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We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time del...
This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient 3P3P formula in λλ-projective coordinates and 5...
We propose a new signature scheme that can be used to authenticate data and prevent pollution attacks in networks that use network coding. At its core, our system is a homomorphic signature scheme tha...
In this article, we deal with fast arithmetic in the Picard group of hyperelliptic curves of genus 3 over binary fields. We investigate both the optimal performance curves, where h(x) = 1, and the m...
Galbraith, Lin and Scott recently constructed efficiently-computable endomorphisms for a large family of elliptic curves defined over Fq2 and showed, in the case where q is prime, that the Gallant-L...
Multiple-point multiplication on elliptic curves is the highest computational complex operation in the elliptic curve cyptographic based digital signature schemes. We describe three algorithms for ...
After Miller's original algorithm for the Tate pairing computation, many improved algorithms have been suggested, to name just a few, by Galbraith et al. and Barreto et al., especially for the field...
The most important and expensive operation in a hyperelliptic curve cryptosystem (HECC) is scalar multiplication by an integer k, i.e., computing an integer k times a divisor D on the Jacobian. Using...
Pairings on elliptic curves have been used as cryptographic primitives for the development of new applications such as identity based schemes. For the practical applications, it is crucial to provi...
Though the implementation of the Tate pairing is commonly believed to be computationally more intensive than other cryptographic operations, such as ECC point multiplication, there has been a substa...
Now, It is believed that the best costs of a point doubling and addition on elliptic curves over binary fields are SM54+ (namely, four finite field multiplications and five field squarings) and , resp...

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