What is the one-time signature scheme with shortest signature size known? There are several one-time signature schemes. The original one - Lamport - has very big signature sizes (several kbs). Is there an one-time signature scheme on which relies only on simple assumptions (one-way functions and random oracle), and on which signatures are no larger than a few bytes?
Well, if we assume a 128 bit hash function (and arrange things such that we assume only (second) preimage resistance), and use a Winternitz scheme with W=65536 (signing/verifying will be expensive), that'll get you down to about 168 bytes (assuming you insert an 8 byte randomizer into the initial hash, needed if we assume that the attacker can choose the message to be signed).

If we are even more aggressive (80 bit hash; may be good enough assuming it doesn't have to be TLA-proof), and W=$2^{29}$ (so Winternitz needs only a single check digit; signing/verifying will be real expensive), and a 4 byte randomizer, that gets you down to 44 bytes; but you had to make a lot of sacrifices to get to that level.