The demand for applications involving Wireless Sensor Network (WSN) or RFID systems is increasing. The sensor in a WSN and RFID tag/reader in a RFID system are called resource constrained devices because these devices have limited processing power, memory size and energy supply. The information transmitted among these low resource devices must be protected from unauthorized access using specifically made cryptographic algorithms. In this paper a new block cipher BEST-1 (Better Encryption Security Technique-1) is proposed with 64 bit block length and 128 bit key length. It is specifically designed for the above mentioned low resource devices. It provides good security and better processing speed as a cryptographic algorithm.