Cryptographic accumulators have often been proposed for use in security protocols, and the theoretical runtimes of algorithms using them have been shown to be reasonably efficient, but their performance in the real world has rarely been measured. In this paper I analyze the performance differences between two cryptographic accumulator constructions, RSA accumulators and bilinear-map accumulator...

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

By the Choi matrix criteria it is easy to determine if a specific linear map completely positive, but establish whether positive much less straightforward. In this paper we consider classes of maps, determined by structural conditions on an associated matrix, for which positivity and complete coincide. The basis our proofs lies in representation ⁎-linear maps going back work R.D. Hill enables u...

Projecting bilinear pairings have frequently been used for designing cryptosystems since they were first derived from composite order bilinear groups. There have been only a few studies on the (im)possibility of projecting bilinear pairings. Groth and Sahai showed that projecting bilinear pairings can be achieved in the prime-order group setting. They constructed both projecting asymmetric bili...

An asymmetric pairing over groups of composite order is a bilinear map e : G1 ×G2 → GT for groups G1 and G2 of composite order N = pq. We observe that a recent construction of pairing-friendly elliptic curves in this setting by Boneh, Rubin, and Silverberg exhibits surprising and unprecedented structure: projecting an element of the order-N group G1 ⊕G2 onto the bilinear groups G1 and G2 requir...

Over the past decade bilinear maps have been used to build a large variety of cryptosystems. In addition to new functionality, we have concurrently seen the emergence of many strong assumptions. In this work, we explore how to build bilinear map cryptosystems under progressively weaker assumptions. We propose k-BDH, a new family of progressively weaker assumptions that generalizes the decisiona...

Identity-Based Encryption is a public key cryptosystem that uses the receiver identifier information such as email address, IP name and etc, to compute private in encrypt message. A message can obtain secret corresponding with his privacy from Private Key Generator he decrypt ciphertext. In this paper, we review Boneh-Franklin’s scheme use bilinear map Weil pairing’s properties propose an ident...

Objective: In this study, we aimed to validate the accuracy of computed tomography-based attenuation correction (CTAC) using the bilinear scaling method.Methods: The measured attenuation coefficient (μm) was compared to a theoretical attenuation coefficient (μt ) using four different CT scanners and an RMI 467 phantom. The effective energy of the CT beam X-rays was calculated, using the aluminu...

In class February 26 I presented a proof of Theorem 0.1 (Cartan). Suppose V is a finite-dimensional vector space over a field k of characteristic zero, and g ⊂ gl(V) is a Lie subalgebra. Write B for the trace form B(X, Y) = def tr(XY) (X, Y ∈ g ⊂ gl(V)). Then g is solvable if and only if the radical of B| g contains the commutator subalgebra [g, g]. In other words, g is solvable if and only if ...