path: root/lib/crypto/doc/src/crypto.xml

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<!DOCTYPE erlref SYSTEM "erlref.dtd">

<erlref>
  <header>
    <copyright>
      <year>1999</year><year>2009</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
    </copyright>
    <legalnotice>
      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.
    
    </legalnotice>

    <title>crypto</title>
    <prepared>Peter H&ouml;gfeldt</prepared>
    <docno></docno>
    <date>2000-06-20</date>
    <rev>B</rev>
  </header>
  <module>crypto</module>
  <modulesummary>Crypto Functions</modulesummary>
  <description>
    <p>This module provides a set of cryptographic functions.
      </p>
    <p>References:</p>
    <list type="bulleted">
      <item>
        <p>md5: The MD5 Message Digest Algorithm (RFC 1321)</p>
      </item>
      <item>
        <p>sha: Secure Hash Standard (FIPS 180-2)</p>
      </item>
      <item>
        <p>hmac: Keyed-Hashing for Message Authentication (RFC 2104)</p>
      </item>
      <item>
        <p>des: Data Encryption Standard (FIPS 46-3)</p>
      </item>
      <item>
        <p>aes: Advanced Encryption Standard (AES) (FIPS 197) </p>
      </item>
      <item>
        <p>ecb, cbc, cfb, ofb: Recommendation for Block Cipher Modes
          of Operation (NIST SP 800-38A).</p>
      </item>
      <item>
        <p>rsa: Recommendation for Block Cipher Modes of Operation
          (NIST 800-38A)</p>
      </item>
      <item>
        <p>dss: Digital Signature Standard (FIPS 186-2)</p>
      </item>
    </list>
    <p>The above publications can be found at <url href="http://csrc.nist.gov/publications">NIST publications</url>, at <url href="http://www.ietf.org">IETF</url>.
      </p>
    <p><em>Types</em></p>
    <pre>
byte() = 0 ... 255
ioelem() = byte() | binary() | iolist()
iolist() = [ioelem()]
Mpint() = <![CDATA[<<ByteLen:32/integer-big, Bytes:ByteLen/binary>>]]>
    </pre>
    <p></p>
  </description>
  <funcs>
    <func>
      <name>start() -> ok</name>
      <fsummary>Start the crypto server.</fsummary>
      <desc>
        <p>Starts the crypto server.</p>
      </desc>
    </func>
    <func>
      <name>stop() -> ok</name>
      <fsummary>Stop the crypto server.</fsummary>
      <desc>
        <p>Stops the crypto server.</p>
      </desc>
    </func>
    <func>
      <name>info() -> [atom()]</name>
      <fsummary>Provide a list of available crypto functions.</fsummary>
      <desc>
        <p>Provides the available crypto functions in terms of a list
          of atoms.</p>
      </desc>
    </func>
    <func>
      <name>info_lib() -> [{Name,VerNum,VerStr}]</name>
      <fsummary>Provides information about the libraries used by crypto.</fsummary>
      <type>
        <v>Name = binary()</v>
        <v>VerNum = integer()</v>
        <v>VerStr = binary()</v>
      </type>
      <desc>
        <p>Provides the name and version of the libraries used by crypto.</p>
        <p><c>Name</c> is the name of the library. <c>VerNum</c> is
        the numeric version according to the library's own versioning
        scheme. <c>VerStr</c> contains a text variant of the version.</p>
        <pre>
> <input>info_lib().</input>
[{&lt;&lt;"OpenSSL"&gt;&gt;,9469983,&lt;&lt;"OpenSSL 0.9.8a 11 Oct 2005"&gt;&gt;}]
        </pre>
      </desc>
    </func>
    <func>
      <name>md5(Data) -> Digest</name>
      <fsummary>Compute an <c>MD5</c>message digest from <c>Data</c></fsummary>
      <type>
        <v>Data = iolist() | binary()</v>
        <v>Digest = binary()</v>
      </type>
      <desc>
        <p>Computes an <c>MD5</c> message digest from <c>Data</c>, where
          the length of the digest is 128 bits (16 bytes).</p>
      </desc>
    </func>
    <func>
      <name>md5_init() -> Context</name>
      <fsummary>Creates an MD5 context</fsummary>
      <type>
        <v>Context = binary()</v>
      </type>
      <desc>
        <p>Creates an MD5 context, to be used in subsequent calls to 
          <c>md5_update/2</c>.</p>
      </desc>
    </func>
    <func>
      <name>md5_update(Context, Data) -> NewContext</name>
      <fsummary>Update an MD5 <c>Context</c>with <c>Data</c>, and return a <c>NewContext</c></fsummary>
      <type>
        <v>Data = iolist() | binary()</v>
