This algorithm is an exact imitation of the localStorage object, but makes use of cookies.

localStoragePolyfill.js

// Source: https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Storage

// Here is another, less exact, imitation of the localStorage object. It is 
// simpler than the previous one, but it is compatible with old browsers, 
// like Internet Explorer < 8 (tested and working even in Internet Explorer 6). 
// It also makes use of cookies.

// Note: The maximum size of data that can be saved is severely restricted 
// by the use of cookies. With this algorithm, use the functions localStorage.setItem() 
// and localStorage.removeItem() to add, change, or remove a key. The use of methods
// localStorage.yourKey = yourValue; and delete localStorage.yourKey; to set or delete 
// a key is not a secure way with this code. You can also change its name and use it only
// to manage a document's cookies regardless of the localStorage object.

// Note: By changing the string "; expires=Tue, 19 Jan 2038 03:14:07 GMT; path=/" to: "; path=/" 
// (and changing the object's name), this will become a sessionStorage polyfill rather than a 
// localStorage polyfill. However, this implementation will share stored values across browser
// tabs and windows (and will only be cleared when all browser windows have been closed), while 
// a fully-compliant sessionStorage implementation restricts stored values to the current browsing 
// context only.

if (!window.localStorage) {
  window.localStorage = {
    getItem: function (sKey) {
      if (!sKey || !this.hasOwnProperty(sKey)) { return null; }
      return unescape(document.cookie.replace(new RegExp("(?:^|.*;\\s*)" + escape(sKey).replace(/[\-\.\+\*]/g, "\\$&") + "\\s*\\=\\s*((?:[^;](?!;))*[^;]?).*"), "$1"));
    },
    key: function (nKeyId) {
      return unescape(document.cookie.replace(/\s*\=(?:.(?!;))*$/, "").split(/\s*\=(?:[^;](?!;))*[^;]?;\s*/)[nKeyId]);
    },
    setItem: function (sKey, sValue) {
      if(!sKey) { return; }
      document.cookie = escape(sKey) + "=" + escape(sValue) + "; expires=Tue, 19 Jan 2038 03:14:07 GMT; path=/";
      this.length = document.cookie.match(/\=/g).length;
    },
    length: 0,
    removeItem: function (sKey) {
      if (!sKey || !this.hasOwnProperty(sKey)) { return; }
      document.cookie = escape(sKey) + "=; expires=Thu, 01 Jan 1970 00:00:00 GMT; path=/";
      this.length--;
    },
    hasOwnProperty: function (sKey) {
      return (new RegExp("(?:^|;\\s*)" + escape(sKey).replace(/[\-\.\+\*]/g, "\\$&") + "\\s*\\=")).test(document.cookie);
    }
  };
  window.localStorage.length = (document.cookie.match(/\=/g) || window.localStorage).length;
}

localStoragePolyfillExact.js

// Source: https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Storage

// Storage objects are a recent addition to the standard. As such they may not be 
// present in all browsers. You can work around this by inserting one of the following 
// two codes at the beginning of your scripts, allowing use of localStorage object in
// implementations which do not natively support it.

// Note: The maximum size of data that can be saved is severely restricted 
// by the use of cookies. With this algorithm, use the functions localStorage.setItem() 
// and localStorage.removeItem() to add, change, or remove a key. The use of methods
// localStorage.yourKey = yourValue; and delete localStorage.yourKey; to set or delete 
// a key is not a secure way with this code. You can also change its name and use it only
// to manage a document's cookies regardless of the localStorage object.

// Note: By changing the string "; expires=Tue, 19 Jan 2038 03:14:07 GMT; path=/" to: "; path=/" 
// (and changing the object's name), this will become a sessionStorage polyfill rather than a 
// localStorage polyfill. However, this implementation will share stored values across browser
// tabs and windows (and will only be cleared when all browser windows have been closed), while 
// a fully-compliant sessionStorage implementation restricts stored values to the current browsing 
// context only.

if (!window.localStorage) {
  Object.defineProperty(window, "localStorage", new (function () {
    var aKeys = [], oStorage = {};
    Object.defineProperty(oStorage, "getItem", {
      value: function (sKey) { return sKey ? this[sKey] : null; },
      writable: false,
      configurable: false,
      enumerable: false
    });
    Object.defineProperty(oStorage, "key", {
      value: function (nKeyId) { return aKeys[nKeyId]; },
      writable: false,
      configurable: false,
      enumerable: false
    });
    Object.defineProperty(oStorage, "setItem", {
      value: function (sKey, sValue) {
        if(!sKey) { return; }
        document.cookie = escape(sKey) + "=" + escape(sValue) + "; expires=Tue, 19 Jan 2038 03:14:07 GMT; path=/";
      },
      writable: false,
      configurable: false,
      enumerable: false
    });
    Object.defineProperty(oStorage, "length", {
      get: function () { return aKeys.length; },
      configurable: false,
      enumerable: false
    });
    Object.defineProperty(oStorage, "removeItem", {
      value: function (sKey) {
        if(!sKey) { return; }
        document.cookie = escape(sKey) + "=; expires=Thu, 01 Jan 1970 00:00:00 GMT; path=/";
      },
      writable: false,
      configurable: false,
      enumerable: false
    });
    this.get = function () {
      var iThisIndx;
      for (var sKey in oStorage) {
        iThisIndx = aKeys.indexOf(sKey);
        if (iThisIndx === -1) { oStorage.setItem(sKey, oStorage[sKey]); }
        else { aKeys.splice(iThisIndx, 1); }
        delete oStorage[sKey];
      }
      for (aKeys; aKeys.length > 0; aKeys.splice(0, 1)) { oStorage.removeItem(aKeys[0]); }
      for (var aCouple, iKey, nIdx = 0, aCouples = document.cookie.split(/\s*;\s*/); nIdx < aCouples.length; nIdx++) {
        aCouple = aCouples[nIdx].split(/\s*=\s*/);
        if (aCouple.length > 1) {
          oStorage[iKey = unescape(aCouple[0])] = unescape(aCouple[1]);
          aKeys.push(iKey);
        }
      }
      return oStorage;
    };
    this.configurable = false;
    this.enumerable = true;
  })());
}