Paper 2015/152

Inverting the Final exponentiation of Tate pairings on ordinary elliptic curves using faults

Ronan Lashermes, Jacques Fournier, and Louis Goubin


The calculation of the Tate pairing on ordinary curves involves two major steps: the Miller Loop (ML) followed by the Final Exponentiation (FE). The first step for achieving a full pairing inversion would be to invert this FE, which in itself is a mathematically difficult problem. To our best knowledge, most fault attack schemes proposed against pairing algorithms have mainly focussed on the ML. They solved, if at all, the inversion of the FE in some special `easy' cases or even showed that the complexity of the FE is an intrinsic countermeasure against a successful full fault attack on the Tate pairing. In this paper, we present a fault attack on the FE whereby the inversion of the final exponentiation becomes feasible using $3$ independent faults.

Available format(s)
Public-key cryptography
Publication info
Published by the IACR in CHES 2013
Tate pairingAte pairingfinal exponentiationfault attacks
Contact author(s)
ronan lashermes @ wanadoo fr
2015-02-27: revised
2015-02-27: received
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Creative Commons Attribution


      author = {Ronan Lashermes and Jacques Fournier and Louis Goubin},
      title = {Inverting the Final exponentiation of Tate pairings on ordinary elliptic curves using faults},
      howpublished = {Cryptology ePrint Archive, Paper 2015/152},
      year = {2015},
      note = {\url{}},
      url = {}
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