In this paper, we propose an efficient $(n-t)$-out-of-$n$ 
threshold ring signature scheme which is efficient 
when $t$ is small compared with $n$. 
Our scheme has a kind of dual structure of 
the Bresson--Stern--Szydlo threshold ring signature scheme, 
which is infeasible when $t$ is small compared with $n$. 
In particular, we modify the trap-door one-way permutations 
in the ring signature scheme, and use a combinatorial notion 
called fair partition. Our scheme is provably secure
in the random oracle model.