Here's what Shopify (our website platform) has to say about their security:
Your online store’s secure shopping cart comes with a 128-bit SSL certificate free of charge. Using the same level of encryption as the large banks, your SSL keeps your information secure at all times.
We’re PCI Compliant
As a certified Level 1 PCI Compliant business, Shopify gives your online store the ability to accept all major credit cards safely and securely, allowing your customers the ultimate convenience.