        <v>Context = NewContext = binary()</v>
      </type>
      <desc>
        <p>Updates an MD5 <c>Context</c> with <c>Data</c>, and returns
          a <c>NewContext</c>.</p>
      </desc>
    </func>
    <func>
      <name>md5_final(Context) -> Digest</name>
      <fsummary>Finish the update of an MD5 <c>Context</c>and return the computed <c>MD5</c>message digest</fsummary>
      <type>
        <v>Context = Digest = binary()</v>
      </type>
      <desc>
        <p>Finishes the update of an MD5 <c>Context</c> and returns
          the computed <c>MD5</c> message digest.</p>
      </desc>
    </func>
    <func>
      <name>sha(Data) -> Digest</name>
      <fsummary>Compute an <c>SHA</c>message digest from <c>Data</c></fsummary>
      <type>
        <v>Data = iolist() | binary()</v>
        <v>Digest = binary()</v>
      </type>
      <desc>
        <p>Computes an <c>SHA</c> message digest from <c>Data</c>, where
          the length of the digest is 160 bits (20 bytes).</p>
      </desc>
    </func>
    <func>
      <name>sha_init() -> Context</name>
      <fsummary>Create an SHA context</fsummary>
      <type>
        <v>Context = binary()</v>
      </type>
      <desc>
        <p>Creates an SHA context, to be used in subsequent calls to 
          <c>sha_update/2</c>.</p>
      </desc>
    </func>
    <func>
      <name>sha_update(Context, Data) -> NewContext</name>
      <fsummary>Update an SHA context</fsummary>
      <type>
        <v>Data = iolist() | binary()</v>
        <v>Context = NewContext = binary()</v>
      </type>
      <desc>
        <p>Updates an SHA <c>Context</c> with <c>Data</c>, and returns
          a <c>NewContext</c>.</p>
      </desc>
    </func>
    <func>
      <name>sha_final(Context) -> Digest</name>
      <fsummary>Finish the update of an SHA context</fsummary>
      <type>
        <v>Context = Digest = binary()</v>
      </type>
      <desc>
        <p>Finishes the update of an SHA <c>Context</c> and returns
          the computed <c>SHA</c> message digest.</p>
      </desc>
    </func>
    <func>
      <name>md5_mac(Key, Data) -> Mac</name>
      <fsummary>Compute an <c>MD5 MAC</c>message authentification code</fsummary>
      <type>
        <v>Key = Data = iolist() | binary()</v>
        <v>Mac = binary()</v>
      </type>
      <desc>
        <p>Computes an <c>MD5 MAC</c> message authentification code
          from <c>Key</c> and <c>Data</c>, where the the length of the
          Mac is 128 bits (16 bytes).</p>
      </desc>
    </func>
    <func>
      <name>md5_mac_96(Key, Data) -> Mac</name>
      <fsummary>Compute an <c>MD5 MAC</c>message authentification code</fsummary>
      <type>
        <v>Key = Data = iolist() | binary()</v>
        <v>Mac = binary()</v>
      </type>
      <desc>
        <p>Computes an <c>MD5 MAC</c> message authentification code
          from <c>Key</c> and <c>Data</c>, where the length of the Mac
          is 96 bits (12 bytes).</p>
      </desc>
    </func>
    <func>
      <name>sha_mac(Key, Data) -> Mac</name>
      <fsummary>Compute an <c>MD5 MAC</c>message authentification code</fsummary>
      <type>
        <v>Key = Data = iolist() | binary()</v>
        <v>Mac = binary()</v>
      </type>
      <desc>
        <p>Computes an <c>SHA MAC</c> message authentification code
          from <c>Key</c> and <c>Data</c>, where the length of the Mac
          is 160 bits (20 bytes).</p>
      </desc>
    </func>
    <func>
      <name>sha_mac_96(Key, Data) -> Mac</name>
      <fsummary>Compute an <c>MD5 MAC</c>message authentification code</fsummary>
      <type>
        <v>Key = Data = iolist() | binary()</v>
        <v>Mac = binary()</v>
      </type>
      <desc>
        <p>Computes an <c>SHA MAC</c> message authentification code
          from <c>Key</c> and <c>Data</c>, where the length of the Mac
          is 96 bits (12 bytes).</p>
      </desc>
    </func>
    <func>
      <name>des_cbc_encrypt(Key, IVec, Text) -> Cipher</name>
      <fsummary>Encrypt <c>Text</c>according to DES in CBC mode</fsummary>
      <type>
        <v>Key = Text = iolist() | binary()</v>
        <v>IVec = Cipher = binary()</v>
      </type>
      <desc>
        <p>Encrypts <c>Text</c> according to DES in CBC
