Security Analysis of the Unrestricted Identity-Based Aggregate Signature Scheme

Aggregate signatures allow anyone to combine different signatures signed by different signers on different messages into a single short signature. An ideal aggregate signature scheme is an identity-based aggregate signature (IBAS) scheme that supports full aggregation since it can reduce the total transmitted data by using an identity string as a public key and anyone can freely aggregate different signatures. Constructing a secure IBAS scheme that supports full aggregation in bilinear maps is an important open problem. Recently, Yuan {\it et al.} proposed an IBAS scheme with full aggregation in bilinear maps and claimed its security in the random oracle model under the computational Diffie-Hellman assumption. In this paper, we show that there exists an efficient forgery attacker on their IBAS scheme and their security proof has a serious flaw.Comment: 9 page

Gravitational waves from cosmic bubble collisions

Cosmic bubbles are nucleated through the quantum tunneling process. After nucleation they would expand and undergo collisions with each other. In this paper, we focus in particular on collisions of two equal-sized bubbles and compute gravitational waves emitted from the collisions. First, we study the mechanism of the collisions by means of a real scalar field and its quartic potential. Then, using this model, we compute gravitational waves from the collisions in a straightforward manner. In the quadrupole approximation, time-domain gravitational waveforms are directly obtained by integrating the energy-momentum tensors over the volume of the wave sources, where the energy-momentum tensors are expressed in terms of the scalar field, the local geometry and the potential. We present gravitational waveforms emitted during (i) the initial-to-intermediate stage of strong collisions and (ii) the final stage of weak collisions: the former is obtained numerically, in \textit{full General Relativity} and the latter analytically, in the flat spacetime approximation. We gain qualitative insights into the time-domain gravitational waveforms from bubble collisions: during (i), the waveforms show the non-linearity of the collisions, characterized by a modulating frequency and cusp-like bumps, whereas during (ii), the waveforms exhibit the linearity of the collisions, featured by smooth monochromatic oscillations.Comment: 17 pages, 5 figure