 ...
     </code>
     <p>Here <c>kb.example.org</c> serves any protocol while <c>www.example.org</c> presents a secure
     web server.
     </p>

     <p>The next example has both <c>Subject</c> and <c>Subject Alternate Name</c> present:</p>
     <code>
 $ openssl x509 -text &lt; cert.pem
 ...
 Subject: C=SE, CN=example.com, CN=*.example.com, O=erlang.org
 ...
 X509v3 extensions:
     X509v3 Subject Alternative Name:
         DNS:kb.example.org, URI:https://www.example.org
 ...
     </code>
     <p>The RFC states that if a certificate defines Reference IDs in a <c>Subject Alternate Name</c>
     field, the <c>Subject</c> field MUST NOT be used for host name checking, even if it contains
     valid CN names.
     Therefore only <c>kb.example.org</c> and <c>https://www.example.org</c> matches. The match fails
     both for <c>example.com</c> and <c>foo.example.com</c> becuase they are in the <c>Subject</c>
     field which is not checked because the <c>Subject Alternate Name</c> field is present.
     </p>
   </section>

   <section>
    <marker id="verify_hostname_examples"></marker>
     <title>Function call examples</title>
     <note>
       <p>Other applications like ssl/tls or https might have options that are passed
       down to the <c>public_key:pkix_verify_hostname</c>. You will probably not
       have to call it directly</p>
     </note>
     <p>Suppose our client expects to connect to the web server https://www.example.net. This
     URI is therefore the Reference IDs of the client.
     The call will be:
     </p>
     <code>
 public_key:pkix_verify_hostname(CertFromHost,
                                 [{uri_id, "https://www.example.net"}
                                 ]).
     </code>
     <p>The call will return <c>true</c> or <c>false</c> depending on the check. The caller
     do not need to handle the matching rules in the rfc. The matching will proceed as:
     </p>
     <list>
       <item>If there is a <c>Subject Alternate Name</c> field, the <c>{uri_id,string()}</c> in the
       function call will be compared to any
       <c>{uniformResourceIdentifier,string()}</c> in the Certificate field.
       If the two <c>strings()</c> are equal (case insensitive), there is a match.
       The same applies for any <c>{dns_id,string()}</c> in the call which is compared
       with all <c>{dNSName,string()}</c> in the Certificate field.
       </item>
       <item>If there is NO <c>Subject Alternate Name</c> field, the <c>Subject</c> field will be
       checked. All <c>CN</c> names will be compared to all hostnames <i>extracted</i> from 
       <c>{uri_id,string()}</c> and from <c>{dns_id,string()}</c>.
       </item>
     </list>
   </section>
   <section>
     <title>Extending the search mechanism</title>
     <p>The caller can use own extraction and matching rules. This is done with the two options
     <c>fqdn_fun</c> and <c>match_fun</c>.
     </p>
     <section>
       <marker id="hostname_extraction"></marker>
       <title>Hostname extraction</title>
       <p>The <c>fqdn_fun</c> extracts hostnames (Fully Qualified Domain Names) from uri_id
       or other ReferenceIDs that are not pre-defined in the public_key function.
       Suppose you have some URI with a very special protocol-part:
       <c>myspecial://example.com"</c>. Since this a non-standard URI there will be no hostname 
       extracted for matching CN-names in the <c>Subject</c>.</p>
       <p>To "teach" the function how to extract, you can give a fun which replaces the default
       extraction function.
       The  <c>fqdn_fun</c> takes one argument and returns
       either a <c>string()</c> to be matched to each CN-name or the atom <c>default</c> which will invoke
       the default fqdn extraction function. The return value <c>undefined</c> removes the current
       URI from the fqdn extraction.
       </p>
       <code>
 ...
 Extract = fun({uri_id, "myspecial://"++HostName}) -> HostName;
              (_Else) -> default
           end,
 ...	 
 public_key:pkix_verify_hostname(CertFromHost, RefIDs,
                                 [{fqdn_fun, Extract}])
 ...
       </code>
     </section>
     <section>
       <marker id="redefining_match_op"></marker>
       <title>Re-defining the match operation</title>
       <p>The default matching handles dns_id and uri_id. In an uri_id the value is tested for
       equality with a value from the <c>Subject Alternate Name</c>. If som other kind of matching
       is needed, use the  <c>match_fun</c> option.
       </p>
       <p>The  <c>match_fun</c> takes two arguments and returns either <c>true</c>,
       <c>false</c> or <c>default</c>. The value  <c>default</c> will invoke the default
       match function.
       </p>
       <code>
 ...
 Match = fun({uri_id,"myspecial://"++A},
             {uniformResourceIdentifier,"myspecial://"++B}) ->
                                                    my_match(A,B);
            (_RefID, _PresentedID) ->
                                default
         end,
 ...
 public_key:pkix_verify_hostname(CertFromHost, RefIDs,
                                 [{match_fun, Match}]),
 ...
       </code>
       <p>In case of a match operation between a ReferenceID and a CN value from the <c>Subject</c>
       field, the first argument to the fun is the extracted hostname from the ReferenceID, and the
       second argument is the tuple <c>{cn, string()}</c> taken from the <c>Subject</c> field. That
       makes it possible to have separate matching rules for Presented IDs from the  <c>Subject</c>
       field and from the <c>Subject Alternate Name</c> field.
       </p>
       <p>The default matching transformes the ascii values in strings to lowercase before comparing.
       The  <c>match_fun</c> is however called without any transfomation applied to the strings.  The
       reason is to enable the user to do unforseen handling of the strings where the original format
       is needed.
       </p>
     </section>
   </section>
   <section>
     <title>"Pinning" a Certificate</title>
     <p>The <url href="https://tools.ietf.org/html/rfc6125">RFC 6125</url> defines <i>pinning</i>
     as:</p>
     <quote>
       <p>"The act of establishing a cached name association between
       the application service's certificate and one of the client's
       reference identifiers, despite the fact that none of the presented
       identifiers matches the given reference identifier. ..."
       </p>
     </quote>
     <p>The purpose is to have a mechanism for a human to accept an otherwise faulty Certificate.
     In for example a web browser, you could get a question like </p>
     <quote>
       <p>Warning: you wanted to visit the site www.example.com,
       but the certificate is for shop.example.com. Accept anyway (yes/no)?"
       </p>
     </quote>
     <p>This could be accomplished with the option <c>fail_callback</c> which will
     be called if the hostname verification fails:
     </p>
     <code>
 -include_lib("public_key/include/public_key.hrl"). % Record def
 ...
 Fail = fun(#'OTPCertificate'{}=C) ->
              case in_my_cache(C) orelse my_accept(C) of
                  true ->
                       enter_my_cache(C),
                       true;
                  false ->
                       false
         end,
 ...
 public_key:pkix_verify_hostname(CertFromHost, RefIDs,
                                 [{fail_callback, Fail}]),
 ...
     </code>
   </section>
 </section>

