Abstract
In this work, we are interested in arithmetic on large prime field and their extensions of small degree. We explain why it is very interesting to use RNS arithmetic for the base field š½p when computations in š½pk have to be done, essentially thanks to lazy reduction. This is for example the case for pairing computations on ordinary curves (as MNT or BN curves). We show that using RNS can considerably decrease the number of basic operations required for a pairing computation in many popular situations.
Ā© Walter de Gruyter 2011
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