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IEEE Transactions on Computers
Use of elliptic curves in cryptography
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Efficient Arithmetic on Koblitz Curves
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IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Point multiplication is required in every elliptic curve cryptosystem and its efficient implementation is essential. Koblitz curves are a family of curves defined over F"2"^"m allowing notably faster computation. We discuss implementation of point multiplication on Koblitz curves with parallel field multipliers. We present a novel parallelization method utilizing point operation interleaving. FPGA implementations are described showing the practical feasibility of our method. They compute point multiplications on average in 4.9@ms, 8.1@ms, and 12.1@ms on the standardized curves NIST K-163, K-233, and K-283, respectively, in an Altera Stratix II FPGA.