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# Efficient subgroup exponentiation in quadratic and sixth degree extensions

Martijn Stam, Arjen K. Lenstra, Efficient subgroup exponentiation in quadratic and sixth degree extensions. Cryptographic Hardware and Embedded Systems - CHES 2002, 4th International Workshop, Redwood Shores, CA, USA, August 13-15, 2002, Revised Papers. ISBN 3-540-00409-2, pp. 318–332. December 2002. No electronic version available. External information

## Abstract

This paper describes several speedups for computation in the order $p+1$ subgroup of $\GaF{p^2}^*$ and the order $p^2-p+1$ subgroup of~$\GaF{p^6}^*$. These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with $p\equiv3\bmod 4$.