Pairings have found a range of applications in many areas of cryptography. As such, to
utilize the enormous potential of pairing-based protocols one needs to efficiently compute
pairings across various computing platforms. In this thesis, we give an introduction to
pairing-based cryptography and describe the Tate pairing and its variants. We then describe
some recent work to realize efficient computation of pairings. We further extend
these optimizations and implement the O-Ate pairing on BN-curves on ARM and x86-64
platforms. Specifically, we extend the idea of lazy reduction to field inversion, optimize
curve arithmetic, and construct efficient tower extensions to optimize field arithmetic. We
also analyze the use of affine coordinates for pairing computation leading us to the conclusion
that they are a competitive choice for fast pairing computation on ARM processors,
especially at high security level. Our resulting implementation is more than three
times faster than any previously reported implementation on ARM processors.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/6722 |
| Date | 30 April 2012 |
| Creators | Grewal, Gurleen |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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