Fail-stop signature (FSS) schemes protect a signer against a forger with unlimited computational power by enabling the signer to provide a proof of forgery, if it occurs. A decade after its invention, there have been several FSS schemes proposed in the literature. Nonetheless, the notion of short FSS scheme has not been addressed yet. Furthermore, the short size in signature schemes has been done mainly with the use of pairings. In this paper, we propose a construction of short FSS scheme based on factorization and discrete logarithm assumption. However, in contrast to the known notion in the literature, our signature scheme does not incorporate any pairing operations. Nonetheless, our scheme is the shortest FSS scheme compared to all existing schemes in the literature that are based on the same assumption. The efficiency of our scheme is comparable to the best known FSS scheme, that is based on the discrete logarithm assumption.