A high performance architecture of elliptic curve scalar multiplication based on the Montgomery ladder method over finite field GF(2m) is proposed. A pseudo-pipelined word serial finite field multiplier with word size w, suitable for the scalar multiplication is also developed. Implemented in hardware, this system performs a scalar multiplication in approximately 6⌈m/w⌉(m−1) clock cycles and the gate delay in the critical path is equal to TAND + ⌈log2(w/k)⌉TXOR, where TAND and TXOR are delays due to two-input AND and XOR gates respectively and 1 ≤ k ≪ w is used to shorten the critical path.
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Ansari et al. (2008) studied this question.
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