"Traditionally, cryptographic protocols were run on servers or personal computers which have large and easily scalable computational resources. For these applications there exist a large variety of well-established cryptographic systems. Right now, we are in the midst of the shift toward ubiquitous computing on resource constrained devices (RCDs): small devices with severe constraints in terms of computing power, code size, and network capacities. RCDs are used virtually everywhere: smart phones, bank cards, electronic ID-cards, medical implants, cars, RFIDs as bar code replacement, etc. Due to their computational constraints, many current cryptographic security solutions are no longer applicable to RCDs. Existing solutions are often “ad-hoc” and do not come with a formal security treatment.The central objective of the ERCC project is to initiate an overarching formal treatment of cryptographic solutions for RCDs, particularly focusing on efficiency. The main conceptual novelty is to follow the concept of provable security. We intend to design new cryptographic protocols that have a mathematical proof of security (assuming the hardness of some mathematical problem) and are still competitive with constructions currently used on RCDs. While we certainly cannot hope that all our new provably secure constructions will be superior to existing ad-hoc constructions, recent preliminary researchresults give rise to optimism. Concretely, we will base our new protocols on hard problems in ideal and structures lattices and we will study weaker (yet still realistic) security models for RCDs allowing for efficient instantiations."