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Let Ea:y2+xy=x3+ax2+1/F2mEa:y2+xy=x3+ax2+1/F2m be a Koblitz curve. The window ττ-adic nonadjacent-form (window ττNAF) is currently the standard representation system to perform scalar multiplications ...
In this work, we retake an old idea that Koblitz presented in his landmark paper, where he suggested the possibility of defining anomalous elliptic curves over the base field \F_4. We present a carefu...
Koblitz curves have been a nice subject of consideration for both theoretical and practical interests. The window τ -adic algorithm of Solinas (window τNAF) is the most powerful method for computing...
We propose a lightweight coprocessor for 16-bit microcontrollers that implements high security elliptic curve cryptography. It uses a 283-bit Koblitz curve and offers 140-bit security. Koblitz curve...
The paper proposes a $\tau^2-$NAF method for scalar multiplication on Koblitz curves, which requires asymptotically $0.215m$ point additions in $GF(2^m)$.
The paper proposes a $\tau^2-$NAF method for scalar multiplication on Koblitz curves, which requires asymptotically $0.215m$ point additions in $GF(2^m)$. For $\tau^2-$NAF method, point quading operat...
We consider digital expansions of scalars for supersingular Koblitz curves in characteristic three. These are positional representations of integers to the base of $\tau$, where $\tau$ is a zero of th...
In order to eciently perform scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such exp...
We describe algorithms for point multiplication on Koblitz curves using multiple-base expansions of the form k = P a( 􀀀 1)b and k = P a( 􀀀1)b( 2 􀀀 􀀀1)c: ...
The paper is an examination of double-base decompositions of integers n, namely expansions loosely of the form n =X i;j AiBj for some base fA;Bg. This was examined in previous works [3, 4], in th...

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