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Elliptic curve point multiplication kP on an elliptic curve is required in every elliptic curve cryptosystem. The operation can be significantly accelerated by using a special type of elliptic curves called the Koblitz curves and by representing the integer k in τ -adic nonadjacent form (τ NAF). Hardware-friendly modifications of existing τ NAF conversion algorithms are presented and an efficient circuitry for the τ NAF conversion is described with performance characteristics on an Altera Stratix-II S60C4 FPGA. To the authors' knowledge, this is the first published hardware implementation of the τ NAF conversion.

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