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With rapid increases in communication and network applications, cryptography has become a crucial issue to ensure the security of transmitted data. In this paper, we propose a microcode-based architecture with a novel reconfigurable datapath which can perform either prime field GF(p) operations or binary extension field GF(2m) operations for arbitrary prime numbers, irreducible polynomials, and precision. Using these field arithmetic units, users are capable of programming cryptographic algorithms in microcode sequences for full compliance with a majority of public-key cryptographic algorithms such as Rivest-Shamir-Adleman (RSA) and elliptic curve cryptosystems. An algorithmic optimization or refinement can thus be made at a higher level based on the reconfigurable datapath. Experimental results show that the developed processor has full cryptography algorithm flexibility, high hardware utilization, and high performance.