class.oauth.php

<?php

/* Generic exception class
 */
class TT_OAuthException extends Exception {
  // pass
}

class TT_OAuthConsumer {
  public $key;
  public $secret;

  function __construct($key, $secret, $callback_url=NULL) {
    $this->key = $key;
    $this->secret = $secret;
    $this->callback_url = $callback_url;
  }

  function __toString() {
    return "TT_OAuthConsumer[key=$this->key,secret=$this->secret]";
  }
}

class TT_OAuthToken {
  // access tokens and request tokens
  public $key;
  public $secret;

  /**
   * key = the token
   * secret = the token secret
   */
  function __construct($key, $secret) {
    $this->key = $key;
    $this->secret = $secret;
  }

  /**
   * generates the basic string serialization of a token that a server
   * would respond to request_token and access_token calls with
   */
  function to_string() {
    return "oauth_token=" .
           TT_OAuthUtil::urlencode_rfc3986($this->key) .
           "&oauth_token_secret=" .
           TT_OAuthUtil::urlencode_rfc3986($this->secret);
  }

  function __toString() {
    return $this->to_string();
  }
}

/**
 * A class for implementing a Signature Method
 * See section 9 ("Signing Requests") in the spec
 */
abstract class TT_OAuthSignatureMethod {
  /**
   * Needs to return the name of the Signature Method (ie HMAC-SHA1)
   * @return string
   */
  abstract public function get_name();

  /**
   * Build up the signature
   * NOTE: The output of this function MUST NOT be urlencoded.
   * the encoding is handled in TT_OAuthRequest when the final
   * request is serialized
   * @param TT_OAuthRequest $request
   * @param TT_OAuthConsumer $consumer
   * @param TT_OAuthToken $token
   * @return string
   */
  abstract public function build_signature($request, $consumer, $token);

  /**
   * Verifies that a given signature is correct
   * @param TT_OAuthRequest $request
   * @param TT_OAuthConsumer $consumer
   * @param TT_OAuthToken $token
   * @param string $signature
   * @return bool
   */
  public function check_signature($request, $consumer, $token, $signature) {
    $built = $this->build_signature($request, $consumer, $token);
    return $built == $signature;
  }
}

/**
 * The HMAC-SHA1 signature method uses the HMAC-SHA1 signature algorithm as defined in [RFC2104] 
 * where the Signature Base String is the text and the key is the concatenated values (each first 
 * encoded per Parameter Encoding) of the Consumer Secret and Token Secret, separated by an '&' 
 * character (ASCII code 38) even if empty.
 *   - Chapter 9.2 ("HMAC-SHA1")
 */
class TT_OAuthSignatureMethod_HMAC_SHA1 extends TT_OAuthSignatureMethod {
  function get_name() {
    return "HMAC-SHA1";
  }

  public function build_signature($request, $consumer, $token) {
    $base_string = $request->get_signature_base_string();
    $request->base_string = $base_string;

    $key_parts = array(
      $consumer->secret,
      ($token) ? $token->secret : ""
    );

    $key_parts = TT_OAuthUtil::urlencode_rfc3986($key_parts);
    $key = implode('&', $key_parts);

    return base64_encode(hash_hmac('sha1', $base_string, $key, true));
  }
}

/**
 * The PLAINTEXT method does not provide any security protection and SHOULD only be used 
 * over a secure channel such as HTTPS. It does not use the Signature Base String.
 *   - Chapter 9.4 ("PLAINTEXT")
 */
class TT_OAuthSignatureMethod_PLAINTEXT extends TT_OAuthSignatureMethod {
  public function get_name() {
    return "PLAINTEXT";
  }

  /**
   * oauth_signature is set to the concatenated encoded values of the Consumer Secret and 
   * Token Secret, separated by a '&' character (ASCII code 38), even if either secret is 
   * empty. The result MUST be encoded again.
   *   - Chapter 9.4.1 ("Generating Signatures")
   *
   * Please note that the second encoding MUST NOT happen in the SignatureMethod, as
   * TT_OAuthRequest handles this!
   */
  public function build_signature($request, $consumer, $token) {
    $key_parts = array(
      $consumer->secret,
      ($token) ? $token->secret : ""
    );

