Schoof-Elkies-Atkin-Mueller program for counting points on a GF(p) elliptic
curve y^2=x^3+Ax+B mod p. 

Precompiled Windows executables of these programs may be downloaded from
ftp://ftp.compapp.dcu.ie/pub/crypto

To build the mueller/process/sea applications, you must compile and link the 
modules together, with MIRACL C++ classes , and with the MIRACL library.

So for MS C++ 

cl /c /O2 /GX ps_big.cpp
cl /c /O2 /GX big.cpp
cl /c /O2 /GX mueller.cpp
link mueller.obj ps_big.obj big.obj miracl.lib

cl /c /O2 /GX process.cpp
link process.obj big.obj miracl.lib

cl /c /O2 /GX modpol.cpp
cl /c /O2 /GX ps_zzn.cpp
cl /c /O2 /GX zzn.cpp
link modpol.obj ps_zzn.obj zzn.obj big.obj miracl.lib

cl /c /O2 /GX sea.cpp
cl /c /O2 /GX poly.cpp
cl /c /O2 /GX polymod.cpp
cl /c /O2 /GX polyxy.cpp
cl /c /O2 /GX ecn.cpp
cl /c /O2 /GX crt.cpp
link sea.obj poly.obj polymod.obj polyxy.obj big.obj zzn.obj ecn.obj 
crt.obj miracl.lib

For Linux GCC

g++ -I. -c -O2 ps_big.cpp
g++ -I. -c -O2 big.cpp
g++ -I. mueller.cpp ps_big.o big.o miracl.a -o mueller

etc.


Note that the headers ps_big.h, ps_zzn.h, poly.h, polymod.h and polyxy.h are 
assumed to be in the local directiory


Instructions for use

First run the utility "mueller" to build up a collection of Modular 
Polynomials. This needs to be done once only - ever, but you can from time 
augment your collection of Polynomials by running it again. Its quite time
consuming, but in less than an hour you should have enough to get started. The
more you have, the bigger the prime modulus that you can use.

Then run the utility "process" to process the raw polynomial file with 
respect to your chosen prime modulus. This need to be done just once for
every prime modulus of interest to you. This takes only a few minutes at 
most.

Alternatively use "modpol", which is a composite of "mueller" and "process".
This may be better if you have difficulty running the memory hungry "mueller"

Finally run this program "sea" specifying the A and B parameters of the 
particular curve. This program can also search through many curves for 
a curve ideal for cryptographic use (with a prime number of points).

For example try:-

mueller 0 120 -o mueller.raw
process -f 65112*2#144-1 -i mueller.raw -o test160.pol
sea -3 49 -i test160.pol

or

modpol -f 65112*2#144-1 0 120 -o test160.pol
sea -3 49 -i test160.pol

(In Unix, use . and ^ instead of * and #)

When using the "sea" program, the -s option is particularly useful
and allows automatic search for an "ideal" curve. If a curve order is
exactly divisible by a small prime, that curve is immediately abandoned, 
and the program moves on to the next, incrementing the B parameter of 
the curve. 


For more information, see the comments at the head of the source file sea.cpp