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Elliptic curve cryptography ECC is preferred for high-speed applications due to the lower computational complexity compared with other public-key cryptographic schemes. As the basic arithmetic, the modular multiplication is the most time-consuming operation in public-key cryptosystems. The existing high-radix Montgomery multipliers performed a single Montgomery multiplication either in approximately $$2n$$ clock cycles, or approximately $$n$$ cycles but with a very low frequency, where $$n$$ is the number of words. In this paper, we first design a novel Montgomery multiplier by combining a quotient pipelining Montgomery multiplication algorithm with a parallel array design. The parallel design with one-way carry propagation can determine the quotients in one clock cycle, thus one Montgomery multiplication can be completed in approximately $$n$$ clock cycles. Meanwhile, by the quotient pipelining technique applied in digital signal processing DSP blocks, our multiplier works in a high frequency. We also implement an ECC processor for generic curves over $$\mathrm{GF}p$$ using the novel multiplier on FPGAs. To the best of our knowledge, our processor is the fastest among the existing ECC implementations over $$\mathrm{GF}p$$ .

A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over $$\mathrm{GF}(p)$$