    $key_parts = TT_OAuthUtil::urlencode_rfc3986($key_parts);
    $key = implode('&', $key_parts);
    $request->base_string = $key;

    return $key;
  }
}

/**
 * The RSA-SHA1 signature method uses the RSASSA-PKCS1-v1_5 signature algorithm as defined in 
 * [RFC3447] section 8.2 (more simply known as PKCS#1), using SHA-1 as the hash function for 
 * EMSA-PKCS1-v1_5. It is assumed that the Consumer has provided its RSA public key in a 
 * verified way to the Service Provider, in a manner which is beyond the scope of this 
 * specification.
 *   - Chapter 9.3 ("RSA-SHA1")
 */
abstract class TT_OAuthSignatureMethod_RSA_SHA1 extends TT_OAuthSignatureMethod {
  public function get_name() {
    return "RSA-SHA1";
  }

  // Up to the SP to implement this lookup of keys. Possible ideas are:
  // (1) do a lookup in a table of trusted certs keyed off of consumer
  // (2) fetch via http using a url provided by the requester
  // (3) some sort of specific discovery code based on request
  //
  // Either way should return a string representation of the certificate
  protected abstract function fetch_public_cert(&$request);

  // Up to the SP to implement this lookup of keys. Possible ideas are:
  // (1) do a lookup in a table of trusted certs keyed off of consumer
  //
  // Either way should return a string representation of the certificate
  protected abstract function fetch_private_cert(&$request);

  public function build_signature($request, $consumer, $token) {
    $base_string = $request->get_signature_base_string();
    $request->base_string = $base_string;

    // Fetch the private key cert based on the request
    $cert = $this->fetch_private_cert($request);

    // Pull the private key ID from the certificate
    $privatekeyid = openssl_get_privatekey($cert);

    // Sign using the key
    $ok = openssl_sign($base_string, $signature, $privatekeyid);

    // Release the key resource
    openssl_free_key($privatekeyid);

    return base64_encode($signature);
  }

  public function check_signature($request, $consumer, $token, $signature) {
    $decoded_sig = base64_decode($signature);

    $base_string = $request->get_signature_base_string();

    // Fetch the public key cert based on the request
    $cert = $this->fetch_public_cert($request);

    // Pull the public key ID from the certificate
    $publickeyid = openssl_get_publickey($cert);

    // Check the computed signature against the one passed in the query
    $ok = openssl_verify($base_string, $decoded_sig, $publickeyid);

    // Release the key resource
    openssl_free_key($publickeyid);

    return $ok == 1;
  }
}

class TT_OAuthRequest {
  private $parameters;
  private $http_method;
  private $http_url;
  // for debug purposes
  public $base_string;
  public static $version = '1.0';
  public static $POST_INPUT = 'php://input';

  function __construct($http_method, $http_url, $parameters=NULL) {
    @$parameters or $parameters = array();
    $parameters = array_merge( TT_OAuthUtil::parse_parameters(parse_url($http_url, PHP_URL_QUERY)), $parameters);
    $this->parameters = $parameters;
    $this->http_method = $http_method;
    $this->http_url = $http_url;
  }


  /**
   * attempt to build up a request from what was passed to the server
   */
  public static function from_request($http_method=NULL, $http_url=NULL, $parameters=NULL) {
    $scheme = (!isset($_SERVER['HTTPS']) || $_SERVER['HTTPS'] != "on")
              ? 'http'
              : 'https';
    @$http_url or $http_url = $scheme .
                              '://' . $_SERVER['HTTP_HOST'] .
                              ':' .
                              $_SERVER['SERVER_PORT'] .
                              $_SERVER['REQUEST_URI'];
    @$http_method or $http_method = $_SERVER['REQUEST_METHOD'];

    // We weren't handed any parameters, so let's find the ones relevant to
    // this request.
    // If you run XML-RPC or similar you should use this to provide your own
    // parsed parameter-list
    if (!$parameters) {
      // Find request headers
      $request_headers = TT_OAuthUtil::get_headers();

      // Parse the query-string to find GET parameters
      $parameters = TT_OAuthUtil::parse_parameters($_SERVER['QUERY_STRING']);

      // It's a POST request of the proper content-type, so parse POST
      // parameters and add those overriding any duplicates from GET
      if ($http_method == "POST"
          && @strstr($request_headers["Content-Type"],
                     "application/x-www-form-urlencoded")
          ) {
        $post_data = TT_OAuthUtil::parse_parameters(
          file_get_contents(self::$POST_INPUT)
        );
        $parameters = array_merge($parameters, $post_data);
      }

