What makes IOTA quantum-secure?

IOTA uses hash-based signatures (https://www.imperialviolet.org/2013/07/18/hashsig.html) instead of elliptic curve cryptography (ECC). Not only is hash-based signatures a lot faster than ECC, but it also greatly simplifies the overall protocol (signing and verification). What actually makes IOTA quantum-secure is the fact that we use Winternitz signatures. IOTA's ternary hash function is called Curl.