          mode. <c>Text</c> must be a multiple of 64 bits (8
          bytes). <c>Key</c> is the DES key, and <c>IVec</c> is an
          arbitrary initializing vector. The lengths of <c>Key</c> and
          <c>IVec</c> must be 64 bits (8 bytes).</p>
      </desc>
    </func>
    <func>
      <name>des_cbc_decrypt(Key, IVec, Cipher) -> Text</name>
      <fsummary>Decrypt <c>Cipher</c>according to DES in CBC mode</fsummary>
      <type>
        <v>Key = Cipher = iolist() | binary()</v>
        <v>IVec = Text = binary()</v>
      </type>
      <desc>
        <p>Decrypts <c>Cipher</c> according to DES in CBC mode.
          <c>Key</c> is the DES key, and <c>IVec</c> is an arbitrary
          initializing vector.  <c>Key</c> and <c>IVec</c> must have
          the same values as those used when encrypting. <c>Cipher</c>
          must be a multiple of 64 bits (8 bytes).  The lengths of
          <c>Key</c> and <c>IVec</c> must be 64 bits (8 bytes).</p>
      </desc>
    </func>
    <func>
      <name>des_cbc_ivec(Data) -> IVec</name>
      <fsummary>Get <c>IVec</c> to be used in next iteration of
                <c>des_cbc_[ecrypt|decrypt]</c></fsummary>
      <type>
        <v>Data = iolist() | binary()</v>
        <v>IVec = binary()</v>
      </type>
      <desc>
        <p>Returns the <c>IVec</c> to be used in a next iteration of 
          <c>des_cbc_[encrypt|decrypt]</c>. <c>Data</c> is the encrypted
          data from the previous iteration step.</p>
      </desc>
    </func>
    <func>
      <name>des3_cbc_encrypt(Key1, Key2, Key3, IVec, Text) -> Cipher</name>
      <fsummary>Encrypt <c>Text</c>according to DES3 in CBC mode</fsummary>
      <type>
        <v>Key1 =Key2 = Key3 Text = iolist() | binary()</v>
        <v>IVec = Cipher = binary()</v>
      </type>
      <desc>
        <p>Encrypts <c>Text</c> according to DES3 in CBC
          mode. <c>Text</c> must be a multiple of 64 bits (8
          bytes). <c>Key1</c>, <c>Key2</c>, <c>Key3</c>, are the DES
          keys, and <c>IVec</c> is an arbitrary initializing
          vector. The lengths of each of <c>Key1</c>, <c>Key2</c>,
          <c>Key3</c> and <c>IVec</c> must be 64 bits (8 bytes).</p>
      </desc>
    </func>
    <func>
      <name>des3_cbc_decrypt(Key1, Key2, Key3, IVec, Cipher) -> Text</name>
      <fsummary>Decrypt <c>Cipher</c>according to DES in CBC mode</fsummary>
      <type>
        <v>Key1 = Key2 = Key3 = Cipher = iolist() | binary()</v>
        <v>IVec = Text = binary()</v>
      </type>
      <desc>
        <p>Decrypts <c>Cipher</c> according to DES3 in CBC mode.
          <c>Key1</c>, <c>Key2</c>, <c>Key3</c> are the DES key, and
          <c>IVec</c> is an arbitrary initializing vector.
          <c>Key1</c>, <c>Key2</c>, <c>Key3</c> and <c>IVec</c> must
          and <c>IVec</c> must have the same values as those used when
          encrypting. <c>Cipher</c> must be a multiple of 64 bits (8
          bytes).  The lengths of <c>Key1</c>, <c>Key2</c>,
          <c>Key3</c>, and <c>IVec</c> must be 64 bits (8 bytes).</p>
      </desc>
    </func>
    <func>
      <name>blowfish_cfb64_encrypt(Key, IVec, Text) -> Cipher</name>
      <fsummary>Encrypt <c>Text</c>using Blowfish in CFB mode with 64
        bit feedback</fsummary>
      <type>
        <v>Key = Text = iolist() | binary()</v>
        <v>IVec = Cipher = binary()</v>
      </type>
      <desc>
        <p>Encrypts <c>Text</c> using Blowfish in CFB mode with 64 bit
          feedback. <c>Key</c> is the Blowfish key, and <c>IVec</c> is an
          arbitrary initializing vector. The length of <c>IVec</c>
          must be 64 bits (8 bytes).</p>
      </desc>
    </func>
    <func>
      <name>blowfish_cfb64_decrypt(Key, IVec, Text) -> Cipher</name>
      <fsummary>Decrypt <c>Text</c>using Blowfish in CFB mode with 64
        bit feedback</fsummary>
      <type>
        <v>Key = Text = iolist() | binary()</v>
        <v>IVec = Cipher = binary()</v>
      </type>
      <desc>
        <p>Decrypts <c>Text</c> using Blowfish in CFB mode with 64 bit
          feedback. <c>Key</c> is the Blowfish key, and <c>IVec</c> is an
          arbitrary initializing vector. The length of <c>IVec</c>
          must be 64 bits (8 bytes).</p>
      </desc>