  <section>
    <title>SSH Files</title>
    
    <p>SSH typically uses PEM files for private keys but has its
    own file format for storing public keys. The <c>public_key</c>
    application can be used to parse the content of SSH public-key files.</p>

    <section>
   <title>RFC 4716 SSH Public-Key Files</title>

    <p>RFC 4716 SSH files looks confusingly like PEM files,
       but there are some differences:</p>
      <code>1> {ok, SshBin} = file:read_file("ssh2_rsa_pub").
{ok, &lt;&lt;"---- BEGIN SSH2 PUBLIC KEY ----\nAAAA"...&gt;&gt;}</code>

    <p>This is equivalent to calling <c>public_key:ssh_decode(SshBin, rfc4716_public_key)</c>:
    </p>
      <code>2> public_key:ssh_decode(SshBin, public_key).
[{#'RSAPublicKey'{modulus = 794430685...91663,
                  publicExponent = 35}, []}]</code>

 </section>

 <section>
   <title>OpenSSH Public-Key Format</title>
   <p>OpenSSH public-key format looks as follows:</p>
      <code>1> {ok, SshBin} = file:read_file("openssh_dsa_pub").
{ok,&lt;&lt;"ssh-dss AAAAB3Nza"...&gt;&gt;}</code>

    <p>This is equivalent to calling <c>public_key:ssh_decode(SshBin, openssh_public_key)</c>:
    </p>
    <code>2>  public_key:ssh_decode(SshBin, public_key).
[{{15642692...694280725,
   #'Dss-Parms'{p = 17291273936...696123221,
                q = 1255626590179665817295475654204371833735706001853,
                g = 10454211196...480338645}},
  [{comment,"dhopson@VMUbuntu-DSH"}]}]</code>
 </section>

 <section>
   <title>Known Hosts - OpenSSH Format</title>
   <p>Known hosts - OpenSSH format looks as follows:</p>
      <code>1> {ok, SshBin} = file:read_file("known_hosts").
{ok,&lt;&lt;"hostname.domain.com,192.168.0.1 ssh-rsa AAAAB...&gt;&gt;}</code>

    <p>Returns a list of public keys and their related attributes.
    Each pair of key and attribute corresponds to one entry in
    the known hosts file:</p>
    
    <code>2>  public_key:ssh_decode(SshBin, known_hosts).
[{#'RSAPublicKey'{modulus = 1498979460408...72721699,
                  publicExponent = 35},
  [{hostnames,["hostname.domain.com","192.168.0.1"]}]},
 {#'RSAPublicKey'{modulus = 14989794604088...2721699,
                  publicExponent = 35},
  [{comment,"foo@bar.com"},
   {hostnames,["|1|BWO5qDxk/cFH0wa05JLdHn+j6xQ=|rXQvIxh5cDD3C43k5DPDamawVNA="]}]}]</code>
  </section>

  <section>
    <title>Authorized Keys - OpenSSH Format</title>
    <p>Authorized keys - OpenSSH format looks as follows:</p>

    <code>1> {ok, SshBin} = file:read_file("auth_keys").
{ok, &lt;&lt;"command=\"dump /home\",no-pty,no-port-forwarding ssh-rsa AAA...&gt;&gt;}</code>

    <p>Returns a list of public keys and their related attributes.
    Each pair of key and attribute corresponds to one entry in
    the authorized key file:</p>

    <code>2> public_key:ssh_decode(SshBin, auth_keys).
[{#'RSAPublicKey'{modulus = 794430685...691663,
                  publicExponent = 35},
  [{comment,"dhopson@VMUbuntu-DSH"},
   {options,["command=\"dump/home\"","no-pty",
             "no-port-forwarding"]}]},
 {{1564269258491...607694280725,
   #'Dss-Parms'{p = 17291273936185...763696123221,
                q = 1255626590179665817295475654204371833735706001853,
                g = 10454211195705...60511039590076780999046480338645}},
  [{comment,"dhopson@VMUbuntu-DSH"}]}]</code>
    </section>

    <section>
      <title>Creating an SSH File from Public-Key Data</title>

      <p>If you got a public key <c>PubKey</c> and a related list of
      attributes <c>Attributes</c> as returned
      by <c>ssh_decode/2</c>, you can create a new SSH file, for example:</p>
      <code>N> SshBin = public_key:ssh_encode([{PubKey, Attributes}], openssh_public_key),
&lt;&lt;"ssh-rsa "...&gt;&gt;
N+1> file:write_file("id_rsa.pub", SshBin).
ok</code>
    </section>
  </section>
</chapter>
