106 research outputs found
An identification scheme based on sparse polynomials
This is a preprint of a book chapter published in Lecture Notes in Computer Science,1751, Springer-Verlag, Berlin (2000). The original publication is available at www.springerlink.com.This paper gives a new example of exploiting the idea of using polynomials with restricted coefficients over finite fields and rings to construct reliable cryptosystems and identification schemes
Integer Linear Programming Modeling of Addition Sequences With Additional Constraints for Evaluation of Power Terms
In this work, an integer linear programming (ILP) based model is proposed for
the computation of a minimal cost addition sequence for a given set of
integers. Since exponents are additive under multiplication, the minimal length
addition sequence will provide an economical solution for the evaluation of a
requested set of power terms. This is turn, finds application in, e.g.,
window-based exponentiation for cryptography and polynomial evaluation. Not
only is an optimal model proposed, the model is extended to consider different
costs for multipliers and squarers as well as controlling the depth of the
resulting addition sequence.Comment: This manuscript was written in 2012, and, hence, lacks more recent
reference
Approximate computations with modular curves
This article gives an introduction for mathematicians interested in numerical
computations in algebraic geometry and number theory to some recent progress in
algorithmic number theory, emphasising the key role of approximate computations
with modular curves and their Jacobians. These approximations are done in
polynomial time in the dimension and the required number of significant digits.
We explain the main ideas of how the approximations are done, illustrating them
with examples, and we sketch some applications in number theory
Разработка нейросетевого метода умножения точки эллиптической кривой на скаляр
Анализ известных методов и алгоритмов вычисления скалярного умножения точки на число, предложен новый модифицированный нейросетевой метод вычисления скалярного умножения с использованием нейронной сети конечного кольц
Fast Scalar Multiplication on Elliptic Curve Cryptography in Selected Intervals Suitable For Wireless Sensor Networks
International audienceIn Wireless Sensor Networks (WSNs), providing a robust security mechanism with limited energy resources is very challenging because of sensor node's limited resources (computation, bandwidth, memory). Asymmetric-key can fulfill the requirement, but if the number of nodes is large, symmetric-key cryptography is the best natural method because of its scalability. Asymmetric-key cryptography is power-hungry; nevertheless, Elliptic Curve Cryptosystems (ECC) are feasible and more flexible for sensor nodes. Scalar multiplication is the most widely used operation on ECC. Various methods for fast scalar multiplication exist, but they are based on the binary/ternary representation of the scalar. In this paper, we present a novel technique to make fast scalar multiplication on Elliptic Curve Cryptosystems over prime field for light-weight embedded devices like sensor nodes. Our method significantly reduces the computation of scalar multiplication by an equivalent representation of points based on point order in a given interval. Since our technique can act as a support for most existing methods, after an analytical and efficiency analysis, we implement and evaluate its performance in different scenari
Generating a Shortest B-Chain using Multi-GPUs
Let B be a finite set of binary operations over the set of natural numbers N. A B-chain for a natural number n, denoted by BC(n), is a sequence of numbers 1 = c0,c1,...,cl = n such that for each i \u3e 0,ci = cj ◦ck, where 0 ≤ j,k ≤ i−1 and ◦ is an operation of B. Generating a shortest B-chain for n plays an important role in increasing the performance of some cryptosystems and protocols. This paper has two purposes. The first is to propose a generic algorithm to generate a shortest B-chain using a single CPU and a single GPU for any B. The second is to propose two strategies to improve the generation of a shortest B-chain using two (or more) GPUs. Using two GPUs, the experimental study shows that the first strategy improves the performance by about 20%, while the second strategy improves the performance by about 30 ∼ 35% in case of B = {+}. It is also possible to combine both strategies when we have at least four GPUs
On the Efficiency of Fast RSA Variants in Modern Mobile Phones
Modern mobile phones are increasingly being used for more services that
require modern security mechanisms such as the public key cryptosystem RSA. It
is, however, well known that public key cryptography demands considerable
computing resources and that RSA encryption is much faster than RSA decryption.
It is consequently an interesting question if RSA as a whole can be executed
efficiently on modern mobile phones. In this paper, we explore the efficiency
on modern mobile phones of variants of the RSA cryptosystem, covering CRT,
MultiPrime RSA, MultiPower RSA, Rebalanced RSA and R Prime RSA by comparing the
encryption and decryption time using a simple Java implementation and a typical
RSA setup.Comment: 5 pages IEEE format, International Journal of Computer Science and
Information Security, IJCSIS December 2009, ISSN 1947 5500,
http://sites.google.com/site/ijcsis
- …