I am currently studying stateful hash based signatures. In the XMSS paper the authors claim that XMSS signatures are 4 times smaller than those of MSS-SPR. However I do not get how it is possible, because I do not understand the differences between both of them.
As the paper of MSS-SPR does not contain any One Time Signature scheme, a fair comparison should use the same OTS in both schemes. The only other difference I get is pseudo-random versus true random but it is unsufficient because it should not affect signature size:
pseudo-random generation of secret keys must not change the signature at all
pseudo-random generation of salt is helpful to reduce the public key size, but should not change the signature size either
So can someone explain to me where does this factor 4 come from?