    </func>
    <func>
      <name>aes_cfb_128_encrypt(Key, IVec, Text) -> Cipher</name>
      <name>aes_cbc_128_encrypt(Key, IVec, Text) -> Cipher</name>
      <fsummary>Encrypt <c>Text</c>according to AES in Cipher Feedback  mode or Cipher Block Chaining mode</fsummary>
      <type>
        <v>Key = Text = iolist() | binary()</v>
        <v>IVec = Cipher = binary()</v>
      </type>
      <desc>
        <p>Encrypts <c>Text</c> according to AES in Cipher Feedback 
          mode (CFB) or Cipher Block Chaining mode (CBC). <c>Text</c>
          must be a multiple of 128 bits (16 bytes). <c>Key</c> is the
          AES key, and <c>IVec</c> is an arbitrary initializing vector.
          The lengths of <c>Key</c> and <c>IVec</c> must be 128 bits
          (16 bytes).</p>
      </desc>
    </func>
    <func>
      <name>aes_cfb_128_decrypt(Key, IVec, Cipher) -> Text</name>
      <name>aes_cbc_128_decrypt(Key, IVec, Cipher) -> Text</name>
      <fsummary>Decrypt <c>Cipher</c>according to AES in Cipher Feedback  mode or Cipher Block Chaining mode</fsummary>
      <type>
        <v>Key = Cipher = iolist() | binary()</v>
        <v>IVec = Text = binary()</v>
      </type>
      <desc>
        <p>Decrypts <c>Cipher</c> according to Cipher Feedback Mode (CFB)
          or Cipher Block Chaining mode (CBC).
          <c>Key</c> is the AES key, and <c>IVec</c> is an arbitrary
          initializing vector. <c>Key</c> and <c>IVec</c> must have
          the same values as those used when encrypting. <c>Cipher</c>
          must be a multiple of 128 bits (16 bytes).  The lengths of
          <c>Key</c> and <c>IVec</c> must be 128 bits (16 bytes).</p>
      </desc>
    </func>
    <func>
      <name>aes_cbc_ivec(Data) -> IVec</name>
      <fsummary>Get <c>IVec</c> to be used in next iteration of
                <c>aes_cbc_*_[ecrypt|decrypt]</c></fsummary>
      <type>
        <v>Data = iolist() | binary()</v>
        <v>IVec = binary()</v>
      </type>
      <desc>
        <p>Returns the <c>IVec</c> to be used in a next iteration of 
          <c>aes_cbc_*_[encrypt|decrypt]</c>. <c>Data</c> is the encrypted
          data from the previous iteration step.</p>
      </desc>
    </func>
    <func>
      <name>erlint(Mpint) -> N</name>
      <name>mpint(N) -> Mpint</name>
      <fsummary>Convert between binary multi-precision integer and erlang big integer</fsummary>
      <type>
        <v>Mpint = binary()</v>
        <v>N = integer()</v>
      </type>
      <desc>
        <p>Convert a binary multi-precision integer <c>Mpint</c> to and from
          an erlang big integer. A multi-precision integer is a binary
          with the following form:
          <c><![CDATA[<<ByteLen:32/integer, Bytes:ByteLen/binary>>]]></c> where both
          <c>ByteLen</c> and <c>Bytes</c> are big-endian. Mpints are used in
          some of the functions in <c>crypto</c> and are not translated
          in the API for performance reasons.</p>
      </desc>
    </func>
    <func>
      <name>rand_bytes(N) -> binary()</name>
      <fsummary>Generate a binary of random bytes</fsummary>
      <type>
        <v>N = integer()</v>
      </type>
      <desc>
        <p>Generates N bytes randomly uniform 0..255, and returns the
          result in a binary. Uses the <c>crypto</c> library pseudo-random
          number generator.</p>
      </desc>
    </func>
    <func>
      <name>rand_uniform(Lo, Hi) -> N</name>
      <fsummary>Generate a random number</fsummary>
      <type>
        <v>Lo, Hi, N = Mpint | integer()</v>
        <v>Mpint = binary()</v>
      </type>
      <desc>
        <p>Generate a random number <c><![CDATA[N, Lo =< N < Hi.]]></c> Uses the
          <c>crypto</c> library pseudo-random number generator. The
          arguments (and result) can be either erlang integers or binary
          multi-precision integers.</p>
      </desc>
    </func>
    <func>
      <name>mod_exp(N, P, M) -> Result</name>
      <fsummary>Perform N ^ P mod M</fsummary>
      <type>
        <v>N, P, M, Result = Mpint</v>
        <v>Mpint = binary()</v>
      </type>
      <desc>
        <p>This function performs the exponentiation <c>N ^ P mod M</c>,
          using the <c>crypto</c> library.</p>
      </desc>
    </func>