      // We have a Authorization-header with OAuth data. Parse the header
      // and add those overriding any duplicates from GET or POST
      if (@substr($request_headers['Authorization'], 0, 6) == "OAuth ") {
        $header_parameters = TT_OAuthUtil::split_header(
          $request_headers['Authorization']
        );
        $parameters = array_merge($parameters, $header_parameters);
      }

    }

    return new TT_OAuthRequest($http_method, $http_url, $parameters);
  }

  /**
   * pretty much a helper function to set up the request
   */
  public static function from_consumer_and_token($consumer, $token, $http_method, $http_url, $parameters=NULL) {
    @$parameters or $parameters = array();
    $defaults = array("oauth_version" => TT_OAuthRequest::$version,
                      "oauth_nonce" => TT_OAuthRequest::generate_nonce(),
                      "oauth_timestamp" => TT_OAuthRequest::generate_timestamp(),
                      "oauth_consumer_key" => $consumer->key);
    if ($token)
      $defaults['oauth_token'] = $token->key;

    $parameters = array_merge($defaults, $parameters);

    return new TT_OAuthRequest($http_method, $http_url, $parameters);
  }

  public function set_parameter($name, $value, $allow_duplicates = true) {
    if ($allow_duplicates && isset($this->parameters[$name])) {
      // We have already added parameter(s) with this name, so add to the list
      if (is_scalar($this->parameters[$name])) {
        // This is the first duplicate, so transform scalar (string)
        // into an array so we can add the duplicates
        $this->parameters[$name] = array($this->parameters[$name]);
      }

      $this->parameters[$name][] = $value;
    } else {
      $this->parameters[$name] = $value;
    }
  }

  public function get_parameter($name) {
    return isset($this->parameters[$name]) ? $this->parameters[$name] : null;
  }

  public function get_parameters() {
    return $this->parameters;
  }

  public function unset_parameter($name) {
    unset($this->parameters[$name]);
  }

  /**
   * The request parameters, sorted and concatenated into a normalized string.
   * @return string
   */
  public function get_signable_parameters() {
    // Grab all parameters
    $params = $this->parameters;

    // Remove oauth_signature if present
    // Ref: Spec: 9.1.1 ("The oauth_signature parameter MUST be excluded.")
    if (isset($params['oauth_signature'])) {
      unset($params['oauth_signature']);
    }

    return TT_OAuthUtil::build_http_query($params);
  }

  /**
   * Returns the base string of this request
   *
   * The base string defined as the method, the url
   * and the parameters (normalized), each urlencoded
   * and the concated with &.
   */
  public function get_signature_base_string() {
    $parts = array(
      $this->get_normalized_http_method(),
      $this->get_normalized_http_url(),
      $this->get_signable_parameters()
    );

    $parts = TT_OAuthUtil::urlencode_rfc3986($parts);

    return implode('&', $parts);
  }

  /**
   * just uppercases the http method
   */
  public function get_normalized_http_method() {
    return strtoupper($this->http_method);
  }

  /**
   * parses the url and rebuilds it to be
   * scheme://host/path
   */
  public function get_normalized_http_url() {
    $parts = parse_url($this->http_url);

    $port = @$parts['port'];
    $scheme = $parts['scheme'];
    $host = $parts['host'];
    $path = @$parts['path'];

    $port or $port = ($scheme == 'https') ? '443' : '80';

    if (($scheme == 'https' && $port != '443')
        || ($scheme == 'http' && $port != '80')) {
      $host = "$host:$port";
    }
    return "$scheme://$host$path";
  }

  /**
   * builds a url usable for a GET request
   */
  public function to_url() {
    $post_data = $this->to_postdata();
    $out = $this->get_normalized_http_url();

    if ($post_data) {
      $out .= '?'.$post_data;
    }
    return $out;
  }

  /**
   * builds the data one would send in a POST request
   */
  public function to_postdata() {
    return TT_OAuthUtil::build_http_query($this->parameters);
  }

  /**
   * builds the Authorization: header
   */
  public function to_header($realm=null) {
    $first = true;
	if($realm) {
      $out = 'Authorization: OAuth realm="' . TT_OAuthUtil::urlencode_rfc3986($realm) . '"';
      $first = false;
    } else
      $out = 'Authorization: OAuth';

