Let G be a Lie group, G its Lie algebra, T G its cotangent bundle and D := tG the Lie algebra of T G. We investigate the group of automorphisms of D. More precisely, we fully characterize the space of all derivations of D. As a byproduct, we also characterize some spaces of operators on G amongst which the space J of bi-invariant tensors on G and prove that if G has a bi-invariant Riemannian or...

One of the biggest reasons for the popularity and versatility of elliptic curves in cryptography, besides the lack of “better-than-black-box” discrete log algorithms, is the presence of a bilinear map. In this short paper, we look into the definitions, motivations, and constructions of VRFs and note that groups equipped with a bilinear map can be used to construct a variety of different VRFs. ∗...

Recently, Boneh and Boyen proposed a new provably secure short signature scheme under the q-strong Diffie-Hellman assumption without random oracles. This scheme is based on bilinear map which is different from Cramer-Shoup signature scheme (which is based on the strong RSA assumption). However, Tan [17] showed that BonehBoyen scheme is subjected to key substitution attacks in the multi-user set...

In this short note, we present an extension of Nguyen’s bilinear-map based accumulator scheme [8] to support non-membership witnesses and corresponding non-membership proofs, i.e., cryptographic proofs that an element has not been accumulated to a given set. This complements the non-membership proofs developed by Li et al. [7] for the RSA accumulator [2, 3, 5], making the functionality of the b...

We show that the wave map equation in R is in general illposed in the critical space Ḣ1/2, and the Besov space Ḃ 1/2,1 2 . The problem is attributed to the bad behaviour of the one-dimensional bilinear expression D(fDg) in these spaces.

The way services offered by cloud computing gets its unprecedented and undisputed popularity, so security concerns. Among them the storage as service model (SaaS) is of forefront these SaaS liberates individuals enterprises from management IT infrastructure data centers to concentrate on their core business. Because untrusted out-of-premise architecture users are reluctant outsource personal im...

One of the leading problems of algebraic complexity theory is matrix multiplication. The näıve multiplication of two n× n matrices uses n multiplications. In 1969 Strassen [19] presented an explicit algorithm for multiplying 2 × 2 matrices using seven multiplications. In the opposite direction, Hopcroft and Kerr [11] and Winograd [20] proved independently that there is no algorithm for multiply...

We propose a new computational complexity assumption from bilinear map, based on which we construct Verifier-Local Revocation group signatures with shorter lengths than previous ones.