New Trapdoor Projection Maps for Composite-Order Bilinear Groups, by Sarah Meiklejohn and Hovav Shacham
An asymmetric pairing over groups of composite order is a bilinear map $e: G_1 \\times G_2 \\to G_T$ for groups $G_1$ and $G_2$ of composite order $N=pq$. We observe that a recent construction of pairing-friendly elliptic curves in this setting by Boneh, Rubin, and Silverberg exhibits surprising and unprecedented structure: projecting an element of the order-$N^2$ group $G_1 \\oplus G_2$ onto the bilinear groups $G_1$ and $G_2$ requires knowledge of a trapdoor. This trapdoor, the square root of a certain number modulo $N$, seems strictly weaker than the trapdoors previously used in composite-order bilinear cryptography.
In this paper, we describe, characterize, and exploit this surprising structure. It is our thesis that the additional structure available in these curves will give rise to novel cryptographic constructions, and we initiate the study of such constructions. Both the subgroup hiding and SXDH assumptions appear to hold in the new setting; in addition, we introduce custom-tailored assumptions designed to capture the trapdoor nature of the projection maps into $G_1$ and $G_2$. Using the old and new assumptions, we describe an extended variant of the Boneh-Goh-Nissim cryptosystem that allows a user, at the time of encryption, to restrict the homomorphic operations that may be performed. We also present a variant of the Groth-Ostrovsky-Sahai NIZK, and new anonymous IBE, signature, and encryption schemes.
Two PhD Positions, University of Bristol
The Government Communications Headquarters (GCHQ) in Cheltenham has agreed in principle to sponsor two PhD/Doctoral Studentships at Bristol University in the area of Cryptography. See the link below for the two project descriptions.
The studentships are only open to UK nationals and the successful candidate will be required to spend in the region of 2 - 4 weeks per year at GCHQ headquarters in Cheltenham. To be considered for this studentship, candidates must therefore be prepared to undergo GCHQ\\\'s security clearance procedures.
The studentships will be funded for a period of 3.5 years. GCHQ will cover the costs of university fees (currently £ 3828 per annum) and will provide an annual stipend to the student corresponding to the National Minimum Stipend (currently £ 13,590 per annum) plus an additional stipend of £ 7,000 per annum. Making a total tax-free stipend of £ 20,590 per annum. A generous travel budget is also provided to enable attendance at international conferences and workshops.
Two Post-Docs, Nanyang Technological University, Singapore
We are looking for two Post-Docs in coding and lattice based cryptography. Contact us if you have (or will have soon) a PhD in Cryptography or a related subject, an excellent publication record and would like to work in a fun environment in Singapore.
More information on Coding and Crypto Research Group at Nanyang Technological University can be found at http://www1.spms.ntu.edu.sg/~ccrg/index.html
The applications will be considered immediately. The positions are for 1 year, but renewable up to 3 years.