    <func>
      <name>rsa_sign(Data, Key) -> Signature</name>
      <name>rsa_sign(DigestType, Data, Key) -> Signature</name> 
      <fsummary>Sign the data using rsa with the given key.</fsummary>
      <type>
        <v>Data = Mpint</v>
        <v>Key = [E, N, D]</v>
        <v>E, N, D = Mpint</v>
        <d>Where <c>E</c> is the public exponent, <c>N</c> is public modulus and 
	  <c>D</c> is the private exponent.</d>
	<v>DigestType = md5 | sha</v>
	<d>The default <c>DigestType</c> is sha.</d>
        <v>Mpint = binary()</v>
        <v>Signature = binary()</v>
      </type>
      <desc>
        <p>Calculates a <c>DigestType</c> digest of the <c>Data</c>
	  and creates a RSA signature with the private key <c>Key</c>
	  of the digest.</p>
      </desc>
    </func>

    <func>
      <name>rsa_verify(Data, Signature, Key) -> Verified</name>
      <name>rsa_verify(DigestType, Data, Signature, Key) -> Verified </name> 
      <fsummary>Verify the digest and signature using rsa with given public key.</fsummary>
      <type>
        <v>Verified = boolean()</v>
        <v>Data, Signature = Mpint</v>
        <v>Key = [E, N]</v>
        <v>E, N = Mpint</v>
        <d>Where <c>E</c> is the public exponent and <c>N</c> is public modulus.</d>
	<v>DigestType = md5 | sha</v>
	<d> The default <c>DigestType</c> is sha.</d>
        <v>Mpint = binary()</v>
      </type>
      <desc>
        <p>Calculates a <c>DigestType</c> digest of the <c>Data</c>
          and verifies that the digest matches the RSA signature using the
          signer's public key <c>Key</c>.
	</p>
      </desc>
    </func>
    
