In cryptographic applications, private key algorithms usually aim at high-throughput data communication, while public key algorithms require much lower throughput for private key exchange and authentication. To increase hardware utilization and reduce area overhead, this paper presents a flexible divider design in GF(2m), which can be configured to operate in either SIMD or SISD mode. When applied to SIMD applications, the divider can perform multiple divisions in parallel and output results per cycle; thus, it is suitable for AES cryptosystems demanding high throughput. In SISD applications, the divider is scalable and can handle different sizes of operand such as those specified in ECC standards. A scalable design can also relax the potential problem of high fanout control signals. Complexity analysis shows the proposed divider, operated in SIMD mode, has lower area complexity and higher throughput in comparison with related work.