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This paper presents a scalar multiplication method for Koblitz curves. Koblitz curves are elliptic curves where the scalar multiplication can be computed in a much faster way than other curves, allowing designs and implementations without arithmetic coprocessor. The new method is as fast as the fastest known techniques on Koblitz curves, but requires much less memory, therefore, it is of particular interest for environments with low resources. Our technique is well-suited for both of hardware and software implementations. In hardware, we show that a normal basis implementation reduces memory consumption by 85% compared to conventional methods, but still has exactly the same computational cost. In software, thanks to a mixed normal-polynomial bases approach, our technique allows memory savings up to 70%, and depending on the instruction set of the CPU, can be as fast as the fastest known scalar multiplication methods, or even beat them largely. Therefore, in software and in hardware, our scalar multiplication technique offers high performance without sacrifice in view of memory.
Public key cryptosystems, Smartcards, Efficiency, Koblitz Curves

K. Okeya, T. Takagi and C. Vuillaume, "Short-Memory Scalar Multiplication for Koblitz Curves," in IEEE Transactions on Computers, vol. 57, no. , pp. 481-489, 2007.
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