    <func>
      <name>rsa_public_encrypt(PlainText, PublicKey, Padding) -> ChipherText</name> 
      <fsummary>Encrypts Msg using the public Key.</fsummary>
      <type>
	<v>PlainText = binary()</v>
	<v>PublicKey = [E, N]</v>
	<v>E, N = Mpint</v>	
	<d>Where <c>E</c> is the public exponent and <c>N</c> is public modulus.</d>
	<v>Padding = rsa_pkcs1_padding | rsa_pkcs1_oaep_padding | rsa_no_padding</v>
        <v>ChipherText = binary()</v>
      </type>
      <desc>
	<p>Encrypts the <c>PlainText</c> (usually a session key) using the <c>PublicKey</c>
	  and returns the cipher. The <c>Padding</c> decides what padding mode is used,
	  <c>rsa_pkcs1_padding</c> is PKCS #1 v1.5 currently the most
	  used mode and <c>rsa_pkcs1_oaep_padding</c> is EME-OAEP as
	  defined in PKCS #1 v2.0 with SHA-1, MGF1 and an empty encoding
	  parameter. This mode is recommended for all new applications.
	  The size of the <c>Msg</c> must be less
	  than <c>byte_size(N)-11</c> if
	  <c>rsa_pkcs1_padding</c> is used, <c>byte_size(N)-41</c> if 
	  <c>rsa_pkcs1_oaep_padding</c> is used and <c>byte_size(N)</c> if <c>rsa_no_padding</c> 
	  is used.
	  Where byte_size(N) is the size part of an <c>Mpint-1</c>.
	</p>
      </desc>
    </func>

    <func>
      <name>rsa_private_decrypt(ChipherText, PrivateKey, Padding) -> PlainText</name> 
      <fsummary>Decrypts ChipherText using the private Key.</fsummary>
      <type>
	<v>ChipherText = binary()</v>
	<v>PrivateKey = [E, N, D]</v>
	<v>E, N, D = Mpint</v>
	<d>Where <c>E</c> is the public exponent, <c>N</c> is public modulus  and 
	  <c>D</c> is the private exponent.</d>
	<v>Padding = rsa_pkcs1_padding | rsa_pkcs1_oaep_padding | rsa_no_padding</v>
        <v>PlainText = binary()</v>
      </type>
      <desc>
	<p>Decrypts the <c>ChipherText</c> (usually a session key encrypted with 
	  <seealso marker="#rsa_public_encrypt/3">rsa_public_encrypt/3</seealso>) 
	  using the <c>PrivateKey</c> and returns the
	  message. The <c>Padding</c> is the padding mode that was
	  used to encrypt the data, 
	  see <seealso marker="#rsa_public_encrypt/3">rsa_public_encrypt/3</seealso>.
	</p>
      </desc>
    </func>
    <func>
      <name>rsa_private_encrypt(PlainText, PrivateKey, Padding) -> ChipherText</name> 
      <fsummary>Encrypts Msg using the private Key.</fsummary>
      <type>
	<v>PlainText = binary()</v>
	<v>PrivateKey = [E, N, D]</v>
	<v>E, N, D = Mpint</v>	
	<d>Where <c>E</c> is the public exponent, <c>N</c> is public modulus and 
	  <c>D</c> is the private exponent.</d>
	<v>Padding = rsa_pkcs1_padding | rsa_no_padding</v>
        <v>ChipherText = binary()</v>
      </type>
      <desc>
	<p>Encrypts the <c>PlainText</c> using the <c>PrivateKey</c>
	  and returns the cipher. The <c>Padding</c> decides what padding mode is used,
	  <c>rsa_pkcs1_padding</c> is PKCS #1 v1.5 currently the most
	  used mode.
	  The size of the <c>Msg</c> must be less than <c>byte_size(N)-11</c> if
	  <c>rsa_pkcs1_padding</c> is used, and <c>byte_size(N)</c> if <c>rsa_no_padding</c> 
	  is used.  Where byte_size(N) is the size part of an <c>Mpint-1</c>.
	</p>
      </desc>
    </func>

