6,893 research outputs found
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
Analysis of Parallel Montgomery Multiplication in CUDA
For a given level of security, elliptic curve cryptography (ECC) offers improved efficiency over classic public key implementations. Point multiplication is the most common operation in ECC and, consequently, any significant improvement in perfor- mance will likely require accelerating point multiplication. In ECC, the Montgomery algorithm is widely used for point multiplication. The primary purpose of this project is to implement and analyze a parallel implementation of the Montgomery algorithm as it is used in ECC. Specifically, the performance of CPU-based Montgomery multiplication and a GPU-based implementation in CUDA are compared
Quantum resource estimates for computing elliptic curve discrete logarithms
We give precise quantum resource estimates for Shor's algorithm to compute
discrete logarithms on elliptic curves over prime fields. The estimates are
derived from a simulation of a Toffoli gate network for controlled elliptic
curve point addition, implemented within the framework of the quantum computing
software tool suite LIQ. We determine circuit implementations for
reversible modular arithmetic, including modular addition, multiplication and
inversion, as well as reversible elliptic curve point addition. We conclude
that elliptic curve discrete logarithms on an elliptic curve defined over an
-bit prime field can be computed on a quantum computer with at most qubits using a quantum circuit of at most Toffoli gates. We are able to classically simulate the
Toffoli networks corresponding to the controlled elliptic curve point addition
as the core piece of Shor's algorithm for the NIST standard curves P-192,
P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to
recent resource estimates for Shor's factoring algorithm. The results also
support estimates given earlier by Proos and Zalka and indicate that, for
current parameters at comparable classical security levels, the number of
qubits required to tackle elliptic curves is less than for attacking RSA,
suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added.
ASIACRYPT 201
Group law computations on Jacobians of hyperelliptic curves
We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form
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