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

An Elliptic Curve-based Signcryption Scheme with Forward Secrecy

An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with the traditional signature-then-encryption schemes. It simultaneously provides the attributes of message confidentiality, authentication, integrity, unforgeability, non-repudiation, public verifiability, and forward secrecy of message confidentiality. Since it is based on elliptic curves and can use any fast and secure symmetric algorithm for encrypting messages, it has great advantages to be used for security establishments in store-and-forward applications and when dealing with resource-constrained devices.Comment: 13 Pages, 5 Figures, 2 Table

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