35 research outputs found
Метод обеспечения защиты информации в автоматизированных системах управления противодействием временной атаке
Предложен метод обеспечения защиты информации в АСУ противодействием
криптографической атаке, на основе замера времени выполнения операций, при формировании цифровой
подписи в группе точек эллиптических кривых. Запропоновано метод забезпечення захисту інформації в АСУ протидією атаці на основі
виміру часу виконання операцій при формування цифрового підпису в групі точок еліптичних кривих. The method defense of information counteraction is offered cryptographic attack, on the basis
gauging time of performance operations, at formation digital signature in group points of elliptic curves
Regular Ternary Algorithm for Scalar Multiplication on Elliptic Curves over Finite Fields of Characteristic Three
In this paper we propose an efficient and regular ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic three.
This method is based on full signed ternary expansion of a scalar to be multiplied. The cost per bit of this algorithm is lower than that of all previous ones
On the automatic construction of indistinguishable operations
An increasingly important design constraint for software running
on ubiquitous computing devices is security, particularly against
physical methods such as side-channel attack. One well studied methodology
for defending against such attacks is the concept of indistinguishable
functions which leak no information about program control
flow since all execution paths are computationally identical. However,
constructing such functions by hand becomes laborious and error prone
as their complexity increases. We investigate techniques for automating
this process and find that effective solutions can be constructed with
only minor amounts of computational effort.Fundação para a Ciência e Tecnologia - SFRH/BPD/20528/2004
Arithmetic progressions on Huff curves
We look at arithmetic progressions on elliptic curves known as Huff curves.
By an arithmetic progression on an elliptic curve, we mean that either the x or
y-coordinates of a sequence of rational points on the curve form an arithmetic
progression. Previous work has found arithmetic progressions on Weierstrass
curves, quartic curves, Edwards curves, and genus 2 curves. We find an
infinite number of Huff curves with an arithmetic progression of length 9
Linear equivalence between elliptic curves in Weierstrass and Hesse form
Elliptic curves in Hesse form admit more suitable arithmetic than ones in Weierstrass form. But elliptic curve cryptosystems usually use Weierstrass form. It is known that both those forms are birationally equivalent. Birational equivalence is relatively hard to compute. We prove that elliptic curves in Hesse form and in Weierstrass form are linearly equivalent over initial field or its small extension and this equivalence is easy to compute. If cardinality of finite field q = 2 (mod 3) and Frobenius trace T = 0 (mod 3), then equivalence is defined over initial finite field. This linear equivalence allows multiplying of an elliptic curve point in Weierstrass form by passing to Hessian curve, computing product point for this curve and passing back. This speeds up the rate of point multiplication about 1,37 times
Addition law structure of elliptic curves
The study of alternative models for elliptic curves has found recent interest
from cryptographic applications, once it was recognized that such models
provide more efficiently computable algorithms for the group law than the
standard Weierstrass model. Examples of such models arise via symmetries
induced by a rational torsion structure. We analyze the module structure of the
space of sections of the addition morphisms, determine explicit dimension
formulas for the spaces of sections and their eigenspaces under the action of
torsion groups, and apply this to specific models of elliptic curves with
parametrized torsion subgroups
New Addition Operation and Its Application for Scalar Multiplication on Hessian Curves over Prime Fields
In this paper, we present a new addition operation on Hessian curves with low cost.
It can be applied to resist the side channel attacks for scalar multiplication,
and also can be used to compute precomputation points for window-based
scalar multiplication on Hessian curves over prime fields.
We propose two new precomputation schemes
that are shown to achieve the lowest cost among all known methods.
By using the fractional NAF and fractional NAF,
if bits and , scheme 1 can save up to ,
scheme 2 can save up to with , where , represent
the inversion and the multiplication, respectively
Twisted Hessian Isogenies
Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Velu’s formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic curves without isomorphisms mapping to and from the Weierstrass form. Previous papers have shown some isogeny formulas for (twisted) Edwards, Huff, and Montgomery forms of elliptic curves. Continuing this line of work, this paper derives an explicit formula for isogenies between elliptic curves in (twisted) Hessian form