P-Adic Point Counting Question

From: Anthony Mulcahy (anthony_at_kcn.ne.jp)
Date: 01/17/04 

Date: Sun, 18 Jan 2004 00:34:30 +0900

Hello,

I have a question regarding p-adic algorithms for counting points on
elliptic curves.

In the algorithms described in the paper "An extension of Satoh's algorithm
and its implementation"
(http://citeseer.nj.nec.com/fouquet00extension.html), there are equations
such as "1 - 504Z + 22A" and "1 + 864A" where Z and A are elements of the
p-adic ring $Z_{q}$ (q = p^d, p a prime). These equations appear to mix
integers such as 1, 504, 22 and 864 with elements of the p-adic ring and I
would like know how are addition and multiplication defined in this case?

The elements of the p-adic ring are represented using a polynomial basis
with p-adic integer coefficients, but I don't see how addition of or
multiplication by integers can be performed.

Thanks,

Anthony Mulcahy

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