On Taking Square Roots without Quadratic Nonresidues over Finite Fields

We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary. In some cases, the square root algorithm runs in $\tilde{O}(\log^2 q)$ bit operations over finite fields with $q$ elements. As an application, we construct a deterministic primality proving algorithm, which runs in $\tilde{O}(\log^3 N)$ for some integers $N$.Comment: 14 page

Neighborhood institutions like coffee shops and bars can have a significant positive or negative impact on local crime rates

Why is there more crime in some neighborhoods than others? While many investigations into the causes of crime tend to focus on individual motivation, new research from James Wo looks at the role of local institutions, such as shops, bars and nonprofits. He finds that these often relatively mundane institutions have meaningful consequences for neighborhood crime levels. While bars and liquor stores have an adverse effect on violent crime (but not for property crime), “third” places such as local coffee shops and cafes have crime reducing effects on both violent and property crime. He argues that city planners, politicians, and residents should take these factors into account when considering where new organizations and businesses are established

Joint Quantization and Diffusion for Compressed Sensing Measurements of Natural Images

Recent research advances have revealed the computational secrecy of the compressed sensing (CS) paradigm. Perfect secrecy can also be achieved by normalizing the CS measurement vector. However, these findings are established on real measurements while digital devices can only store measurements at a finite precision. Based on the distribution of measurements of natural images sensed by structurally random ensemble, a joint quantization and diffusion approach is proposed for these real-valued measurements. In this way, a nonlinear cryptographic diffusion is intrinsically imposed on the CS process and the overall security level is thus enhanced. Security analyses show that the proposed scheme is able to resist known-plaintext attack while the original CS scheme without quantization cannot. Experimental results demonstrate that the reconstruction quality of our scheme is comparable to that of the original one.Comment: 4 pages, 4 figure