IOTA does not use traditional asymmetrical (public-key) cryptography algorithms which depend on not being able to efficiently computing discrete logarithms or factoring numbers (which are believed to be easy on a quantum computer).

Instead, its signatures are based on the Winternitz signature scheme (slightly modified for ternary) which only depend on the impossibility of reversing hash functions (Kerl in case of IOTA which is a ternary version of Keccak), which is believed not to be that as easy on a quantum computer as factoring a number (although any reversing of a (hash) function can be done more easily on a quantum computer than a traditional computer).

Disadvantage of Winternitz scheme is that signatures are one-time (every signature reveals parts of your key); therefore users have to be careful not to reuse addresses that have been spent.

Source: https://iota.stackexchange.com/questions/203/how-does-iota-m...

I also found something about 'the length of the computation of the hash function' somewhere as making it more quantum resistant but can no longer find the reference.

Seemed a bit fishy to me too.

Math project is more likely.