Distance Lower Bounding

Xifan Zheng, Reihaneh Safavi–Naini, Hadi Ahmadi

Abstract. Distance (upper)-bounding (DUB) allows a verifier to know whether a proving party is located within a certain distance bound. DUB protocols have many applications in secure authentication and location based services. We consider the dual problem of distance lower bound-ing (DLB), where the prover proves it is outside a distance bound to the verifier. We motivate this problem through a number of application scenarios, and model security against distance fraud (DF), Man-in-the-Middle (MiM), and collusion fraud (CF) attacks. We prove impossibility of security against these attacks without making physical assumptions. We propose approaches to the construction of secure protocols under reasonable assumptions, and give detailed design of our DLB protocol and prove its security using the above model. This is the first treatment of the DLB problem in the untrusted prover setting, with a number of applications and raising new research questions. We discuss our results and propose directions for future research. 1

Stefan Hollands, Ko Sanders

Stefan A. Brands, David Chaum

Ito, Ryo, Ryuhei Mori

Quantum channel discrimination is a fundamental problem in quantum information science. In this study, we consider general quantum channel discrimination problems, and derive the lower bounds of the error probability. Our lower bounds are based on the triangle inequalities of the Bures angle and the trace distance. As a consequence of the lower bound based on the Bures angle, we prove the optimality of Grover's search if the number of marked elements is fixed to some integer $\ell$. This result generalizes Zalka's result for $\ell=1$. We also present several numerical results in which our lower bounds based on the trace distance outperform recently obtained lower bounds.

Weigang Chen, Liuguo Yin, Jianhua Lü

Minimum distance lower bounds are derived using graphical enumeration and integer programming for girth-constrained repeat-accumulate (RA) code ensembles. Moreover, the worst subgraphs in Tanner graphs leading to the minimum distance lower bounds and the probabilities they occur are analyzed.

Stefan A. Brands, David Chaum