    $total = array();
    foreach ($this->parameters as $k => $v) {
      if (substr($k, 0, 5) != "oauth") continue;
      if (is_array($v)) {
        throw new TT_OAuthException('Arrays not supported in headers');
      }
      $out .= ($first) ? ' ' : ',';
      $out .= TT_OAuthUtil::urlencode_rfc3986($k) .
              '="' .
              TT_OAuthUtil::urlencode_rfc3986($v) .
              '"';
      $first = false;
    }
    return $out;
  }

  public function __toString() {
    return $this->to_url();
  }


  public function sign_request($signature_method, $consumer, $token) {
    $this->set_parameter(
      "oauth_signature_method",
      $signature_method->get_name(),
      false
    );
    $signature = $this->build_signature($signature_method, $consumer, $token);
    $this->set_parameter("oauth_signature", $signature, false);
  }

  public function build_signature($signature_method, $consumer, $token) {
    $signature = $signature_method->build_signature($this, $consumer, $token);
    return $signature;
  }

  /**
   * util function: current timestamp
   */
  private static function generate_timestamp() {
    return time();
  }

  /**
   * util function: current nonce
   */
  private static function generate_nonce() {
    $mt = microtime();
    $rand = mt_rand();

    return md5($mt . $rand); // md5s look nicer than numbers
  }
}

class TT_OAuthServer {
  protected $timestamp_threshold = 300; // in seconds, five minutes
  protected $version = '1.0';             // hi blaine
  protected $signature_methods = array();

  protected $data_store;

  function __construct($data_store) {
    $this->data_store = $data_store;
  }

  public function add_signature_method($signature_method) {
    $this->signature_methods[$signature_method->get_name()] =
      $signature_method;
  }

  // high level functions

  /**
   * process a request_token request
   * returns the request token on success
   */
  public function fetch_request_token(&$request) {
    $this->get_version($request);

    $consumer = $this->get_consumer($request);

    // no token required for the initial token request
    $token = NULL;

    $this->check_signature($request, $consumer, $token);

    // Rev A change
    $callback = $request->get_parameter('oauth_callback');
    $new_token = $this->data_store->new_request_token($consumer, $callback);

    return $new_token;
  }

  /**
   * process an access_token request
   * returns the access token on success
   */
  public function fetch_access_token(&$request) {
    $this->get_version($request);

    $consumer = $this->get_consumer($request);

    // requires authorized request token
    $token = $this->get_token($request, $consumer, "request");

    $this->check_signature($request, $consumer, $token);

    // Rev A change
    $verifier = $request->get_parameter('oauth_verifier');
    $new_token = $this->data_store->new_access_token($token, $consumer, $verifier);

    return $new_token;
  }

  /**
   * verify an api call, checks all the parameters
   */
  public function verify_request(&$request) {
    $this->get_version($request);
    $consumer = $this->get_consumer($request);
    $token = $this->get_token($request, $consumer, "access");
    $this->check_signature($request, $consumer, $token);
    return array($consumer, $token);
  }

  // Internals from here
  /**
   * version 1
   */
  private function get_version(&$request) {
    $version = $request->get_parameter("oauth_version");
    if (!$version) {
      // Service Providers MUST assume the protocol version to be 1.0 if this parameter is not present. 
      // Chapter 7.0 ("Accessing Protected Ressources")
      $version = '1.0';
    }
    if ($version !== $this->version) {
      throw new TT_OAuthException("OAuth version '$version' not supported");
    }
    return $version;
  }

  /**
   * figure out the signature with some defaults
   */
  private function get_signature_method(&$request) {
    $signature_method =
        @$request->get_parameter("oauth_signature_method");

    if (!$signature_method) {
      // According to chapter 7 ("Accessing Protected Ressources") the signature-method
      // parameter is required, and we can't just fallback to PLAINTEXT
      throw new TT_OAuthException('No signature method parameter. This parameter is required');
    }

    if (!in_array($signature_method,
                  array_keys($this->signature_methods))) {
      throw new TT_OAuthException(
        "Signature method '$signature_method' not supported " .
        "try one of the following: " .
        implode(", ", array_keys($this->signature_methods))
      );
    }
    return $this->signature_methods[$signature_method];
  }

