CONTENTS - Emerald

each factor to the power e to get a collection of partial results, which can then be combined.
Speed-up may be obtained if partial results can be calculated in parallel and/or
with the aid of a stored table. Experimental results on performance are reported.
041709 `Still faster modular multiplication'
CD Walter, Electronics Letters v 31 no 4 (16/2/95) pp 263{264
The author shows how to organise hardware for Montgomery multiplication in such
away that almost all the adders are kept busy for almost all the time, regardless of
the length of the multiplicand. The trick is in managing the propagation of quotient
digits when reductions are performed, and the e ect is that one requires only half the
adder depth.
041710 `Computing in the Jacobian of a Plane Algebraic Curve'
EJ Volchek, ANTS 94 pp 221{233
The authors extend an algorithm of Brill and Noether to perform addition operations
in the Jacobian of a plane algebraic curve over an algebraic number eld with
arbitrary singularities. If M is the larger of the degree and the genus of the curve, then
the cost of addition is O(M 7 ) eld operations.
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