    <func>
      <name>rsa_public_decrypt(ChipherText, PublicKey, Padding) -> PlainText</name> 
      <fsummary>Decrypts ChipherText using the public Key.</fsummary>
      <type>
	<v>ChipherText = binary()</v>
	<v>PublicKey = [E, N]</v>
	<v>E, N = Mpint</v>
	<d>Where <c>E</c> is the public exponent and <c>N</c> is public modulus</d>
	<v>Padding = rsa_pkcs1_padding | rsa_no_padding</v>
        <v>PlainText = binary()</v>
      </type>
      <desc>
	<p>Decrypts the <c>ChipherText</c> (encrypted with 
	  <seealso marker="#rsa_private_encrypt/3">rsa_private_encrypt/3</seealso>) 
	  using the <c>PrivateKey</c> and returns the
	  message. The <c>Padding</c> is the padding mode that was
	  used to encrypt the data, 
	  see <seealso marker="#rsa_private_encrypt/3">rsa_private_encrypt/3</seealso>.
	</p>
      </desc>
    </func>
      
    <func>
      <name>dss_sign(Data, Key) -> Signature</name>
      <fsummary>Sign the data using dsa with given private key.</fsummary>
      <type>
        <v>Digest = Mpint</v>
        <v>Key = [P, Q, G, X]</v>
        <v>P, Q, G, X = Mpint</v>
	<d> Where <c>P</c>, <c>Q</c> and <c>G</c> are the dss
	  parameters and <c>X</c> is the private key.</d>
        <v>Mpint = binary()</v>
        <v>Signature = binary()</v>
      </type>
      <desc>
        <p>Calculates the sha digest of the <c>Data</c>
	  and creates a DSS signature with the private key <c>Key</c>
	  of the digest.</p>
      </desc>
    </func>

    <func>
      <name>dss_verify(Data, Signature, Key) -> Verified</name>
      <fsummary>Verify the data and signature using dsa with given public key.</fsummary>
      <type>
        <v>Verified = boolean()</v>
        <v>Digest, Signature = Mpint</v>
        <v>Key = [P, Q, G, Y]</v>
        <v>P, Q, G, Y = Mpint</v>
	<d> Where <c>P</c>, <c>Q</c> and <c>G</c> are the dss
	  parameters and <c>Y</c> is the public key.</d>
        <v>Mpint = binary()</v>
      </type>
      <desc>
        <p>Calculates the sha digest of the <c>Data</c> and verifies that the
          digest matches the DSS signature using the public key <c>Key</c>.
	</p>
      </desc>
    </func>

    <func>
      <name>rc4_encrypt(Key, Data) -> Result</name>
      <fsummary>Encrypt data using RC4</fsummary>
      <type>
	<v>Key, Data = iolist() | binary()</v>
	<v>Result = binary()</v>
      </type>
      <desc>
	<p>Encrypts the data with RC4 symmetric stream encryption.
	  Since it is symmetric, the same function is used for
	  decryption.</p>
      </desc>
    </func>

    <func>
      <name>dh_generate_key(DHParams) -> {PublicKey,PrivateKey} </name>
      <name>dh_generate_key(PrivateKey, DHParams) -> {PublicKey,PrivateKey} </name>
      <fsummary>Generates a Diffie-Hellman public key</fsummary>
      <type>
	<v>DHParameters = [P, G]</v>
	<v>P, G = Mpint</v>
	<d> Where <c>P</c> is the shared prime number and <c>G</c> is the shared generator.</d>
	<v>PublicKey, PrivateKey = Mpint()</v>
      </type>
      <desc>
	<p>Generates a Diffie-Hellman <c>PublicKey</c> and <c>PrivateKey</c> (if not given).
	</p>
      </desc>
    </func>

    <func>
      <name>dh_compute_key(OthersPublicKey, MyPrivateKey, DHParams) -> SharedSecret</name>
      <fsummary>Computes the shared secret</fsummary>
      <type>
	<v>DHParameters = [P, G]</v>
	<v>P, G = Mpint</v>
	<d> Where <c>P</c> is the shared prime number and <c>G</c> is the shared generator.</d>
	<v>OthersPublicKey, MyPrivateKey = Mpint()</v>
	<v>SharedSecret = binary()</v>
      </type>
      <desc>
	<p>Computes the shared secret from the private key and the other party's public key.
	</p>
      </desc>
    </func>
   

