The problem of computing Bilinear-Diffie-Hellman maps is considered. It is shown that the problem of computing the map is equivalent to computing a diagonal version of it. Various lower bounds on the degree of any polynomial that interpolates this diagonal version of the map are found that shows that such an interpolation will involve a polynomial of large degree, relative to the size of the se...

Bilinear maps are popular cryptographic primitives which have been commonly used in various modern cryptographic protocols. However, the cost of computation for bilinear maps is expensive because of their realization using variants of Weil and Tate pairings of elliptic curves. Due to increasing availability of cloud computing services, devices with limited computational resources can outsource ...

1 Classical Lie algebras A Lie algebra is a vector space g with a bilinear map [, ] : g× g → g such that (a) [x, y] = −[y, x], for x, y ∈ g, and (b) (Jacobi identity) [x, [y, z]] + [z, [x, y]] + [y, [z, x]] = 0, for all x, y, z ∈ g. A bilinear form 〈, 〉 : g× g → C is ad-invariant if, for all x, y, z ∈ g, 〈adx(y), z〉 = −〈y, adx(z)〉, where adx(y) = [x, y], (1.1) for x, y,∈ g. The Killing form is ...

We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular also in this setting. consider several operations the two types objects, obtain an interesting bilinear map between arising from product operation.

Secure and reliable group communication is an increasingly active research area by growing popularity in group-oriented and collaborative application. One of the important challenges is to design secure and efficient group key management. While centralized management is often appropriate for key distribution in large multicast-style groups, many collaborative group settings require distributed ...

In this paper, we present a new identity-based signature scheme with message recovery based on bilinear map. Our scheme is proved secure against existential forgery on adaptive chosen message and ID attack under the random oracle model. This new scheme shortens the total length of the original message and the appended signature and adapts to the ubiquitous network scenario very well.

In this paper, we propose a new ID-based threshold signature scheme from the bilinear pairings, which is provably secure in the random oracle model under the bilinear Diffie–Hellman assumption. Our scheme adopts the approach that the private key associated with an identity rather than the master key of PKG is shared. Comparing to the-state-of-art work by Baek and Zheng, our scheme has the follo...

In attribute-based signatures, each signer receives a signing key from the authority, which is associated with the signer’s attribute, and using the signing key, the signer can issue a signature on any message under a predicate, if his attribute satisfies the predicate. One of the ultimate goals in this area is to support a wide class of predicates, such as the class of arbitrary circuits, with...

Determining orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial in the definition of the discrete fractional Fourier transform. In this work, we disclose eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As jω in the analog s-d...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...