  /**
   * try to find the consumer for the provided request's consumer key
   */
  private function get_consumer(&$request) {
    $consumer_key = @$request->get_parameter("oauth_consumer_key");
    if (!$consumer_key) {
      throw new TT_OAuthException("Invalid consumer key");
    }

    $consumer = $this->data_store->lookup_consumer($consumer_key);
    if (!$consumer) {
      throw new TT_OAuthException("Invalid consumer");
    }

    return $consumer;
  }

  /**
   * try to find the token for the provided request's token key
   */
  private function get_token(&$request, $consumer, $token_type="access") {
    $token_field = @$request->get_parameter('oauth_token');
    $token = $this->data_store->lookup_token(
      $consumer, $token_type, $token_field
    );
    if (!$token) {
      throw new TT_OAuthException("Invalid $token_type token: $token_field");
    }
    return $token;
  }

  /**
   * all-in-one function to check the signature on a request
   * should guess the signature method appropriately
   */
  private function check_signature(&$request, $consumer, $token) {
    // this should probably be in a different method
    $timestamp = @$request->get_parameter('oauth_timestamp');
    $nonce = @$request->get_parameter('oauth_nonce');

    $this->check_timestamp($timestamp);
    $this->check_nonce($consumer, $token, $nonce, $timestamp);

    $signature_method = $this->get_signature_method($request);

    $signature = $request->get_parameter('oauth_signature');
    $valid_sig = $signature_method->check_signature(
      $request,
      $consumer,
      $token,
      $signature
    );

    if (!$valid_sig) {
      throw new TT_OAuthException("Invalid signature");
    }
  }

  /**
   * check that the timestamp is new enough
   */
  private function check_timestamp($timestamp) {
    if( ! $timestamp )
      throw new TT_OAuthException(
        'Missing timestamp parameter. The parameter is required'
      );
    
    // verify that timestamp is recentish
    $now = time();
    if (abs($now - $timestamp) > $this->timestamp_threshold) {
      throw new TT_OAuthException(
        "Expired timestamp, yours $timestamp, ours $now"
      );
    }
  }

  /**
   * check that the nonce is not repeated
   */
  private function check_nonce($consumer, $token, $nonce, $timestamp) {
    if( ! $nonce )
      throw new TT_OAuthException(
        'Missing nonce parameter. The parameter is required'
      );

    // verify that the nonce is uniqueish
    $found = $this->data_store->lookup_nonce(
      $consumer,
      $token,
      $nonce,
      $timestamp
    );
    if ($found) {
      throw new TT_OAuthException("Nonce already used: $nonce");
    }
  }

}

class TT_OAuthDataStore {
  function lookup_consumer($consumer_key) {
    // implement me
  }

  function lookup_token($consumer, $token_type, $token) {
    // implement me
  }

  function lookup_nonce($consumer, $token, $nonce, $timestamp) {
    // implement me
  }

  function new_request_token($consumer, $callback = null) {
    // return a new token attached to this consumer
  }

  function new_access_token($token, $consumer, $verifier = null) {
    // return a new access token attached to this consumer
    // for the user associated with this token if the request token
    // is authorized
    // should also invalidate the request token
  }

}

class TT_OAuthUtil {
  public static function urlencode_rfc3986($input) {
  if (is_array($input)) {
    return array_map(array('TT_OAuthUtil', 'urlencode_rfc3986'), $input);
  } else if (is_scalar($input)) {
    return str_replace(
      '+',
      ' ',
      str_replace('%7E', '~', rawurlencode($input))
    );
  } else {
    return '';
  }
}


  // This decode function isn't taking into consideration the above
  // modifications to the encoding process. However, this method doesn't
  // seem to be used anywhere so leaving it as is.
  public static function urldecode_rfc3986($string) {
    return urldecode($string);
  }

