This paper describes several speedups for computation in the order p + 1 subgroup of F*p2 and the order p2 - p + 1 subgroup of F*p. 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 = 3 mod 4.
['Martijn Stam', 'Arjen K. Lenstra']
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions