Inverting the Final Exponentiation of Tate Pairings on Ordinary Elliptic Curves Using Faults
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- Lashermes R., Fournier J., Goubin L. (2013) Inverting the Final Exponentiation of Tate Pairings on Ordinary Elliptic Curves Using Faults. In: Bertoni G., Coron JS. (eds) Cryptographic Hardware and Embedded Systems - CHES 2013. CHES 2013. Lecture Notes in Computer Science, vol 8086. Springer, Berlin, Heidelberg
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.
KeywordsTate pairing Ate pairing final exponentiation fault attacks
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