public function getProfilePassword(Request $request) {
    return view('profile/password', ['user' => Auth::user()]);
}

public function postProfilePassword(Request $request) {
    $user = Auth::user();

    $this->validate($request, [
        'old_password'          => 'required',
        'password'              => 'required|min:4',
        'password_confirmation' => 'required|confirmed'
    ]);

    $user->password = Hash::make(Input::get('new_password'));
    $user->save();
}

<form action="{{ route('profile/updatepassword') }}" method="post" enctype="multipart/form-data">
    <div class="form-group">
          <label for="name">Current Password</label>
          <input type="password" name="old_password" class="form-control" id="old_password">
    </div>
    <div class="form-group">
          <label for="name">Password</label>
          <input type="password" name="password" class="form-control" id="password">
    </div>
    <div class="form-group">
          <label for="name">New Password</label>
          <input type="password" name="password_confirmation" class="form-control" id="password_confirmation">
    </div>
    <button type="submit" class="btn btn-primary">Change Password</button>
    <input type="hidden" value="{{ Session::token() }}" name="_token">
 </form>

if (Hash::check("param1", "param2")) {
 //add logic here
}

param1 - user password that has been entered on the form
param2 - old password hash stored in database

'new_password' => 'required',
'new_confirm_password' => 'required|same:new_password'