# Difference Between Gravity-SPHINCS and SPHINCS+?

What are the differences between Gravity-SPHINCS and SPHINCS+ from security and practicality standpoints? Are they just different implementations of the underlying SPHINCS algorithms or are they functional variations on the underlying algorithms?

• The difference between the security reductions is that Gravity-SPHINCS really needs a collision resistant hash function while SPHINCS+ can go with a second-preimage resistant one for the internal functions (the 2n to n bit and n to n bit hashes). The reason is that although a collision for those inner hashes does not really allow an attack on Gravity-SPHINCS, it allows for massive multi-target attacks: Find a preimage for one out of $~2^{80}$ values. – mephisto Dec 29 '17 at 20:20