We suggest to use short secret keys in the anonymous group 
identification scheme proposed by Lee, Deng, and Zhu and prove 
that this scheme is secure under the discrete logarithm with 
short exponents assumption that solving the discrete logarithm problem 
modulo an $n$-bit prime $p$ is hard even when the exponent is a small $c$-bit number.
We show that the communication and the computation costs are lower than 
those of the Lee-Deng-Zhu scheme.