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This paper presents a systematic design approach to provide the optimized Rivest-Shamir-Adleman (RSA) processors based on high-radix Montgomery multipliers satisfying various user requirements, such as circuit area, operating time, and resistance against side-channel attacks. In order to involve the tradeoff between the performance and the resistance, we apply four types of exponentiation algorithms: two variants of the binary method with/without Chinese Remainder Theorem (CRT). We also introduces three multiplier-based datapath-architectures using different intermediate data forms: 1) single form, 2) semi carry-save form, and 3) carry-save form, and combined them with a wide variety of arithmetic components. Their radices are parameterized from 28 to 2128. A total of 242 datapaths for 1024-bit RSA processors were obtained for each radix. The potential of the proposed approach is demonstrated through an experimental synthesis of all possible processors with a 90-nm CMOS standard cell library. As a result, the smallest design of 861 gates with 118.47 ms/RSA to the fastest design of 0.67 ms/RSA at 153thinspace 862 gates were obtained. In addition, the use of the CRT technique reduced the RSA operation time of the fastest design to 0.24 ms. Even if we employed the exponentiation algorithm resistant to typical side-channel attacks, the fastest design can perform the RSA operation in less than 1.0 ms.