Candidate Multilinear Maps

From the Preface Cryptography seems like “black magic.” enabling tasks that often seem paradoxical or simply just impossible. Like the space explorers, cryptographers often wonder, “what are the boundaries of this world of 'black magic'?” This work lays one of the founding stones in furthering our understanding of these edges. In it, Garg describes plausible lattice-based constructions with properties that approximate the sought-after multilinear maps in hard-discrete-logarithm groups. The security of his constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness of the NTRU function. These new constructions radically enhance the cryptography tool set and open a floodgate of applications. We present a survey of these applications. This book is based on Sanjam Garg's PhD thesis, which was an extended version of a paper titled “Candidate Multilinear Maps from Ideal Lattices,” co-authored with Craig Gentry and Shai Halevi. His original thesis won the 2013 ACM Dissertation Award.