    <func>
      <name>exor(Data1, Data2) -> Result</name>
      <fsummary>XOR data</fsummary>
      <type>
	<v>Data1, Data2 = iolist() | binary()</v>
	<v>Result = binary()</v>
      </type>
      <desc>
	<p>Performs bit-wise XOR (exclusive or) on the data supplied.</p>
      </desc>
    </func>
  </funcs>

  <section>
    <title>DES in CBC mode</title>
    <p>The Data Encryption Standard (DES) defines an algorithm for
      encrypting and decrypting an 8 byte quantity using an 8 byte key
      (actually only 56 bits of the key is used).
      </p>
    <p>When it comes to encrypting and decrypting blocks that are
      multiples of 8 bytes various modes are defined (NIST SP
      800-38A). One of those modes is the Cipher Block Chaining (CBC)
      mode, where the encryption of an 8 byte segment depend not only
      of the contents of the segment itself, but also on the result of
      encrypting the previous segment: the encryption of the previous
      segment becomes the initializing vector of the encryption of the
      current segment.
      </p>
    <p>Thus the encryption of every segment depends on the encryption
      key (which is secret) and the encryption of the previous
      segment, except the first segment which has to be provided with
      an initial initializing vector. That vector could be chosen at
      random, or be a counter of some kind. It does not have to be
      secret.
      </p>
    <p>The following example is drawn from the old FIPS 81 standard
      (replaced by NIST SP 800-38A), where both the plain text and the
      resulting cipher text is settled. The following code fragment
      returns `true'.
      </p>
    <pre><![CDATA[

      Key = <<16#01,16#23,16#45,16#67,16#89,16#ab,16#cd,16#ef>>,
      IVec = <<16#12,16#34,16#56,16#78,16#90,16#ab,16#cd,16#ef>>,
      P = "Now is the time for all ",
      C = crypto:des_cbc_encrypt(Key, IVec, P),
         % Which is the same as 
      P1 = "Now is t", P2 = "he time ", P3 = "for all ",
      C1 = crypto:des_cbc_encrypt(Key, IVec, P1),
      C2 = crypto:des_cbc_encrypt(Key, C1, P2),
      C3 = crypto:des_cbc_encrypt(Key, C2, P3),

      C = <<C1/binary, C2/binary, C3/binary>>,
      C = <<16#e5,16#c7,16#cd,16#de,16#87,16#2b,16#f2,16#7c,
             16#43,16#e9,16#34,16#00,16#8c,16#38,16#9c,16#0f,
             16#68,16#37,16#88,16#49,16#9a,16#7c,16#05,16#f6>>,
      <<"Now is the time for all ">> == 
                        crypto:des_cbc_decrypt(Key, IVec, C).
    ]]></pre>
    <p>The following is true for the DES CBC mode. For all
      decompositions <c>P1 ++ P2 = P</c> of a plain text message
      <c>P</c> (where the length of all quantities are multiples of 8
      bytes), the encryption <c>C</c> of <c>P</c> is equal to <c>C1 ++
      C2</c>, where <c>C1</c> is obtained by encrypting <c>P1</c> with
      <c>Key</c> and the initializing vector <c>IVec</c>, and where
      <c>C2</c> is obtained by encrypting <c>P2</c> with <c>Key</c>
      and the initializing vector <c>last8(C1)</c>,
      where <c>last(Binary)</c> denotes the last 8 bytes of the
      binary <c>Binary</c>.
      </p>
    <p>Similarly, for all decompositions <c>C1 ++ C2 = C</c> of a
      cipher text message <c>C</c> (where the length of all quantities
      are multiples of 8 bytes), the decryption <c>P</c> of <c>C</c>
      is equal to <c>P1 ++ P2</c>, where <c>P1</c> is obtained by
      decrypting <c>C1</c> with <c>Key</c> and the initializing vector
      <c>IVec</c>, and where <c>P2</c> is obtained by decrypting
      <c>C2</c> with <c>Key</c> and the initializing vector
      <c>last8(C1)</c>, where <c>last8(Binary)</c> is as above.
      </p>
    <p>For DES3 (which uses three 64 bit keys) the situation is the
      same.
    </p>
  </section>
</erlref>