In this paper, we propose a secure identification scheme for RFID with efficient time and memory, and also an efficient update of pre-computed values on the server side. Although RFID (Radio Frequency IDentification) is becoming popular, a privacy problem still remains, where an adversary can trace users' behavior by linking identification log by legitimate/adversary readers. For this problem, a hash-chain scheme has been proposed as a secure identification for low-cost RFID tags, and its long identification time has been reduced by Avoine et al. using pre-computation on the server side. However, Avoine's scheme uses static pre-computation, and therefore pre-computed values include ones which are already used and no longer used. In this paper, we optimize a lookup of pre-computed values using d-left hashing, and provide efficient update of pre-computed values. We also show reasonable analytical result for memory and pre-computation / identification / update time.