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Details of Grant 

EPSRC Reference: EP/L018543/1
Title: Multilinear Maps in Cryptography
Principal Investigator: Paterson, Professor KG
Other Investigators:
Albrecht, Dr M
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: Royal Holloway, Univ of London
Scheme: Standard Research
Starts: 31 January 2014 Ends: 15 January 2018 Value (£): 519,992
EPSRC Research Topic Classifications:
Fundamentals of Computing
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
24 Oct 2013 EPSRC ICT Responsive Mode - Oct 2013 Announced
Summary on Grant Application Form
Bilinear maps have proven to be incredibly useful tools in cryptography. Initially a tool for cryptanalysis, the fact that they could be used for positive cryptographic applications was realised around the year 2000 by Joux, Sakai et al. and Boneh-Franklin. Since then, there has been an enormous explosion of research, and now growing commercial interest, in bilinear maps and their cryptographic applications. Early on in the development of this new field, it was recognised that multilinear maps, if they could be efficiently and securely realised, could allow even more far-reaching and surprising cryptographic applications. However, there was little activity on multilinear maps, due largely to a negative result of Boneh-Silverberg from 2003, which identified significant obstacles to the construction of multilinear maps using extensions of the known techniques for bilinear maps. Without a suitable instantiation, serious cryptographers could not sensibly proceed into this territory, no matter how attractive the possibilities.

The situation concerning multilinear maps changed dramatically in late 2012, when Garg, Gentry and Halevi proposed a candidate for objects approximating multilinear maps ``closely enough'' to allow new applications. This was rapidly followed by another proposal from Coron, Lepoint and Tibouchi. Both candidates rely on novel, non-standard hardness assumptions for the construction of secure cryptographic primitives. Very quickly, researchers have begun to take advantage of the availability of these candidates to propose innovative cryptographic schemes, with several papers recently appearing at leading conferences (including work by the PI and Visiting Researcher Hofheinz). With this sudden upswing in activity, it seems that we are at the start of an explosion in the development of multilinear maps in cryptography, akin to that experienced 12 years ago with bilinear maps.

The main purpose of this proposal is to bring together, in a timely fashion, a team of researchers with the skills and experience needed to take a leading role in this new wave of research. The team will comprise: the PI (Paterson), the named PDRA (Albrecht), a second PDRA (tbh), and the two Visiting Researchers (Galbraith, Hofheinz). We will work on three main objectives: applications, cryptanalysis and alternative constructions. Between them, these objectives cover a broad set of problems which need to be addressed in order to build confidence in the recent multilinear map proposals, and to open up the area to other researchers.

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