Hi, I found the solution. Get the following file in your current template

/template/checkout/onepage/payment.phtml

find the below code

var payment = new Payment('co-payment-form', '<?php echo $this->getUrl('checkout/onepage/savePayment') ?>');

change to

var payment = new Payment('co-payment-form', '<?php echo $this->getUrl('checkout/onepage/savePayment',array('_secure'=>true)) ?>');

And

find the below code

var activateGiftCard = new OnepageGiftcard('activateGiftCard',"<?php echo $this->getUrl('giftcards/cart/ajaxActivateGiftCard') ?>");
var agreeMethod = new OnepageGiftcard('giftcardAgree', "<?php echo $this->getUrl('giftcards/cart/agreeToUse') ?>");
var deActivateGiftCard = new OnepageGiftcard( null, "<?php echo $this->getUrl('giftcards/cart/ajaxDeActivateGiftCard') ?>");

change to

var activateGiftCard = new OnepageGiftcard('activateGiftCard',"<?php echo $this->getUrl('giftcards/cart/ajaxActivateGiftCard',array('_secure'=>true)) ?>");
var agreeMethod = new OnepageGiftcard('giftcardAgree', "<?php echo $this->getUrl('giftcards/cart/agreeToUse',array('_secure'=>true)) ?>");
var deActivateGiftCard = new OnepageGiftcard( null, "<?php echo $this->getUrl('giftcards/cart/ajaxDeActivateGiftCard',array('_secure'=>true)) ?>");

Thanks.