Finding ECM-friendly curves through a study of Galois properties

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM

Montgomery Arithmetic from a Software Perspective

This chapter describes Peter L. Montgomery\u27s modular multiplication method and the various improvements to reduce the latency for software implementations on devices which have access to many computational units

An Observation about Variations of the Diffie-Hellman Assumption

We generalize the Strong Boneh-Boyen (SBB) signature scheme to sign vectors; we call this scheme GSBB. We show that if a particular (but most natural) average case reduction from SBB to GSBB exists, then the Strong Diffie-Hellman (SDH) and the Computational Diffie-Hellman (CDH) have the same worst-case complexity

Combining contact tracing with targeted indoor residual spraying significantly reduces dengue transmission

The widespread transmission of dengue viruses (DENV), coupled with the alarming increase of birth defects and neurological disorders associated with Zika virus, has put the world in dire need of more efficacious tools for Aedes aegypti–borne disease mitigation. We quantitatively investigated the epidemiological value of location-based contact tracing (identifying potential out-of-home exposure locations by phone interviews) to infer transmission foci where high-quality insecticide applications can be targeted. Space-time statistical modeling of data from a large epidemic affecting Cairns, Australia, in 2008–2009 revealed a complex pattern of transmission driven primarily by human mobility (Cairns accounted for ~60% of virus transmission to and from residents of satellite towns, and 57% of all potential exposure locations were nonresidential). Targeted indoor residual spraying with insecticides in potential exposure locations reduced the probability of future DENV transmission by 86 to 96%, compared to unsprayed premises. Our findings provide strong evidence for the effectiveness of combining contact tracing with residual spraying within a developed urban center, and should be directly applicable to areas with similar characteristics (for example, southern USA, Europe, or Caribbean countries) that need to control localized Aedes-borne virus transmission or to protect pregnant women’s homes in areas with active Zika transmission. Future theoretical and empirical research should focus on evaluation of the applicability and scalability of this approach to endemic areas with variable population size and force of DENV infection

Real quadratic fields with large class number

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46217/1/208_2005_Article_BF01351721.pd