  // Utility function for turning the Authorization: header into
  // parameters, has to do some unescaping
  // Can filter out any non-oauth parameters if needed (default behaviour)
  public static function split_header($header, $only_allow_oauth_parameters = true) {
    $pattern = '/(([-_a-z]*)=("([^"]*)"|([^,]*)),?)/';
    $offset = 0;
    $params = array();
    while (preg_match($pattern, $header, $matches, PREG_OFFSET_CAPTURE, $offset) > 0) {
      $match = $matches[0];
      $header_name = $matches[2][0];
      $header_content = (isset($matches[5])) ? $matches[5][0] : $matches[4][0];
      if (preg_match('/^oauth_/', $header_name) || !$only_allow_oauth_parameters) {
        $params[$header_name] = TT_OAuthUtil::urldecode_rfc3986($header_content);
      }
      $offset = $match[1] + strlen($match[0]);
    }

    if (isset($params['realm'])) {
      unset($params['realm']);
    }

    return $params;
  }

  // helper to try to sort out headers for people who aren't running apache
  public static function get_headers() {
    if (function_exists('apache_request_headers')) {
      // we need this to get the actual Authorization: header
      // because apache tends to tell us it doesn't exist
      $headers = apache_request_headers();

      // sanitize the output of apache_request_headers because
      // we always want the keys to be Cased-Like-This and arh()
      // returns the headers in the same case as they are in the
      // request
      $out = array();
      foreach( $headers AS $key => $value ) {
        $key = str_replace(
            " ",
            "-",
            ucwords(strtolower(str_replace("-", " ", $key)))
          );
        $out[$key] = $value;
      }
    } else {
      // otherwise we don't have apache and are just going to have to hope
      // that $_SERVER actually contains what we need
      $out = array();
      if( isset($_SERVER['CONTENT_TYPE']) )
        $out['Content-Type'] = $_SERVER['CONTENT_TYPE'];
      if( isset($_ENV['CONTENT_TYPE']) )
        $out['Content-Type'] = $_ENV['CONTENT_TYPE'];

      foreach ($_SERVER as $key => $value) {
        if (substr($key, 0, 5) == "HTTP_") {
          // this is chaos, basically it is just there to capitalize the first
          // letter of every word that is not an initial HTTP and strip HTTP
          // code from przemek
          $key = str_replace(
            " ",
            "-",
            ucwords(strtolower(str_replace("_", " ", substr($key, 5))))
          );
          $out[$key] = $value;
        }
      }
    }
    return $out;
  }

  // This function takes a input like a=b&a=c&d=e and returns the parsed
  // parameters like this
  // array('a' => array('b','c'), 'd' => 'e')
  public static function parse_parameters( $input ) {
    if (!isset($input) || !$input) return array();

    $pairs = explode('&', $input);

    $parsed_parameters = array();
    foreach ($pairs as $pair) {
      $split = explode('=', $pair, 2);
      $parameter = TT_OAuthUtil::urldecode_rfc3986($split[0]);
      $value = isset($split[1]) ? TT_OAuthUtil::urldecode_rfc3986($split[1]) : '';

      if (isset($parsed_parameters[$parameter])) {
        // We have already recieved parameter(s) with this name, so add to the list
        // of parameters with this name

        if (is_scalar($parsed_parameters[$parameter])) {
          // This is the first duplicate, so transform scalar (string) into an array
          // so we can add the duplicates
          $parsed_parameters[$parameter] = array($parsed_parameters[$parameter]);
        }

        $parsed_parameters[$parameter][] = $value;
      } else {
        $parsed_parameters[$parameter] = $value;
      }
    }
    return $parsed_parameters;
  }

  // @TODO Replace with WordPress add_query_arg method? Note the key and value sorting.
  public static function build_http_query($params) {
    if (!$params) return '';
    // Urlencode both keys and values
    $keys = TT_OAuthUtil::urlencode_rfc3986(array_keys($params));
    $values = TT_OAuthUtil::urlencode_rfc3986(array_values($params));
    $params = array_combine($keys, $values);
    // Parameters are sorted by name, using lexicographical byte value ordering.
    // Ref: Spec: 9.1.1 (1)
    uksort($params, 'strcmp');

    $pairs = array();
    foreach ($params as $parameter => $value) {
      if (is_array($value)) {
        // If two or more parameters share the same name, they are sorted by their value
        // Ref: Spec: 9.1.1 (1)
        natsort($value);
        foreach ($value as $duplicate_value) {
          $pairs[] = $parameter . '=' . $duplicate_value;
        }
      } else {
        $pairs[] = $parameter . '=' . $value;
      }
    }
    // For each parameter, the name is separated from the corresponding value by an '=' character (ASCII code 61)
    // Each name-value pair is separated by an '&' character (ASCII code 38)
    return implode('&', $pairs);
  }
}