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Fast architectures for the $\eta_T$ pairing over small-characteristic supersingular elliptic curves

Abstract : This paper is devoted to the design of fast parallel accelerators for the cryptographic $\eta_T$ pairing on supersingular elliptic curves over finite fields of characteristics two and three. We propose here a novel hardware implementation of Miller's algorithm based on a parallel pipelined Karatsuba multiplier. After a short description of the strategies we considered to design our multiplier, we point out the intrinsic parallelism of Miller's loop and outline the architecture of coprocessors for the $\eta_T$ pairing over $\F_{2^m}$ and $\F_{3^m}$. Thanks to a careful choice of algorithms for the tower field arithmetic associated with the $\eta_T$ pairing, we manage to keep the pipelined multiplier at the heart of each coprocessor busy. A final exponentiation is still required to obtain a unique value, which is desirable in most cryptographic protocols. We supplement our pairing accelerators with a coprocessor responsible for this task. An improved exponentiation algorithm allows us to save hardware resources. According to our place-and-route results on Xilinx FPGAs, our designs improve both the computation time and the area-time trade-off compared to previously published coprocessors.
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Contributor : Jérémie Detrey Connect in order to contact the contributor
Submitted on : Thursday, November 25, 2010 - 3:05:28 PM
Last modification on : Tuesday, July 5, 2022 - 8:38:18 AM
Long-term archiving on: : Friday, December 2, 2016 - 6:59:28 PM


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Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals, Eiji Okamoto, Francisco Rodríguez-Henríquez. Fast architectures for the $\eta_T$ pairing over small-characteristic supersingular elliptic curves. IEEE Transactions on Computers, 2011, Special Section on Computer Arithmetic, 60 (2), pp.266-281. ⟨10.1109/TC.2010.163⟩. ⟨inria-00424016v2⟩



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