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This paper presents a series of Montgomery scalar multiplication algorithms on general short Weierstrass curves over odd characteristic fields, which need only 12 field multiplications plus 12 ~ 20 fi...
In this paper we introduce new methods for computing constant-time variable-base point multiplications over the Galbraith-Lin-Scott (GLS) and the Koblitz families of elliptic curves. Using a left-to...
In this paper, we revisit the recent small characteristic discrete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain ...
Precomputation techniques are useful to improve realtime performance of complex algorithms at the expense of extra memory, and extra preparatory computations. This practice is neglected especially ...
We describe a method to perform scalar multiplication on two classes of ordinary elliptic curves, namely $E: y^2 = x^3 + Ax$ in prime characteristic $p\equiv 1$ mod~4, and $E: y^2 = x^3 + B$ in prime ...
We present ShMAC (Shallow MAC), a fixed input length message authentication code that performs most of the computation prior to the availability of the message. Specifically, ShMAC’s message- depend...
We present an innovative technique to add elliptic curve points with the form P ± Q , and discuss its application to the generation of precomputed tables for the scalar multiplication. Our analysis ...
We present a new methodology to derive faster composite operations of the form dP+Q, where d is a small integer ≥ 2, for generic ECC scalar multiplications over prime fields. In particular, we prese...
This paper presents a new approach to precompute all odd points [3]P, [5]P, [2k −1]P, k ≥ 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multi...

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