  1-out-of-n oblivious signature by Chen (ESORIC 1994) is a protocol between
the user and the signer. In this scheme, the user makes a list of n messages
and chooses the message that the user wants to obtain a signature from the
list. The user interacts with the signer by providing this message list and
obtains the signature for only the chosen message without letting the signer
identify which messages the user chooses. Tso et al. (ISPEC 2008) presented a
formal treatment of 1-out-of-n oblivious signatures. They defined
unforgeability and ambiguity for 1-out-of-n oblivious signatures as a security
requirement. In this work, first, we revisit the unforgeability security
definition by Tso et al. and point out that their security definition has
problems. We address these problems by modifying their security model and
redefining unforgeable security. Second, we improve the generic construction of
a 1-out-of-n oblivious signature scheme by Zhou et al. (IEICE Trans 2022). We
reduce the communication cost by modifying their scheme with a Merkle tree.
Then we prove the security of our modified scheme.
