Avoiding full extension field arithmetic in pairing computations
Costello, Craig, Boyd, Colin, Gonzalez Nieto, Juan M., & Wong, Kenneth Koon-Ho (2010) Avoiding full extension field arithmetic in pairing computations. In Progress in Cryptology - AFRICACRYPT 2010, Springer Verlag, Stellenbosch, South Africa, pp. 203-224.
The most costly operations encountered in pairing computations are those that take place in the full extension ﬁeld Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subﬁelds. Consequently, full extension ﬁeld operations have the greatest eﬀect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subﬁeld operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suﬀer for larger embedding degrees where the expensive extension ﬁeld operations far outweigh the operations in the smaller subﬁelds. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension ﬁeld operations that occur in an iteration of the Miller loop, resulting in signiﬁcant speed ups in most practical situations of between 5 and 30 percent.
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|Item Type:||Conference Paper|
|Keywords:||Pairings, Miller's algorithm, Tate pairing, ate pairing|
|Subjects:||Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Institutes > Information Security Institute
|Copyright Owner:||Copyright 2010 Springer|
|Copyright Statement:||This is the author-version of the work. Conference proceedings published by Springer Verlag, will be available via SpringerLink http://www.springer.de/comp/lncs/|
|Deposited On:||20 Aug 2010 01:17|
|Last Modified:||29 Feb 2012 14:17|
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