2,215 research outputs found
Fast and compact elliptic-curve cryptography

Elliptic curve cryptosystems have improved greatly in speed over the past few years. In this paper we outline a new elliptic curve signature and key agreement implementation which achieves record speeds while remaining relatively compact. For example, on Intel Sandy Bridge, a curve with about points produces a signature in just under 60k clock cycles, verifies in under 169k clock cycles, and computes a Diffie-Hellman shared secret in under 153k clock cycles. Our implementation has a small footprint: the library is under 55kB. We also post competitive timings on ARM processors, verifying a signature in under 626k Tegra-2 cycles. We introduce faster field arithmetic, a new point compression algorithm, an improved fixed-base scalar multiplication algorithm and a new way to verify signatures without inversions or coordinate recovery. Some of these improvements should be applicable to other systems
Still Wrong Use of Pairings in Cryptography
Several pairing-based cryptographic protocols are recently proposed with a
wide variety of new novel applications including the ones in emerging
technologies like cloud computing, internet of things (IoT), e-health systems
and wearable technologies. There have been however a wide range of incorrect
use of these primitives. The paper of Galbraith, Paterson, and Smart (2006)
pointed out most of the issues related to the incorrect use of pairing-based
cryptography. However, we noticed that some recently proposed applications
still do not use these primitives correctly. This leads to unrealizable,
insecure or too inefficient designs of pairing-based protocols. We observed
that one reason is not being aware of the recent advancements on solving the
discrete logarithm problems in some groups. The main purpose of this article is
to give an understandable, informative, and the most up-to-date criteria for
the correct use of pairing-based cryptography. We thereby deliberately avoid
most of the technical details and rather give special emphasis on the
importance of the correct use of bilinear maps by realizing secure
cryptographic protocols. We list a collection of some recent papers having
wrong security assumptions or realizability/efficiency issues. Finally, we give
a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page
LPKI - A Lightweight Public Key Infrastructure for the Mobile Environments
The non-repudiation as an essential requirement of many applications can be
provided by the asymmetric key model. With the evolution of new applications
such as mobile commerce, it is essential to provide secure and efficient
solutions for the mobile environments. The traditional public key cryptography
involves huge computational costs and is not so suitable for the
resource-constrained platforms. The elliptic curve-based approaches as the
newer solutions require certain considerations that are not taken into account
in the traditional public key infrastructures. The main contribution of this
paper is to introduce a Lightweight Public Key Infrastructure (LPKI) for the
constrained platforms such as mobile phones. It takes advantages of elliptic
curve cryptography and signcryption to decrease the computational costs and
communication overheads, and adapting to the constraints. All the computational
costs of required validations can be eliminated from end-entities by
introduction of a validation authority to the introduced infrastructure and
delegating validations to such a component. LPKI is so suitable for mobile
environments and for applications such as mobile commerce where the security is
the great concern.Comment: 6 Pages, 6 Figure
Point compression for the trace zero subgroup over a small degree extension field
Using Semaev's summation polynomials, we derive a new equation for the
-rational points of the trace zero variety of an elliptic curve
defined over . Using this equation, we produce an optimal-size
representation for such points. Our representation is compatible with scalar
multiplication. We give a point compression algorithm to compute the
representation and a decompression algorithm to recover the original point (up
to some small ambiguity). The algorithms are efficient for trace zero varieties
coming from small degree extension fields. We give explicit equations and
discuss in detail the practically relevant cases of cubic and quintic field
extensions.Comment: 23 pages, to appear in Designs, Codes and Cryptograph
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
We give a general framework for uniform, constant-time one-and
two-dimensional scalar multiplication algorithms for elliptic curves and
Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer
surface, where we can exploit faster and more uniform pseudomultiplication,
before recovering the proper "signed" output back on the curve or Jacobian.
This extends the work of L{\'o}pez and Dahab, Okeya and Sakurai, and Brier and
Joye to genus 2, and also to two-dimensional scalar multiplication. Our results
show that many existing fast pseudomultiplication implementations (hitherto
limited to applications in Diffie--Hellman key exchange) can be wrapped with
simple and efficient pre-and post-computations to yield competitive full scalar
multiplication algorithms, ready for use in more general discrete
logarithm-based cryptosystems, including signature schemes. This is especially
interesting for genus 2, where Kummer surfaces can outperform comparable
elliptic curve systems. As an example, we construct an instance of the Schnorr
signature scheme driven by Kummer surface arithmetic
Efficient algorithms for pairing-based cryptosystems
We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable
to that of RSA in larger characteristics.We also propose faster algorithms for scalar multiplication in characteristic 3 and square root extraction
over Fpm, the latter technique being also useful in contexts other than that of pairing-based cryptography
An Outline of Security in Wireless Sensor Networks: Threats, Countermeasures and Implementations
With the expansion of wireless sensor networks (WSNs), the need for securing
the data flow through these networks is increasing. These sensor networks allow
for easy-to-apply and flexible installations which have enabled them to be used
for numerous applications. Due to these properties, they face distinct
information security threats. Security of the data flowing through across
networks provides the researchers with an interesting and intriguing potential
for research. Design of these networks to ensure the protection of data faces
the constraints of limited power and processing resources. We provide the
basics of wireless sensor network security to help the researchers and
engineers in better understanding of this applications field. In this chapter,
we will provide the basics of information security with special emphasis on
WSNs. The chapter will also give an overview of the information security
requirements in these networks. Threats to the security of data in WSNs and
some of their counter measures are also presented
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